https://learningspot.co/ 2026-03-28T11:36:55+00:00 daily 1.0000 https://learningspot.co/assets/images/scroll_up.png Top https://learningspot.co/assets/images/logo.png https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/9.png A number line representing natural numbers starting from 1 and an arrow pointing to the right till infinity. https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/3.png Comma Placement in the Indian System - 99,88,77,654. First comma after 3 digits from the right. Second comma after next 2 digits. Third comma after another 2 digits. https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/10.png A mind map for Indian System of Numeration. Branches include: Periods & Places (O, T, L, C), Comma Rule (3-2-2), and Digit Values (FV vs PV). https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/4.png Comma Placement in the International System - 987,654,321. First comma after 3 digits from the right. Second comma after next 3 digits. https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/11.png A comparison chart between Indian Periods & Places (Lakhs, Crores) and International Periods & Places (Millions, Billions). https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/5.png Comparing numbers with the same number of digits - 58,349 and 58,612. Digits at each place value is compared to each other. https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/12.png https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/13.png A mind map for Formation of Numbers. Contains: Descending order, Ascending order, Special Rule for 0 and Repetition. https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/14.png Forming Numbers with Repetition - for Greatest number fill all boxes with 'Biggest Digit' & for Smallest number fill first box with Smallest Non-Zero and all other boxes are 'Absolute Smallest'. https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/6.png Golden Rule of Unit Conversion - From Larger Unit to Smaller Unit (Multiply) and from Smalller Unit to Larger Unit (Divide). https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/15.png A concept map for Measurement & Conversion. Three branches: Length (km-m-cm-mm), Mass (kg-g-mg) and Capacity (L-mL). https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/7.png A flowchart for rounding off a number. Identify the rounding digit and the deciding digit to its right. Is deciding digit 5 or more?. If yes, round up. If no, round down. https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/16.png A mind map on Estimation and Rounding off. Branches: Rounding Rules (Up vs Down), Places (T, H, T) and Applications. https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/8.png Examples of Roman numerals in modern use: a clock face, a book and a building cornerstone. https://learningspot.co/maths/concepts-class-6/ch-1-knowing-our-numbers-images/17.png A mind map for 'Roman Numerals'. Branches: 7 Symbols, Addition Rule, Subtraction Rule and Large Numbers (Vinculum - Bar). https://learningspot.co/maths/concepts-class-6/ch-2-whole-numbers.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-2-whole-numbers-images/10.png A Venn diagram showing a large rectangle labeled 'Whole Numbers (W)' which contains a smaller rectangle inside it labeled 'Natural Numbers (N)'. The number 0 is shown inside the W rectangle but outside the N rectangle. https://learningspot.co/maths/concepts-class-6/ch-2-whole-numbers-images/11.png A number line starting from 0 and extending to the right with an arrow. The points 0, 1, 2, 3, 4, 5, and 6 are marked at equal intervals. https://learningspot.co/maths/concepts-class-6/ch-2-whole-numbers-images/16.png A visual comparison. Box 1: 0 / 5 = 0 (If you have 0 pizzas for 5 people, everyone gets 0). Box 2: 5 / 0 = UNDEFINED (If you have 5 pizzas for 0 people, the situation is impossible/undefined). A warning sign is placed next to 'Dividing by Zero'. https://learningspot.co/maths/concepts-class-6/ch-2-whole-numbers-images/17.png A mind map showing the four operations (+, -, ×, ÷). Branches show properties like Closure, Commutative, and Associative. Addition and Multiplication have checkmarks for these properties, while Subtraction and Division have red 'X' marks. https://learningspot.co/maths/concepts-class-6/ch-2-whole-numbers-images/12.png Two arrangements of 6 dots. The first is a 2x3 grid, and the second is a 3x2 grid, both forming rectangles. https://learningspot.co/maths/concepts-class-6/ch-2-whole-numbers-images/13.png A sequence of dot patterns showing the first three square numbers: a single dot for 1, a 2x2 grid for 4, and a 3x3 grid for 9. https://learningspot.co/maths/concepts-class-6/ch-2-whole-numbers-images/14.png A sequence of dot patterns showing the first three triangular numbers: a single dot for 1, a triangle of 3 dots, and a triangle of 6 dots. https://learningspot.co/maths/concepts-class-6/ch-2-whole-numbers-images/15.png An animation showing the dot pattern for the triangular number 6. Another dot pattern for the triangular number 10 is shown, flipped, and then they are combined to form a 4x4 square of 16 dots. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/11.png A mind map with 'Factors' at the center. Branches: 1 is a factor of every number; Every number is a factor of itself; Factors are finite (countable); Factors are always less than or equal to the number; Every factor is an exact divisor. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/12.png A flowchart for finding multiples. Step 1: Start with the number itself (n x 1). Step 2: Multiply by 2. Step 3: Multiply by 3. Step 4: Continue as long as needed. A note at the bottom says: 'The list never ends!' https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/6.png A diagram showing that 4 is a factor of 20, and an arrow pointing the other way showing that 20 is a multiple of 4. This illustrates the inverse relationship. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/13.png A mind map with 'Common Shared Values' at the center. Two main branches: 'Factors' leading to HCF (Greatest shared divisor) and 'Multiples' leading to LCM (First shared result). https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/14.png A mind map centered on Natural Numbers. Two main branches: 1. By Divisibility (Even and Odd), 2. By Factors (Prime, Composite, and the special case '1'). Sub-branches include definitions and examples. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/7.png A 10x10 grid of numbers from 1 to 100. The number 1 is crossed out. Prime numbers like 2, 3, 5, 7 are circled, and their multiples are shaded or crossed out, leaving the remaining primes visible. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/15.png A side-by-side comparison. Twin Primes: Must be prime, distance is 2 (e.g., 5 and 7). Co-Primes: Don't have to be prime, only share 1 as a factor (e.g., 8 and 9). A 'No Sharing' sign is placed between co-primes. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/16.png An illustration of the number 6. Its proper divisors (1, 2, 3) are shown as building blocks that, when stacked, equal the height of the number 6 itself. Formula: 1 + 2 + 3 = 6. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/17.png A colorful table summarizing all tests. 2: Even end. 3: Sum of 3. 4: Last 2. 5: 0 or 5. 6: 2 and 3. 8: Last 3. 9: Sum of 9. 10: Ends in 0. 11: Odd-Even difference. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/18.png A flowchart for checking if a number 'n' is prime. Step 1: Is n divisible by 2? (If yes, composite). Step 2: Is n divisible by 3, 5, 7...? Step 3: Stop when the prime being tested is greater than the square root of n. Final decision: If no factors found, it's Prime. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/8.png A number line showing the factors of 36. The square root, 6, is in the middle. The factor pairs (1,36), (2,18), (3,12), and (4,9) are shown straddling the square root. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/19.png A mind map titled 'General Properties of Divisibility'. Five main branches: 1. Divisibility by Factors (The Hierarchy), 2. Co-prime Product Rule, 3. Sum Rule, 4. Difference Rule, and 5. Multiples Rule. Each branch includes a short rule and a small example. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/9.png Factor tree for 36 showing branches 36 to 4 and 9, then 4 to 2 and 2, and 9 to 3 and 3 https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/10.png Alternative factor tree for 36 showing branches 36 to 2 and 18, then 18 to 2 and 9, and 9 to 3 and 3 https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/20.png A flowchart for the Division Method. Step 1: Start with the smallest prime (2). Step 2: Can it divide the number exactly? If yes, divide and write the quotient. If no, move to the next prime (3, 5, 7...). Step 3: Repeat the process with the new quotient. Step 4: Stop when the quotient becomes 1. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/21.png Mind map: Unique Prime Factorisation - Unique Set, Order doesn't matter, Fundamental Theorem https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/22.png Mind map of HCF showing three main branches: Listing Factors (for small numbers), Prime Factorization (using exponents), and Long Division (for large numbers). https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/23.png A mind map of LCM showing the three methods: Listing Multiples for small numbers, Prime Factorization using highest powers, and Common Division for multiple large numbers. https://learningspot.co/maths/concepts-class-6/ch-3-playing-with-numbers-images/24.png Mind map showing the central formula a × b = HCF × LCM, with branches for Verification, Finding a Missing Number, and finding HCF/LCM. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/1.png Representation of multiple points labeled A, B, C, and D as small dots on a plane https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/2.png Representation of a straight Line AB with arrows on both ends, passing through points A and B. It is also labeled as line l. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/3.png Diagram showing three collinear points A, B, C on a single straight line, and a non-collinear point D which is not on the same line. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/4.png A parallelogram shape representing a plane in geometry, which extends infinitely. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/5.png Diagram showing two lines L1 and L2 intersecting at a point P https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/6.png Diagram showing two parallel lines L1 and L2 https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/7.png A single point P with several lines passing through it, resembling the spokes of a wheel, demonstrating that an infinite number of lines can pass through one point. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/8.png Two distinct points, A and B, with a single, unique straight line passing through both of them. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/9.png Two distinct lines, labeled l and m, are shown crossing each other at a single, clearly marked point P. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/10.png An illustration showing the two possibilities for distinct lines in a plane: on the left, two intersecting lines cross at one point, and on the right, two parallel lines never meet. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/11.png Three non-collinear points A, B, and C, with a unique plane represented as a parallelogram passing through all of them. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/12.png A single line l with multiple planes passing through it at various angles, similar to the pages of a book sharing a common spine. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/13.png A plane containing two points, A and B. The line passing through A and B is shown to lie entirely within the plane. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/14.png Two distinct planes, represented by intersecting parallelograms. Their intersection is clearly highlighted as a straight line. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/15.png Representation of a Line Segment AB with clear endpoints at A and B. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/16.png Line segment AB with M as its midpoint, showing that AM is equal to MB. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/17.png Two congruent line segments, AB and CD, are shown. Each has a single tick mark to indicate they are of equal length. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/18.png Representation of a Ray starting at point A (the endpoint) and passing through point B to extend infinitely. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/19.png Opposite rays OA and OB sharing the common endpoint O and forming the line AB. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/21.png Diagram of a line passing through A and B with arrows at both ends. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/22.png Diagram of a line segment with endpoints A and B. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/23.png Diagram of a ray starting at A and extending through B. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/24.png Representation of an Angle showing a vertex B and two arms, ray BA and ray BC. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/25.png Two diagrams comparing angle naming. The left diagram shows a single angle at vertex B, which can be called angle B. The right diagram shows three angles at vertex P, making 'angle P' ambiguous. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/26.png A diagram showing angle ABC. Point P is located in the shaded interior region. Point Q is in the unshaded exterior region. Point R is on the arm BC. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/27.png Comparison showing simple curves (an arc and a circle) that do not cross themselves, and non-simple curves (a loop and a figure-eight) that do. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/28.png Examples of Open Curves: a simple arc, a zigzag line, and the letter C. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/29.png Examples of Closed Curves: a circle, a square, and an irregular loop. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/30.png Comparison of a circle (simple closed curve) and a figure-eight (non-simple closed curve). https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/31.png A simple closed curve with Point A in the interior, Point C in the exterior, and Point B on the boundary. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/32.png Six figures are shown. The first three (a triangle, a square, a pentagon) are labeled as polygons. The last three (an open curve, a circle, and a self-intersecting star) are labeled as not polygons. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/33.png A pentagon ABCDE with labels showing its sides, vertices, adjacent sides, adjacent vertices, and a diagonal AC. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/34.png Triangle Icon https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/35.png Quadrilateral Icon https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/36.png Pentagon Icon https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/37.png Hexagon Icon https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/38.png Heptagon Icon https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/39.png Octagon Icon https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/40.png Nonagon Icon https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/41.png Decagon Icon https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/42.png A convex pentagon where all vertices point out and a concave hexagon where one vertex points inward, creating a reflex angle. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/43.png Comparison showing a regular hexagon (all sides and angles equal) and an irregular hexagon (sides and angles are not all equal). https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/44.png A chart showing the six main types of triangles: Equilateral, Isosceles, Scalene based on sides, and Acute, Right, Obtuse based on angles. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/45.png A triangle ABC showing its three sides, three vertices, and three interior angles labeled. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/46.png A triangle ABC with a line segment AD drawn from vertex A, perpendicular to the base BC. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/47.png A triangle ABC with a line segment AM connecting vertex A to the midpoint M of the opposite side BC. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/48.png A triangle ABC with a line segment AD from vertex A to side BC, dividing angle BAC into two equal angles. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/49.png A family tree diagram showing the relationships between quadrilaterals, starting from the general quadrilateral. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/50.png A single quadrilateral ABCD illustrating all its components. Adjacent sides AB and BC are highlighted. Opposite sides AB and DC are shown in parallel. Adjacent angles A and B are marked. Opposite angles A and C are indicated. The two diagonals, AC and BD, are drawn as dashed lines inside the quadrilateral. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/51.png A circle with its center O. Several radii are drawn from O to points on the circle, all having the same length, r. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/52.png https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/53.png A circle with center O and a single radius OA labeled. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/54.png A circle with a chord PQ connecting two points on its boundary. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/55.png A circle with center O and a diameter AB passing through it. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/56.png A circle showing a minor arc AB in red and a major arc ACB in blue. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/57.png A circle divided by a chord into a smaller minor segment (shaded) and a larger major segment. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/58.png A circle showing a minor sector (shaded) formed by two radii and a minor arc, and the remaining major sector. https://learningspot.co/maths/concepts-class-6/ch-4-basic-geometrical-ideas-images/59.png A circle with a secant line passing through it and a tangent line touching it at a single point. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/1.png Two line segments, AB and CD, are shown. CD is clearly longer than AB. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/2.png A depiction of using tracing paper. A traced line segment AB is being placed over another line segment CD to compare their lengths. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/3.png Two line segments, AB and CD, being measured with a ruler. The ruler shows AB is 3 cm and CD is 4 cm. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/4.png A divider is first used to measure segment AB, then moved to segment CD to compare its length. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/5.png A ruler is placed correctly along a line segment AB, starting from the 0 cm mark. The length is read at endpoint B. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/6.png A standard semi-circular protractor showing inner and outer scales from 0 to 180 degrees. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/7.png A protractor correctly placed on an angle ABC to measure its size. The reading on the outer scale is 60 degrees. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/8.png A zero angle where two rays lie on top of each other. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/9.png An acute angle, clearly less than 90 degrees. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/10.png A right angle, marked with a small square at the vertex to indicate 90 degrees. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/11.png An obtuse angle, clearly more than 90 degrees. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/12.png A straight angle, forming a straight line. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/13.png A reflex angle, showing the turn greater than 180 degrees. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/14.png A complete angle, indicated by a full circle around the vertex. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/15.png Two lines, l and m, intersecting at a point. The angle of intersection is marked with a square symbol, indicating a 90-degree angle. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/16.png A line segment AB is being cut by a line l at its midpoint M. A right angle symbol at M and tick marks on AM and MB indicate that l is a perpendicular bisector. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/17.png An equilateral triangle with tick marks on all three sides indicating they are equal in length. All angles are marked as 60 degrees. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/18.png An isosceles triangle with tick marks on two sides, indicating they are equal. The angles opposite these sides are also shown to be equal. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/19.png A scalene triangle with different side lengths and different angle measures shown. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/20.png An acute-angled triangle with all three angles shown as less than 90 degrees. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/21.png A right-angled triangle with one angle marked as 90 degrees. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/22.png An obtuse-angled triangle with one angle shown to be greater than 90 degrees. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/23.png A family tree diagram showing the relationships between different types of quadrilaterals. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/24.png A trapezium with one pair of parallel sides indicated by arrows. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/25.png A parallelogram with properties like parallel opposite sides and equal opposite angles marked. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/26.png A rhombus with four equal sides and diagonals that are perpendicular to each other. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/27.png A rectangle with four right angles and equal length diagonals. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/28.png A square with four equal sides, four right angles, and equal, perpendicular diagonals. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/29.png A kite with two pairs of equal adjacent sides marked. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/30.png A cube with six identical square faces. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/31.png A cuboid with six rectangular faces. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/40.png Two prisms side-by-side. The left one is a right prism with vertical sides. The right one is an oblique prism that is slanted. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/41.png A triangular prism, showing its two triangular bases. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/42.png A rectangular prism (cuboid). https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/43.png Two pyramids side-by-side. The left one is a right pyramid with the apex centered over the base. The right one is an oblique pyramid with the apex off-center. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/44.png A triangular pyramid (tetrahedron). https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/45.png A square pyramid. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/32.png A cylinder showing its two circular bases and one curved side. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/33.png A cone showing its circular base, curved surface, and a single apex. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/34.png A sphere, which is a perfectly round 3D shape with a single continuous curved surface. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/35.png A cube with square faces. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/36.png A cuboid with rectangular faces. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/46.png A triangular prism. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/47.png A square pyramid. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/37.png A cylinder with two circular bases. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/38.png A cone with a circular base and an apex. https://learningspot.co/maths/concepts-class-6/ch-5-understanding-elementary-shapes-images/39.png A sphere, a perfectly round 3D shape. https://learningspot.co/maths/concepts-class-6/ch-6-integers.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/1.png Venn Diagram showing Natural Numbers inside Whole Numbers, which are inside Integers https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/2.png Number line showing integers https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/3.png Number line with -3, 0, 5 marked https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/4.png A number line showing that the distance of +5 from 0 is 5 units, and the distance of -5 from 0 is also 5 units. Thus, |5|=5 and |-5|=5. https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/5.png https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/6.png A number line showing the integers from -8 to 1. The positions of -7 and -2 are circled. https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/7.png A number line with points marked at -6, -3, 0, 2, and 5. https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/8.png Number line showing 3 + (-5) https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/9.png Number line showing -2 + (-4) https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/10.png Number line showing -1 + 6 https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/11.png A flowchart starting with 'Are signs the same?'. If yes, add and keep sign. If no, subtract smaller from larger and keep sign of the larger absolute value. https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/12.png A central hub 'Properties of Addition' branching into Closure, Commutative, Associative, Additive Identity, and Additive Inverse with brief formulas. https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/13.png Graphic showing two minus signs merging to form a plus sign. 'Subtracting a negative is like adding!' https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/14.png Number line showing 5 - 8 https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/15.png Number line showing -10 - (-4) https://learningspot.co/maths/concepts-class-6/ch-6-integers-images/16.png https://learningspot.co/maths/concepts-class-6/ch-7-fractions.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/1.png Pizza divided into 8 slices, 3 eaten https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/2.png Group of circles, some red, some blue https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/3.png Number line showing 1/2 https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/4.png Number line showing 2/3 https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/5.png Number line showing 7/4 or 1 3/4 https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/6.png Number line showing 3/5 https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/7.png https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/8.png Visual representation of equivalent fractions 1/2, 2/4, 3/6, 4/8 https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/9.png Flowchart showing two paths: 1. Multiply Top and Bottom by any number (except 0 or 1). 2. Divide Top and Bottom by a Common Factor. https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/10.png Two fractions a/b and c/d with oval loops drawn diagonally (a with d, and b with c) resembling butterfly wings. The products are written at the top of the antennae. https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/11.png A central hub 'Simplifying Fractions' branching to 'Method 1: HCF', 'Method 2: Repeated Division', and 'Check: No common factors except 1'. https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/12.png Flowchart: 1. Find LCM of denominators. 2. Divide LCM by old denominator to find the factor. 3. Multiply Top and Bottom by that factor. https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/13.png Visual comparison of 3/8 and 5/8 https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/14.png Concept map with 'Comparing Unlike Fractions' in the center. Branches lead to 'Step 1: Find LCM', 'Step 2: Multiply Top and Bottom', and 'Step 3: Compare New Numerators'. https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/15.png Two identical circles representing pizzas. The left one is cut in half with one slice shaded (1/2). The right one is cut into thirds with one slice shaded (1/3). The 1/2 slice is visibly larger than the 1/3 slice. https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/16.png Flowchart: 1. Confirm denominators are the same. 2. Add or Subtract Numerators. 3. Keep the Denominator exactly the same. 4. Simplify the result if possible. https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/17.png A vertical flowchart showing 4 steps: 1. Find LCM, 2. Make Equivalent Fractions, 3. Add or Subtract Numerators, 4. Simplify the Result. https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/18.png A split flowchart showing Method 1: Convert everything to improper fractions (Best for subtraction). Method 2: Group whole numbers and group fractions (Best for simple addition). https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/19.png A diagram showing two fractions with arrows pointing straight across from numerator to numerator and denominator to denominator. Caption: Top times Top, Bottom times Bottom. https://learningspot.co/maths/concepts-class-6/ch-7-fractions-images/20.png A colorful poster showing: K - Keep the first fraction. C - Change the sign to multiply. F - Flip the second fraction (Reciprocal). https://learningspot.co/maths/concepts-class-6/ch-8-decimals.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/1.png A colorful chart showing the decimal point as a divider. Left side: Hundreds, Tens, Ones. Right side: Tenths, Hundredths, Thousandths. Highlights the 'th' suffix for decimals. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/2.png Number line showing 0.7 https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/3.png Number line showing 1.2 https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/4.png Number line showing 2.45 https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/5.png Number line showing 3.8 https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/6.png An illustration showing fractions like 3/10, 45/100, and 7/100. Arrows show the decimal point jumping left. For 7/100, it shows adding a 'placeholder zero' to make the second jump possible. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/7.png A table showing pairs: 2 x 5 = 10; 4 x 25 = 100; 5 x 20 = 100; 8 x 125 = 1000; 50 x 2 = 100. Labels these as 'Friendly Multipliers'. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/8.png Side-by-side comparison of 3/8 (0.375, Stop sign) and 1/3 (0.333..., Infinity symbol). Shows 0.3 with a bar on top. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/9.png Flowchart: 1. Remove decimal point (this is your Numerator). 2. Count digits after decimal. 3. Put 1 followed by that many zeros (Denominator). 4. Simplify to lowest terms. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/10.png Side-by-side comparison. Left: Like Decimals (0.5, 2.3) showing 1 decimal place. Right: Unlike Decimals (0.5, 1.23) showing different lengths after the decimal. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/11.png Flowchart: 1. Count decimal places for each number. 2. Find the winner (the number with the most places). 3. Add 'Hero Zeros' to the others until they all match the winner. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/12.png https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/13.png Flowchart: 1. Count decimal places. 2. Find the maximum. 3. Add trailing zeros to match. 4. Compare the numbers as if the decimal wasn't there. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/14.png Flowchart: 1. Line up the decimal points. 2. Pad empty spots with zeros. 3. Add column by column from right to left. 4. Drop the decimal point straight down. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/15.png Flowchart: 1. Line up the Dots. 2. Fill gaps with Zeros. 3. Subtract (Borrow if needed). 4. Drop the Decimal point straight down. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/16.png Flowchart: 1. Ignore decimal points and multiply as whole numbers. 2. Count total decimal places in both numbers. 3. Start from right of product and jump left that many times. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/17.png An illustration of 3.45 x 10. The single zero in 10 is shown pushing the decimal point one 'hop' to the right to make 34.5. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/18.png A long division box showing the decimal point in the dividend and an arrow pointing straight up to the quotient, showing perfect alignment. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/19.png An illustration of 1.44 ÷ 1.2. Arrows show the decimal point in 1.2 moving 1 place right, and the decimal point in 1.44 also moving 1 place right to become 14.4 ÷ 12. https://learningspot.co/maths/concepts-class-6/ch-8-decimals-images/20.png An illustration of 234.5 ÷ 100. The two zeros in 100 are shown pulling the decimal point two 'hops' to the left to make 2.345. https://learningspot.co/maths/concepts-class-6/ch-9-data-handling.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-9-data-handling-images/1.png A mind map with 'Data Handling' in the center, branching to 'Observation' (Single bit), 'Frequency' (Count), 'Raw Data' (Original), and 'Tally' (Counting Tool). https://learningspot.co/maths/concepts-class-6/ch-9-data-handling-images/2.png A flowchart starting with Raw Data (Messy List), moving to Organising (Sorting/Tallying), and ending with Organised Data (Table/Graph). https://learningspot.co/maths/concepts-class-6/ch-9-data-handling-images/3.png Labeled diagram of a pictograph showing the Title, Categories, Symbols, and the most important part—the Key. https://learningspot.co/maths/concepts-class-6/ch-9-data-handling-images/4.png A visual formula showing: (Number of Symbols) × (Value in Key) = Total Quantity. https://learningspot.co/maths/concepts-class-6/ch-9-data-handling-images/5.png https://learningspot.co/maths/concepts-class-6/ch-9-data-handling-images/6.png Illustration showing: Full Symbol = 10 units; Half Symbol = 5 units. It uses a split sun or apple as an example. https://learningspot.co/maths/concepts-class-6/ch-9-data-handling-images/7.png A labeled bar graph showing Title, Vertical Axis (y-axis), Horizontal Axis (x-axis), Scale, Axis Labels, and Bars with uniform width. https://learningspot.co/maths/concepts-class-6/ch-9-data-handling-images/8.png Bar graph showing favourite colours https://learningspot.co/maths/concepts-class-6/ch-9-data-handling-images/9.png Bar graph showing bicycles manufactured per year https://learningspot.co/maths/concepts-class-6/ch-9-data-handling-images/10.png Bar graph showing money collected per class https://learningspot.co/maths/concepts-class-6/ch-10-mensuration.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-10-mensuration-images/1.png Polygon with sides labeled and a dashed line showing the walking path along the boundary https://learningspot.co/maths/concepts-class-6/ch-10-mensuration-images/2.png Rectangle with length and breadth labeled https://learningspot.co/maths/concepts-class-6/ch-10-mensuration-images/3.png Square with side labeled https://learningspot.co/maths/concepts-class-6/ch-10-mensuration-images/4.png Triangle with sides labeled a, b, c https://learningspot.co/maths/concepts-class-6/ch-10-mensuration-images/5.png A character walking along the boundary of an irregular polygon with arrows showing the path. Caption: Perimeter is the total path around the outside. https://learningspot.co/maths/concepts-class-6/ch-10-mensuration-images/6.png A table showing Regular Triangle (3s), Square (4s), Pentagon (5s), and Hexagon (6s) with their formulas. https://learningspot.co/maths/concepts-class-6/ch-10-mensuration-images/7.png Irregular shape on a grid for area calculation https://learningspot.co/maths/concepts-class-6/ch-10-mensuration-images/8.png Rectangle on a grid showing l x b squares https://learningspot.co/maths/concepts-class-6/ch-10-mensuration-images/9.png Square on a grid showing s x s squares https://learningspot.co/maths/concepts-class-6/ch-11-algebra.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-11-algebra-images/1.png A comparison chart showing Arithmetic (5 + 3 = 8) on one side and Algebra (x + 3 = 8) on the other. It explains that in Algebra, we use letters to find unknowns. https://learningspot.co/maths/concepts-class-6/ch-11-algebra-images/2.png A labeled diagram of the expression 4x + 7. 4 is the Coefficient, x is the Variable, + is the Operator, and 7 is the Constant. The whole parts 4x and 7 are labeled as Terms. https://learningspot.co/maths/concepts-class-6/ch-11-algebra-images/3.png An image of a balance scale showing an Equation (3x + 2 = 11) balanced on both sides, and an Expression (3x + 2) shown as just a single pile of blocks with no scale. https://learningspot.co/maths/concepts-class-6/ch-11-algebra-images/4.png An illustration of a box with a question mark on it transforming into the letter 'm'. Arrows show that the number 40 fits into the box to make 40 + 10 = 50. https://learningspot.co/maths/concepts-class-6/ch-11-algebra-images/5.png A table showing translation of keywords: Addition (sum, plus, increased by), Subtraction (difference, less than, subtracted from), Multiplication (product, times, twice), Division (quotient, ratio, divided by). https://learningspot.co/maths/concepts-class-6/ch-11-algebra-images/6.png Balance scale representing an equation https://learningspot.co/maths/concepts-class-6/ch-11-algebra-images/7.png https://learningspot.co/maths/concepts-class-6/ch-12-ratio-and-proportion.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-12-ratio-and-proportion-images/1.png Mind map centered on Ratio, branching into: Comparison by Division, Notation (a:b), Terms (Antecedent/Consequent), and Rules (Same units, No units, Order matters). https://learningspot.co/maths/concepts-class-6/ch-12-ratio-and-proportion-images/2.png Diagram showing a:b. The first term 'a' is labeled Antecedent. The second term 'b' is labeled Consequent. https://learningspot.co/maths/concepts-class-6/ch-12-ratio-and-proportion-images/3.png https://learningspot.co/maths/concepts-class-6/ch-12-ratio-and-proportion-images/4.png Flowchart: 1. Start with known value of 'n' items. 2. Divide by 'n' to find value of 1 item. 3. Multiply by required number 'm' to find final value. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/1.png Butterfly with line of symmetry https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/2.png Shape folded along line of symmetry https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/3.png An isosceles triangle with a single vertical line of symmetry. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/4.png A kite with one vertical line of symmetry along its main diagonal. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/5.png A semicircle with a single vertical line of symmetry. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/6.png The letters A, M, T, U, V, W, Y, each with a single vertical line of symmetry shown. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/7.png The letters B, C, D, E, K, each with a single horizontal line of symmetry shown. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/8.png A rectangle showing its one horizontal and one vertical line of symmetry. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/9.png A rhombus showing that its two diagonals are its lines of symmetry. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/10.png A square showing its four lines of symmetry: one horizontal, one vertical, and two diagonal. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/11.png An equilateral triangle with its three lines of symmetry. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/12.png A regular hexagon showing its six lines of symmetry. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/13.png A circle with several lines of symmetry passing through its center, indicating there are infinite possibilities. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/14.png The letters H, I, O, X, each with both horizontal and vertical lines of symmetry shown. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/21.png A scalene triangle, which has no lines of symmetry. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/22.png A parallelogram. An attempt to fold along a diagonal shows the halves do not match. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/23.png An irregular quadrilateral with no lines of symmetry. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/24.png The letters F, G, J, L, N, P, Q, R, S, Z, which are all asymmetrical. https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/15.png Letter H with horizontal and vertical lines of symmetry https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/16.png Object and its reflection in a mirror line https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/17.png Square divided by vertical line, showing one half as reflection of other https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/18.png Half shape and line of symmetry, showing how to complete by reflection https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/19.png Half shape and line of symmetry given https://learningspot.co/maths/concepts-class-6/ch-13-symmetry-images/20.png Completed symmetrical figure by reflection https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry.html 2026-03-28T11:39:47+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/1.png Image of a ruler https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/2.png Image of a compass https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/3.png Image of a divider https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/4.png Image of a protractor https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/5.png A 45-45-90 degree set square https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/6.png A 30-60-90 degree set square https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/38.png Setting compass radius using a ruler https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/39.png Steps to draw a circle with compass https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/7.png Drawing a line segment with a ruler https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/36.png Measuring the given line segment AB using a compass. The compass needle is at A and the pencil tip is at B. https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/37.png Constructing the copy CD. The compass needle is at C, and an arc is drawn to intersect line l at D. https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/8.png Line l and point P on it https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/9.png Drawing arcs from point P on the line https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/10.png Drawing arc from A above the line https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/11.png Drawing arc from B to intersect the first arc https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/12.png Drawing line through P and Q https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/13.png Drawing line l and point Q outside https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/14.png Drawing arc from Q intersecting the line https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/15.png Drawing arc from A below the line https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/16.png Drawing arc from B to intersect the first arc https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/17.png Drawing line through Q and R https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/18.png Drawing line segment AB https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/19.png Drawing arcs from A above and below AB https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/20.png Drawing arcs from B to intersect arcs from A https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/21.png Drawing line through P and Q https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/22.png Setting up protractor to draw an angle https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/23.png Marking 75 degrees on the protractor https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/24.png Drawing the second arm of the angle with ruler https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/25.png Drawing arc from O intersecting ray OA https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/26.png Drawing arc from B intersecting the first arc https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/27.png Drawing ray OC https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/28.png Constructing 120 degree angle by marking two 60 degree arcs https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/29.png Final constructed 120 degree angle https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/30.png Constructing 90 degree angle by bisecting the angle between 60 and 120 degree marks https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/31.png Final constructed 90 degree angle with construction lines. https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/32.png Drawing arc from vertex intersecting arms https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/33.png Drawing arc from P inside the angle https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/34.png Drawing arc from Q intersecting arc from P https://learningspot.co/maths/concepts-class-6/ch-14-practical-geometry-images/35.png Drawing ray BR https://learningspot.co/maths/concepts-class-7/ch-1-integers.html 2026-03-28T11:40:31+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/1.png Number line showing positive integers to the right of zero, and negative integers to the left of zero. https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/2.png Number line showing addition of 2 and 3. Start at 2 and move 3 steps right to reach 5. https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/3.png Number line showing addition of -2 and -3. Start at -2 and move 3 steps left to reach -5. https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/4.png Number line showing addition of 5 and -3. Start at 5 and move 3 steps left to reach 2. https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/5.png Number line showing subtraction of 6 from 4. Start at 4 and move 6 steps left to reach -2. https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/6.png Number line showing subtraction of -4 from 3. Start at 3 and move 4 steps right to reach 7. https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/7.png A mind map showing the five properties of integers: Closure, Commutative, Associative, Additive Identity, and Additive Inverse, with branches for Addition and Subtraction. https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/8.png A 3x3 Tic-Tac-Toe grid. The main diagonal has '+' signs. All other spaces have '-' signs. This shows that + times + is +, - times - is +, and any mixed pair is -. https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/9.png A central hub 'Multiplication of Integers' branching into: Closure, Commutative, Associative, Multiplicative Identity (1), Zero Property (0), and Distributive (over Addition and Subtraction). https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/10.png A graphic showing two negative signs joining to form a plus sign (Even = Positive). Below it, three negative signs where two join to form a plus but one remains negative (Odd = Negative). https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/11.png A split graphic showing: 'Same Signs = Positive (+)' with examples (+/+=+ and -/-=+) and 'Different Signs = Negative (-)' with examples (+/-=- and -/+= -). https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/12.png A summary chart for Division Properties of Integers. 1. Shows 'NO' for Closure, Commutative, and Associative properties with 'not equal to' examples. 2. Zero Rules: 0 ÷ a = 0, but a ÷ 0 = Undefined. 3. One Rules: a ÷ 1 = a, a ÷ a = 1, and a ÷ -1 = -a. 4. Verification that Distributive property does not hold for division. https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/13.png A vertical ladder representing the BODMAS rule. Top rung: Brackets (B). Second rung: Orders/Powers (O). Third rung: Division and Multiplication (D & M) side-by-side. Bottom rung: Addition and Subtraction (A & S) side-by-side. https://learningspot.co/maths/concepts-class-7/ch-1-integers-images/14.png A diagram showing nested brackets. The innermost is a bar (Vinculum), surrounded by Parentheses (round), then Braces (curly), and finally Square brackets (box). Arrows show the 'outward' flow of solving from inside to outside. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals.html 2026-03-28T11:40:31+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/1.png A mind map with 'Types of Fractions' at the center. Branches lead to Proper (N < D), Improper (N ≥ D), Mixed (Whole + Proper), Like (Same D), Unlike (Different D), and Unit (N = 1). https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/2.png A decision tree for comparing fractions. Ask: Same Denominator? (Compare Numerators). Same Numerator? (Smaller Denom is bigger). Different both? (Use Butterfly Method or LCM). https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/3.png A 4-step flowchart: 1. Find LCM of denominators. 2. Create Equivalent Fractions. 3. Add/Subtract Numerators. 4. Simplify the result. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/4.png A concept map showing two paths: Method A (Convert everything to improper fractions first) and Method B (Separate whole numbers and fractional parts). It notes that Method A is safer for subtraction. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/5.png A mind map with 'Fraction Addition' in the center. Branches lead to: Closure (still a fraction), Commutative (order doesn't matter), Associative (grouping doesn't matter), and Additive Identity (0). https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/6.png A 4-step flowchart: 1. Convert mixed numbers to improper fractions. 2. Cross-cancel common factors (if any). 3. Multiply numerators and denominators. 4. Convert back to mixed number if needed. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/7.png A mind map with 'Multiplication Properties' at the center. Branches lead to: Commutative (order), Associative (grouping), Identity (times 1), Zero Property (times 0), and Distributive Laws. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/8.png https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/9.png A comparison table. Property: Commutative. Multiplication: Yes (a×b=b×a). Division: No (a÷b ≠ b÷a). Property: Associative. Multiplication: Yes. Division: No. This emphasizes division's lack of flexibility. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/10.png A place value chart showing Thousands, Hundreds, Tens, Ones, the Decimal Point, Tenths, Hundredths, and Thousandths. Arrows show that moving right divides by 10, and moving left multiplies by 10. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/11.png https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/12.png Visual showing 0.75. The decimal point is turned into a 1 below, and the two digits (7 and 5) are turned into two zeros, creating 75/100. Arrows show the simplification to 3/4. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/13.png A mind map with 'Types of Decimals' at the center. Branches lead to Terminating (stops) and Non-terminating (continues), which further splits into Repeating (Recurring) and Non-repeating (Irrational). https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/14.png Graphic comparing 0.5 and 0.45. By adding a trailing zero to 0.5, it becomes 0.50. Now it is clear that 50 hundredths is greater than 45 hundredths. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/15.png A step-by-step flowchart: 1. Remove decimals and multiply like whole numbers. 2. Count the TOTAL decimal places in both numbers. 3. Place the decimal in the answer starting from the right. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/16.png An illustration showing 4.32 ÷ 0.24. Two matching curved arrows show the decimal point moving two places to the right in both numbers, transforming the problem into 432 ÷ 24. https://learningspot.co/maths/concepts-class-7/ch-2-fractions-and-decimals-images/17.png A vertical ladder showing BODMAS. B-Brackets, O-Orders/Of (often fractions), D-Division, M-Multiplication, A-Addition, S-Subtraction. Arrows show the left-to-right flow for DM and AS. https://learningspot.co/maths/concepts-class-7/ch-3-data-handling.html 2026-03-28T11:40:31+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-7/ch-3-data-handling-images/1.png A mind map with 'Data Handling' in the center. Branches lead to: 1. Types of Data (Raw, Arrayed), 2. Key Terms (Observation, Frequency), 3. Organisation (Frequency Table, Tally Marks), and 4. Range Calculation. https://learningspot.co/maths/concepts-class-7/ch-3-data-handling-images/2.png Bar graph showing marks obtained by a student in English (75), Hindi (60), Mathematics (90), Science (80), and Social Science (70). Subjects on X-axis, Marks on Y-axis with scale 1 unit = 10 marks. https://learningspot.co/maths/concepts-class-7/ch-3-data-handling-images/3.png Double bar graph comparing Term 1 and Term 2 marks for English, Hindi, Mathematics, Science, and Social Science. Subjects on X-axis, Marks on Y-axis. A key indicates which bar represents Term 1 and which represents Term 2. https://learningspot.co/maths/concepts-class-7/ch-3-data-handling-images/4.png Mind map showing Mean, Median, and Mode with brief descriptions https://learningspot.co/maths/concepts-class-7/ch-3-data-handling-images/5.png Flowchart showing the choice between simple mean, frequency table mean, and grouped data mean https://learningspot.co/maths/concepts-class-7/ch-3-data-handling-images/6.png Flowchart showing steps to find the median: Sort data, count n, and apply odd/even rules https://learningspot.co/maths/concepts-class-7/ch-3-data-handling-images/7.png Bar graph showing the highest bar representing the Mode of the dataset https://learningspot.co/maths/concepts-class-7/ch-3-data-handling-images/8.png Mind map defining Experiment, Outcome, Sample Space, and Event https://learningspot.co/maths/concepts-class-7/ch-3-data-handling-images/9.png Probability line from 0 to 1 showing Impossible, Unlikely, Even Chance, Likely, and Certain https://learningspot.co/maths/concepts-class-7/ch-4-simple-equations.html 2026-03-28T11:40:31+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-7/ch-4-simple-equations-images/1.png Flowchart showing steps to solve an equation: Simplify, then Add/Subtract, then Multiply/Divide https://learningspot.co/maths/concepts-class-7/ch-4-simple-equations-images/2.png Flowchart showing steps: 1. Read, 2. Define Variable, 3. Write Equation, 4. Solve https://learningspot.co/maths/concepts-class-7/ch-4-simple-equations-images/3.png Table showing transposition rules: plus becomes minus, minus becomes plus, multiply becomes divide, divide becomes multiply https://learningspot.co/maths/concepts-class-7/ch-4-simple-equations-images/4.png Flowchart showing steps: Group variables on LHS, Group constants on RHS, Simplify, Solve https://learningspot.co/maths/concepts-class-7/ch-4-simple-equations-images/5.png Flowchart showing steps: 1. Read, 2. Define Variable, 3. Write Equation, 4. Solve, 5. Check https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles.html 2026-03-28T11:40:31+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/1.png Two adjacent angles, one 30 degrees and the other 60 degrees, forming a right angle (90 degrees). https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/2.png Two adjacent angles, one 110 degrees and the other 70 degrees, forming a straight angle (180 degrees). https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/3.png Two angles sharing a common vertex and a common arm, with non-common arms on opposite sides of the common arm. https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/4.png Two adjacent angles forming a straight line. Angle 1 and Angle 2 sum up to 180 degrees. https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/5.png Two intersecting lines forming four angles. Angle 1 is vertically opposite to Angle 3. Angle 2 is vertically opposite to Angle 4. https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/6.png Lines PQ and RS intersecting at O. Angle POR is given as 50 degrees. https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/7.png Lines PQ and RS intersecting at O. Angle POR is given as 50 degrees, labeled Angle 1. Angle POS is labeled Angle 2, Angle SOQ is labeled Angle 3, Angle ROQ is labeled Angle 4. https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/8.png Two lines, l and m, intersecting at a single point P. https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/9.png Two parallel lines, l and m, that never meet. https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/10.png A line t (transversal) intersecting two other lines l and m at two distinct points. https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/11.png Transversal t intersecting lines l and m, forming angles 1, 2, 3, 4 at the intersection with l, and angles 5, 6, 7, 8 at the intersection with m. https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/12.png Lines l and m are parallel, intersected by transversal t. Angle 1 is 70 degrees. Other angles are 2, 3, 4, 5, 6, 7, 8. https://learningspot.co/maths/concepts-class-7/ch-5-lines-and-angles-images/13.png Transversal n intersects lines l and m. An interior angle on one side of n on line l is 100 degrees. An interior angle on the same side of n on line m is 80 degrees. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties.html 2026-03-28T11:40:31+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/1.png A triangle ABC with vertices A, B, C, sides AB, BC, CA, and interior angles at A, B, C. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/2.png An equilateral triangle with all three sides marked equal and all three angles marked as 60 degrees. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/3.png An isosceles triangle with two sides marked equal and the angles opposite these sides marked equal. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/4.png A scalene triangle with all three sides of different lengths and all three angles different. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/5.png An acute-angled triangle with all three angles less than 90 degrees (e.g., 60, 70, 50 degrees). https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/6.png A right-angled triangle with one angle marked as 90 degrees. The side opposite the right angle is the hypotenuse. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/7.png An obtuse-angled triangle with one angle greater than 90 degrees (e.g., 110 degrees) and the other two angles acute. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/8.png A triangle ABC with a median AD drawn from vertex A to the midpoint D of the opposite side BC. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/9.png An acute triangle showing an altitude from a vertex drawn perpendicular to the opposite side, lying completely inside the triangle. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/10.png A right-angled triangle showing that two of its altitudes are its own perpendicular sides. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/11.png An obtuse triangle showing an altitude from an acute vertex drawn to the extension of the opposite side, lying outside the triangle. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/12.png Triangle ABC with angles 1, 2, 3. A line XAY is drawn parallel to BC through vertex A. Angle XAB is angle 4, Angle YAC is angle 5. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/13.png Triangle ABC with side BC extended to D, forming exterior angle ACD. Interior opposite angles are A and B. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/14.png Triangle ABC with median AD, where D is the midpoint of BC. Median BE, where E is midpoint of AC. Median CF, where F is midpoint of AB. All three medians intersect at centroid G. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/15.png Triangle ABC. Altitude AD from A perpendicular to BC. Altitude BE from B perpendicular to AC. Altitude CF from C perpendicular to AB. All three altitudes intersect at orthocenter H. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/16.png Obtuse triangle PQR, with PQ extended. Altitude from R is RS perpendicular to extended PQ. Orthocenter lies outside. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/17.png Isosceles triangle ABC with AB = AC. Angle B is opposite side AC, and Angle C is opposite side AB. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/18.png Isosceles triangle ABC with AB = AC. Altitude AD is drawn from A to BC, which also bisects angle A and side BC. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/19.png Equilateral triangle PQR with PQ = QR = RP. Each angle P, Q, R is 60 degrees. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/20.png Triangle ABC with sides a, b, c. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/21.png https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/22.png A right-angled triangle ABC, with the right angle at C. Side AB is the hypotenuse, and sides AC and BC are the legs. https://learningspot.co/maths/concepts-class-7/ch-6-the-triangle-and-its-properties-images/23.png A right-angled triangle with squares drawn on each of its three sides. The area of the square on the hypotenuse equals the sum of the areas of the squares on the other two sides. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles.html 2026-03-28T11:40:31+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/1.png Two line segments AB and CD, both of length 5 cm, indicating they are congruent. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/2.png Two angles, angle ABC and angle PQR, both measuring 45 degrees, indicating they are congruent. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/3.png Two squares, S1 and S2, both with side length 4 cm, indicating they are congruent. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/4.png Two rectangles, R1 (length l1, breadth b1) and R2 (length l2, breadth b2). They are congruent if l1=l2 and b1=b2. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/5.png Two circles, C1 and C2, both with the same radius r, indicating they are congruent. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/6.png Diagram showing arrows connecting A to P, B to Q, and C to R based on the congruence statement https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/7.png Two triangles ABC and PQR. If AB=PQ, BC=QR, and CA=RP, then triangle ABC is congruent to triangle PQR by SSS criterion. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/8.png Two triangles ABC and PQR. If AB=PQ, angle B = angle Q, and BC=QR, then triangle ABC is congruent to triangle PQR by SAS criterion. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/9.png Two triangles ABC and PQR. If angle B = angle Q, BC=QR, and angle C = angle R, then triangle ABC is congruent to triangle PQR by ASA criterion. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/10.png Two triangles ABC and PQR. If angle B = angle Q, angle C = angle R, and side AB=PQ (non-included side to B and C), then triangle ABC is congruent to triangle PQR by AAS criterion. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/11.png Two right-angled triangles ABC (right angle at B) and PQR (right angle at Q). If hypotenuse AC=PR and side AB=PQ (or BC=QR), then triangle ABC is congruent to triangle PQR by RHS criterion. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/12.png Figure shows a point A, from which lines AC, AD, and AB are drawn. AB is between AC and AD. AC=AD is marked. AB bisects angle CAD. https://learningspot.co/maths/concepts-class-7/ch-7-congruence-of-triangles-images/13.png Isosceles triangle PQR with PQ=PR. D is midpoint of QR. Line segment PD is drawn. https://learningspot.co/maths/concepts-class-7/ch-8-comparing-quantities.html 2026-03-28T11:40:31+00:00 daily 0.9500 https://learningspot.co/assets/images/placeholder-image.png Concept map showing ratio notation, antecedent, and consequent https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry.html 2026-03-28T11:40:31+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/1.png A line l and a point A not on the line. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/2.png Step 1: Line l, point A not on l, point B on l, segment AB drawn as a transversal. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/3.png Step 2: Arc drawn with center B, intersecting l at C and BA at D. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/4.png Step 3: An arc of the same radius is drawn with center A, intersecting AB at G. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/5.png Step 5: Arc drawn with center G and radius CD, intersecting the other arc at H. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/6.png Step 6: Line m drawn passing through A and H, parallel to line l. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/7.png A line segment BC of length 7 cm is drawn using a ruler. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/8.png An arc is drawn above the line segment BC with center B and radius 5 cm. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/9.png A second arc is drawn with center C and radius 6 cm, intersecting the first arc at point A. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/10.png The points A, B, and C are joined to form the final triangle ABC with side lengths labeled. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/11.png A line segment QR of length 6.5 cm is drawn. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/12.png An angle of 75 degrees is constructed at point Q on the line segment QR. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/13.png An arc with radius 5.5 cm and center Q cuts the ray QX at point P. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/14.png Points P and R are joined to form the final triangle PQR. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/15.png A line segment DE of length 7 cm is drawn. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/16.png A ray DX is drawn from point D, making a 40-degree angle with the segment DE. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/17.png A ray EY is drawn from point E, making a 60-degree angle with the segment DE. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/18.png The rays DX and EY intersect at point F, forming the triangle DEF. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/19.png A line segment MN of length 3 cm is drawn. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/20.png A ray MX is drawn perpendicular to MN at point M, forming a 90-degree angle. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/21.png An arc with radius 5 cm and center N cuts the perpendicular ray MX at point L. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/22.png Points L and N are joined, forming the hypotenuse and completing the right-angled triangle LMN. https://learningspot.co/maths/concepts-class-7/ch-10-practical-geometry-images/23.png Two equilateral triangles of different sizes, both having 60 degree angles. https://learningspot.co/maths/concepts-class-8/ch-3-understanding-quadrilaterals.html 2026-03-28T11:41:25+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-8/placeholder_simple_curve.png Examples of simple curves https://learningspot.co/maths/concepts-class-8/placeholder_non_simple_curve.png Examples of non-simple curves https://learningspot.co/maths/concepts-class-8/placeholder_open_curve.png Examples of open curves https://learningspot.co/maths/concepts-class-8/placeholder_closed_curve.png Examples of closed curves https://learningspot.co/maths/concepts-class-8/placeholder_polygons.png Examples of polygons (triangle, square, pentagon) https://learningspot.co/maths/concepts-class-8/placeholder_non_polygons.png Examples of non-polygons (open curve, not simple curve, not made of line segments) https://learningspot.co/maths/concepts-class-8/placeholder_convex_polygon.png Example of a convex polygon https://learningspot.co/maths/concepts-class-8/placeholder_concave_polygon.png Example of a concave polygon https://learningspot.co/maths/concepts-class-8/placeholder_regular_polygons.png Examples of regular polygons https://learningspot.co/maths/concepts-class-8/placeholder_irregular_polygons.png Examples of irregular polygons https://learningspot.co/maths/concepts-class-8/placeholder_polygon_triangulation.png Polygon divided into triangles from one vertex https://learningspot.co/maths/concepts-class-8/placeholder_quadrilateral_triangulation.png Quadrilateral divided into two triangles by a diagonal https://learningspot.co/maths/concepts-class-8/placeholder_exterior_angles_polygon.png Exterior angles of a polygon https://learningspot.co/maths/concepts-class-8/placeholder_quadrilateral_abcd.png Quadrilateral ABCD https://learningspot.co/maths/concepts-class-8/placeholder_parallelogram.png Parallelogram ABCD with parallel sides indicated https://learningspot.co/maths/concepts-class-8/placeholder_parallelogram_diagonals.png Diagonals of a parallelogram bisecting each other https://learningspot.co/maths/concepts-class-8/placeholder_rhombus.png Rhombus ABCD with equal sides marked https://learningspot.co/maths/concepts-class-8/placeholder_rectangle.png Rectangle ABCD with right angles marked https://learningspot.co/maths/concepts-class-8/placeholder_square.png Square ABCD with equal sides and right angles marked https://learningspot.co/maths/concepts-class-8/placeholder_trapezium.png Trapezium ABCD with AB parallel to DC https://learningspot.co/maths/concepts-class-8/placeholder_isosceles_trapezium.png Isosceles Trapezium ABCD with AD=BC and angles A=B, C=D https://learningspot.co/maths/concepts-class-8/placeholder_kite.png Kite ABCD with AD=CD and AB=CB https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry.html 2026-03-28T11:41:25+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/1.png Step 1: Draw diagonal AC 7cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/2.png Locate point B by arcs from A and C https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/3.png Step 3: Join AB and BC https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/4.png Locate point D by arcs from A and C https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/5.png Step 5: Join AD and CD https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/6.png Complete quadrilateral ABCD https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/7.png Step 1: Draw diagonal PR 6cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/8.png Locate point Q by arcs from P and R https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/9.png Step 3: Join PQ and QR https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/10.png Draw arc from P for PS https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/11.png Locate point S by arc from Q https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/12.png Complete quadrilateral PQRS https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/13.png Draw side MI 3.5cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/14.png Construct angle 75 at M https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/15.png Construct angle 105 at I https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/16.png Mark point S on IY https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/17.png Construct angle 120 at S and find T https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/18.png Complete quadrilateral MIST https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/19.png Step 1: A line segment QR of length 6 cm is drawn. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/20.png Step 2: A ray QX is drawn at an angle of 105 degrees to QR. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/21.png Step 3: Point P is marked on ray QX at a distance of 4 cm from Q. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/22.png Step 4: A ray RY is drawn at an angle of 80 degrees to QR. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/23.png Step 5: Point S is marked on ray RY at a distance of 5 cm from R. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/24.png Step 6: Points P and S are joined to complete the quadrilateral PQRS. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/25.png Step 1: Draw side AB 6cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/26.png Construct angle 60 at A https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/27.png Mark point D on AX https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/28.png Draw arc from B for BC https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/29.png Locate point C by arcs from B and D https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/30.png Complete parallelogram ABCD https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/31.png Draw diagonal PR 7cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/32.png Locate point Q by arcs from P and R https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/33.png Step 3: Join PQ and QR https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/34.png Draw arc from P for PS https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/35.png Locate point S by arcs from P and R https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/36.png Complete parallelogram PQRS https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/37.png Draw diagonal AC 6cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/38.png Find midpoint O of AC https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/39.png Construct angle 70 at O and draw line XY https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/40.png Mark points B and D on XY from O https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/41.png Join vertices to form parallelogram ABCD https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/42.png Step 1: Diagonal QS of 10 cm is drawn. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/43.png Step 2: Midpoint O of QS is located using a ruler. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/44.png Step 3: Arcs of 4 cm radius are drawn from O on both sides of QS. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/45.png Step 4: Arc from Q of 6 cm intersects an arc from O to locate point R. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/46.png Step 5: Arc from S of 6 cm intersects the other arc from O to locate point P. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/47.png Step 6: Vertices are joined to form the parallelogram PQRS. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/48.png Draw side PQ 5cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/49.png Construct angle 90 at Q https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/50.png Mark point R on QX https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/51.png Draw arc from P for PS https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/52.png Locate point S by arcs from P and R https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/53.png Complete rectangle PQRS https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/54.png Step 1: Draw a line segment AB of 8 cm. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/55.png Step 2: Construct a 90-degree angle at point B. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/56.png Step 3: An arc from A with radius 10 cm intersects the perpendicular at C. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/57.png Step 4: Draw an arc from C with a radius of 8 cm. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/58.png Step 5: Arcs from C (radius 8cm) and B (radius 10cm) intersect at D. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/59.png Step 6: The completed rectangle ABCD. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/60.png Step 1: Draw diagonal AC = 6 cm. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/61.png Step 2: Locate the midpoint O of AC. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/62.png Step 3: Construct a line YOX through O at an angle of 60 degrees to AC. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/63.png Step 4: Cut arcs of 3 cm on YOX to get points B and D. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/64.png Step 5: Join the vertices AB, BC, CD, and DA. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/65.png The complete rectangle ABCD. https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/66.png Draw diagonal AC 8cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/67.png Find midpoint O of AC https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/68.png Construct angle 60 at O https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/69.png Mark points B and D on XY https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/70.png Join vertices to form the rectangle https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/71.png Step 1: Draw side JU 4cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/72.png Step 2: Construct angle 60 at J https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/73.png Step 3: Mark point P on ray JX such that JP=4cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/74.png Step 4: Draw an arc from U with a radius of 4cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/75.png Step 5: Locate point M by arcs from U and P https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/76.png Step 6: The completed rhombus JUMP https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/77.png Draw diagonal AC 6cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/78.png Find midpoint O of AC https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/79.png Construct perpendicular line XY at O https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/80.png Mark points B and D on XY from O https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/81.png Join vertices to form rhombus ABCD https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/82.png Complete rhombus ABCD https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/83.png Step 1: Draw side AB 4cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/84.png Step 2: Construct angle 90 at B https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/85.png Step 3: Mark point C on BX such that BC=4cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/86.png Step 4: Draw an arc from A with a radius of 4cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/87.png Step 5: Locate point D by arcs from A and C https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/88.png Step 6: The completed square ABCD https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/89.png Draw diagonal AC 6cm https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/90.png Find midpoint O of AC https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/91.png Construct perpendicular line XY at O https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/92.png Mark points B and D on XY from O https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/93.png Join vertices to form square ABCD https://learningspot.co/maths/concepts-class-8/ch-4-practical-geometry%20Images/94.png Complete square ABCD https://learningspot.co/maths/concepts-class-8/ch-5-data-handling.html 2026-03-28T11:41:25+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-8/placeholder_ch5_bar_graph_ex1.png Bar graph showing student preferences for subjects https://learningspot.co/maths/concepts-class-8/placeholder_ch5_double_bar_graph_ex2.png Double bar graph showing student marks in two terms https://learningspot.co/maths/concepts-class-8/placeholder_ch5_histogram_ex5.png Histogram for grouped age data https://learningspot.co/maths/concepts-class-8/placeholder_ch5_pie_chart_s1.png Step 1: Draw a circle https://learningspot.co/maths/concepts-class-8/placeholder_ch5_pie_chart_s2.png Step 2: Draw a radius https://learningspot.co/maths/concepts-class-8/placeholder_ch5_pie_chart_s3.png Step 3: Draw sector for Food https://learningspot.co/maths/concepts-class-8/placeholder_ch5_pie_chart_s4.png Step 4: Draw sector for Clothing https://learningspot.co/maths/concepts-class-8/placeholder_ch5_pie_chart_s5.png Step 5: Draw sectors for Education, Rent, Savings https://learningspot.co/maths/concepts-class-8/placeholder_ch5_pie_chart_ex6.png Complete Pie chart showing family expenditure distribution https://learningspot.co/maths/concepts-class-8/ch-10-visualising-solid-shapes.html 2026-03-28T11:41:25+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-8/placeholder_2d_shapes.png Examples of 2D shapes: square, circle, triangle https://learningspot.co/maths/concepts-class-8/placeholder_3d_shapes.png Examples of 3D shapes: cube, cylinder, cone https://learningspot.co/maths/concepts-class-8/placeholder_cube_net.png Net of a cube https://learningspot.co/maths/concepts-class-8/placeholder_cylinder_net.png Net of a cylinder https://learningspot.co/maths/concepts-class-8/placeholder_cuboid_3d.png 3D view of a cuboid https://learningspot.co/maths/concepts-class-8/placeholder_cuboid_front_view.png Front view of a cuboid (a rectangle) https://learningspot.co/maths/concepts-class-8/placeholder_cuboid_side_view.png Side view of a cuboid (a rectangle) https://learningspot.co/maths/concepts-class-8/placeholder_cuboid_top_view.png Top view of a cuboid (a rectangle) https://learningspot.co/maths/concepts-class-8/placeholder_cylinder_3d.png 3D view of a cylinder https://learningspot.co/maths/concepts-class-8/placeholder_cylinder_front_view.png Front view of a cylinder (a rectangle) https://learningspot.co/maths/concepts-class-8/placeholder_cylinder_side_view.png Side view of a cylinder (a rectangle) https://learningspot.co/maths/concepts-class-8/placeholder_cylinder_top_view.png Top view of a cylinder (a circle) https://learningspot.co/maths/concepts-class-8/placeholder_stacked_cubes_3d.png 3D view of stacked cubes https://learningspot.co/maths/concepts-class-8/placeholder_stacked_cubes_front.png Front view of stacked cubes https://learningspot.co/maths/concepts-class-8/placeholder_stacked_cubes_side.png Side view of stacked cubes https://learningspot.co/maths/concepts-class-8/placeholder_stacked_cubes_top.png Top view of stacked cubes https://learningspot.co/maths/concepts-class-8/placeholder_polyhedra_examples.png Examples of polyhedra: cube, pyramid, prism https://learningspot.co/maths/concepts-class-8/placeholder_concave_polyhedron.png Example of a concave polyhedron https://learningspot.co/maths/concepts-class-8/placeholder_prism.png Example of a triangular prism https://learningspot.co/maths/concepts-class-8/placeholder_pyramid.png Example of a square pyramid https://learningspot.co/maths/concepts-class-8/ch-11-mensuration.html 2026-03-28T11:41:25+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-8/placeholder_quadrilateral_diag_h1_h2.png Quadrilateral with diagonal d and perpendicular heights h1, h2 https://learningspot.co/maths/concepts-class-8/ch-15-introduction-to-graphs.html 2026-03-28T11:41:25+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-8/placeholder_cartesian_plane.png Cartesian coordinate plane with x and y axes, origin https://learningspot.co/maths/concepts-class-8/placeholder_quadrants.png Quadrants of the Cartesian plane https://learningspot.co/maths/concepts-class-8/placeholder_plot_points.png Plotting points on a Cartesian plane https://learningspot.co/maths/concepts-class-8/placeholder_line_graph_temp_axes.png Line graph axes setup with kink https://learningspot.co/maths/concepts-class-8/placeholder_line_graph_temp_points.png Line graph with points plotted https://learningspot.co/maths/concepts-class-8/placeholder_line_graph_temp.png Line graph showing daily temperature https://learningspot.co/maths/concepts-class-8/placeholder_linear_graph_points.png Plotting points for a linear graph https://learningspot.co/maths/concepts-class-8/placeholder_linear_graph_points_connected.png Plotted points connected by a straight line https://learningspot.co/maths/concepts-class-8/placeholder_linear_graph_distance_time_points.png Plotting points for distance vs time https://learningspot.co/maths/concepts-class-8/placeholder_linear_graph_distance_time.png Linear graph showing distance vs time at constant speed https://learningspot.co/maths/concepts-class-8/placeholder_linear_graph_distance_time_read.png Reading distance from linear graph at 1.5 hours https://learningspot.co/maths/concepts-class-9/ch-1-number-systems.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_real_number_line_integers.png Real Number Line showing integers https://learningspot.co/maths/concepts-class-9/placeholder_numline_0_1_divided_2.png Number line segment 0 to 1 divided into 2 parts https://learningspot.co/maths/concepts-class-9/placeholder_image_for_1_2_on_number_line Number line showing 1/2 https://learningspot.co/maths/concepts-class-9/placeholder_numline_0_1_divided_4.png Number line segment 0 to 1 divided into 4 parts https://learningspot.co/maths/concepts-class-9/placeholder_image_for_3_4_on_number_line Number line showing 3/4 https://learningspot.co/maths/concepts-class-9/placeholder_numline_2_3_divided_3.png Number line segment 2 to 3 divided into 3 parts https://learningspot.co/maths/concepts-class-9/placeholder_image_for_7_3_on_number_line Number line showing 7/3 https://learningspot.co/maths/concepts-class-9/placeholder_numline_-2_-1_divided_3.png Number line segment -2 to -1 divided into 3 parts https://learningspot.co/maths/concepts-class-9/placeholder_image_for_-5_3_on_number_line Number line showing -5/3 https://learningspot.co/maths/concepts-class-9/placeholder_numline_origin_1unit.png Number line with origin and 1 unit marked https://learningspot.co/maths/concepts-class-9/placeholder_sqrt2_step2.png Construct perpendicular of length 1 at 1 https://learningspot.co/maths/concepts-class-9/placeholder_sqrt2_step3.png Join O and B to form hypotenuse https://learningspot.co/maths/concepts-class-9/placeholder_sqrt2_step5.png Draw arc from O with radius OB to the number line https://learningspot.co/maths/concepts-class-9/placeholder_image_for_sqrt2_on_number_line Construction of sqrt(2) on number line https://learningspot.co/maths/concepts-class-9/placeholder_sqrt3_step2.png Construct perpendicular of length 1 at point sqrt(2) https://learningspot.co/maths/concepts-class-9/placeholder_sqrt3_step3.png Join O and Q to form hypotenuse https://learningspot.co/maths/concepts-class-9/placeholder_sqrt3_step5.png Draw arc from O with radius OQ to the number line https://learningspot.co/maths/concepts-class-9/placeholder_image_for_sqrt3_on_number_line Construction of sqrt(3) on number line https://learningspot.co/maths/concepts-class-9/placeholder_sqrt_spiral.png Square root spiral construction https://learningspot.co/maths/concepts-class-9/placeholder_numline_pointA.png Draw a line and mark point A as 0 https://learningspot.co/maths/concepts-class-9/placeholder_sqrtx_step2.png Mark point B at x units from A=0 https://learningspot.co/maths/concepts-class-9/placeholder_sqrtx_step3.png Extend AB by 1 unit to C https://learningspot.co/maths/concepts-class-9/placeholder_sqrtx_step4.png Find midpoint M of AC https://learningspot.co/maths/concepts-class-9/placeholder_sqrtx_step5.png Draw a semicircle with diameter AC https://learningspot.co/maths/concepts-class-9/placeholder_sqrtx_step6.png Draw perpendicular at B intersecting semicircle at D https://learningspot.co/maths/concepts-class-9/placeholder_sqrtx_step8.png Transfer length BD to number line from origin A https://learningspot.co/maths/concepts-class-9/placeholder_image_for_sqrtx_on_number_line Construction of sqrt(x) on number line https://learningspot.co/maths/concepts-class-9/placeholder_image_for_magnification_2_665_step1 Magnification step 1 for 2.665 https://learningspot.co/maths/concepts-class-9/placeholder_image_for_magnification_2_665_step2 Magnification step 2 for 2.665 https://learningspot.co/maths/concepts-class-9/placeholder_image_for_magnification_2_665_step3 Magnification step 3 for 2.665 https://learningspot.co/maths/concepts-class-9/placeholder_image_for_magnification_2_665_step4 Magnification step 4 for 2.665 https://learningspot.co/maths/concepts-class-9/placeholder_image_for_magnification_5_3778_step1 Magnification step 1 for 5.3778 https://learningspot.co/maths/concepts-class-9/placeholder_image_for_magnification_5_3778_step2 Magnification step 2 for 5.3778 https://learningspot.co/maths/concepts-class-9/placeholder_image_for_magnification_5_3778_step3 Magnification step 3 for 5.3778 https://learningspot.co/maths/concepts-class-9/placeholder_image_for_magnification_5_3778_step4 Magnification step 4 for 5.3778 https://learningspot.co/maths/concepts-class-9/placeholder_image_for_magnification_5_3778_step5 Magnification step 5 for 5.3778 https://learningspot.co/maths/concepts-class-9/ch-3-coordinate-geometry.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_image_for_cartesian_plane_axes_origin Cartesian plane showing x and y axes, origin, and positive/negative directions https://learningspot.co/maths/concepts-class-9/placeholder_image_for_cartesian_plane_quadrants Cartesian plane showing the four quadrants and the signs of coordinates in each https://learningspot.co/maths/concepts-class-9/placeholder_plotting_3_2.png Steps to plot point (3, 2) https://learningspot.co/maths/concepts-class-9/placeholder_plotting_-4_1.png Steps to plot point (-4, 1) https://learningspot.co/maths/concepts-class-9/placeholder_plotting_2_-3.png Steps to plot point (2, -3) https://learningspot.co/maths/concepts-class-9/placeholder_plotting_-1_-2.png Steps to plot point (-1, -2) https://learningspot.co/maths/concepts-class-9/placeholder_image_for_plotting_points Cartesian plane showing plotted points with various coordinates https://learningspot.co/maths/concepts-class-9/ch-4-linear-equations-in-two-variables.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_graph_x+y=4_points.png Graph of x+y=4 showing points (0,4), (4,0), (2,2) https://learningspot.co/maths/concepts-class-9/placeholder_image_for_graph_x+y=4 Graph of x+y=4 showing points (0,4), (4,0), (2,2) and the line passing through them https://learningspot.co/maths/concepts-class-9/placeholder_graph_y=2x-1_points.png Graph of y=2x-1 showing points (0,-1), (1,1), (-1,-3) https://learningspot.co/maths/concepts-class-9/placeholder_image_for_graph_y=2x-1 Graph of y=2x-1 showing points (0,-1), (1,1), (-1,-3) and the line https://learningspot.co/maths/concepts-class-9/placeholder_graph_2x+y=6_points.png Graph of 2x+y=6 showing points (0,6), (3,0), (1,4) https://learningspot.co/maths/concepts-class-9/placeholder_image_for_graph_2x+y=6 Graph of 2x+y=6 showing points (0,6), (3,0), (1,4) and the line https://learningspot.co/maths/concepts-class-9/placeholder_graph_y=3_points.png Points for y=3 plotted https://learningspot.co/maths/concepts-class-9/placeholder_image_for_graph_y=3 Graph of y=3, a horizontal line 3 units above x-axis https://learningspot.co/maths/concepts-class-9/placeholder_graph_x=-2_points.png Points for x=-2 plotted https://learningspot.co/maths/concepts-class-9/placeholder_image_for_graph_x=-2 Graph of x=-2, a vertical line 2 units left of y-axis https://learningspot.co/maths/concepts-class-9/ch-6-lines-and-angles.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_angle_arms_vertex.png Angle showing arms and vertex https://learningspot.co/maths/concepts-class-9/placeholder_transversal_lines.png Transversal line n intersecting lines l and m https://learningspot.co/maths/concepts-class-9/placeholder_transversal_8angles.png Transversal intersecting two lines showing 8 numbered angles https://learningspot.co/maths/concepts-class-9/placeholder_corresponding_angles.png Corresponding angles marked in a diagram https://learningspot.co/maths/concepts-class-9/placeholder_alternate_interior_angles.png Alternate interior angles marked in a diagram https://learningspot.co/maths/concepts-class-9/placeholder_alternate_exterior_angles.png Alternate exterior angles marked in a diagram https://learningspot.co/maths/concepts-class-9/placeholder_consecutive_interior_angles.png Consecutive interior angles marked in a diagram https://learningspot.co/maths/concepts-class-9/placeholder_consecutive_exterior_angles.png Consecutive exterior angles marked in a diagram https://learningspot.co/maths/concepts-class-9/ch-7-triangles.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_triangle_ac_greater_ab.png Triangle ABC with AC greater than AB https://learningspot.co/maths/concepts-class-9/placeholder_theorem_7_6_construction.png Triangle ABC with point D on AC such that AD=AB, and BD joined https://learningspot.co/maths/concepts-class-9/placeholder_triangle_angle_b_greater_c.png Triangle ABC with angle B greater than angle C https://learningspot.co/maths/concepts-class-9/placeholder_triangle_abc.png Triangle ABC https://learningspot.co/maths/concepts-class-9/placeholder_triangle_inequality_construction.png Triangle ABC with BA extended to D such that AD=AC, and DC joined https://learningspot.co/maths/concepts-class-9/placeholder_perpendicular_shortest.png Point P not on line l, PM perpendicular to l, Q any other point on l https://learningspot.co/maths/concepts-class-9/ch-8-quadrilaterals.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_quadrilateral_ABCD.jpg Diagram of a quadrilateral ABCD showing vertices A, B, C, D and sides AB, BC, CD, DA https://learningspot.co/maths/concepts-class-9/placeholder_quadrilateral_AC_diagonal.jpg Diagram of a quadrilateral ABCD with diagonal AC drawn, dividing it into two triangles ABC and ADC https://learningspot.co/maths/concepts-class-9/placeholder_parallelogram_diag_AC.jpg Diagram of a parallelogram ABCD with diagonal AC https://learningspot.co/maths/concepts-class-9/placeholder_parallelogram_diags_intersect.jpg Diagram of a parallelogram ABCD with diagonals AC and BD intersecting at O https://learningspot.co/maths/concepts-class-9/placeholder_quadrilateral_diag_AC.jpg Diagram of a quadrilateral ABCD with diagonal AC https://learningspot.co/maths/concepts-class-9/placeholder_quadrilateral_diags_bisect.jpg Diagram of a quadrilateral ABCD with diagonals AC and BD intersecting at O, showing AO=CO and BO=DO https://learningspot.co/maths/concepts-class-9/placeholder_rectangle_diagonals.jpg Diagram of a rectangle ABCD with diagonals AC and BD https://learningspot.co/maths/concepts-class-9/placeholder_parallelogram_equal_diags.jpg Diagram of a parallelogram ABCD with equal diagonals AC and BD https://learningspot.co/maths/concepts-class-9/placeholder_rhombus.jpg Diagram of a rhombus ABCD with all sides marked equal https://learningspot.co/maths/concepts-class-9/placeholder_rhombus_diagonals.jpg Diagram of a rhombus ABCD with diagonals AC and BD intersecting at O https://learningspot.co/maths/concepts-class-9/placeholder_parallelogram_perp_diags.jpg Diagram of a parallelogram ABCD with diagonals AC and BD intersecting perpendicularly at O https://learningspot.co/maths/concepts-class-9/placeholder_square.jpg Diagram of a square ABCD with all sides equal and all angles 90 degrees https://learningspot.co/maths/concepts-class-9/placeholder_quadrilateral_equal_perp_bisecting_diags.jpg Diagram of a quadrilateral ABCD with equal and perpendicular diagonals bisecting each other at O https://learningspot.co/maths/concepts-class-9/placeholder_triangle_midpoints_EF.jpg Diagram of triangle ABC with E as midpoint of AB and F as midpoint of AC, and line segment EF https://learningspot.co/maths/concepts-class-9/placeholder_triangle_midpoints_EF_extended_CD.jpg Diagram of triangle ABC with E midpoint of AB, F midpoint of AC, EF extended to D such that EF=FD, and CD joined https://learningspot.co/maths/concepts-class-9/placeholder_triangle_midpoint_parallel.jpg Diagram of triangle ABC with E midpoint of AB, and a line through E parallel to BC intersecting AC at F https://learningspot.co/maths/concepts-class-9/placeholder_triangle_midpoint_parallel_construction.jpg Diagram of triangle ABC with E midpoint of AB, EF parallel to BC, EF extended to D, and CD drawn parallel to AB https://learningspot.co/maths/concepts-class-9/ch-9-areas-of-parallelograms-and-triangles.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_example_9_1.jpg Parallelogram ABCD with altitudes AE to DC and CF to AD https://learningspot.co/maths/concepts-class-9/placeholder_theorem_9_5.jpg Triangle ABC with median AD to side BC https://learningspot.co/maths/concepts-class-9/placeholder_theorem_9_5_construction.jpg Triangle ABC with median AD and altitude AM from A to BC https://learningspot.co/maths/concepts-class-9/ch-10-circles.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_angle_subtended.jpg Diagram of a circle with chord AB, center O, point P on major arc, and point Q on minor arc, showing angles AOB, APB, AQB https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_1.jpg Circle with center O and two equal chords AB and CD, showing angles AOB and COD at the center https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_2.jpg Circle with center O and two chords AB and CD, showing equal angles AOB and COD at the center https://learningspot.co/maths/concepts-class-9/placeholder_distance_of_chord.jpg Circle with center O, chord AB, and perpendicular OM from O to AB. OM is the distance of the chord from the center. https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_4.jpg Circle with center O, chord AB, and line segment OM where M is the midpoint of AB https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_4_construction.jpg Circle with center O, chord AB, line segment OM through midpoint M, and radii OA and OB drawn. https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_5.jpg Circle with center O, equal chords AB and CD, and perpendiculars OM to AB and ON to CD https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_5_construction.jpg Circle with center O, equal chords AB and CD, perpendiculars OM to AB and ON to CD, and radii OA and OC drawn. https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_6.jpg Circle with center O, chords AB and CD, and perpendiculars OM and ON such that OM=ON https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_6_construction.jpg Circle with center O, chords AB and CD, perpendiculars OM and ON, and radii OA and OC drawn. https://learningspot.co/maths/concepts-class-9/placeholder_example_10_1.jpg Circle with center O, radius OA=5cm, chord AB=8cm, and perpendicular OM to AB https://learningspot.co/maths/concepts-class-9/placeholder_angle_subtended_arc.jpg Circle with center O, arc PQ, point R on major arc, showing angle POQ at center and angle PRQ on circumference https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_8.jpg Circle with diameter AB through center O, and point C on the semicircle, showing angle ACB https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_9.jpg Circle with chord AB, points C and D on the same segment (major arc), showing angles ACB and ADB https://learningspot.co/maths/concepts-class-9/placeholder_theorem_10_9_construction.jpg Circle with chord AB, points C and D on same segment, center O, radii OA and OB drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/1.png Step 1: A line segment AB of length 7.6 cm is drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/2.png Step 2: Arcs are drawn from point A with a radius greater than half of AB. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/3.png Step 3: Arcs are drawn from point B with the same radius, intersecting the previous arcs at P and Q. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/4.png Step 4: The line PQ is drawn, which is the perpendicular bisector of AB, intersecting it at M. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/5.png Diagram for justification showing triangles PAQ, PBQ, PAM, and PBM. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/6.png Step 1: An angle BAC of 70 degrees is drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/7.png Step 2: An arc is drawn from vertex A, intersecting AB at P and AC at Q. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/8.png Step 3: An arc is drawn from point P inside the angle. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/9.png Step 4: A second arc is drawn from Q with the same radius, intersecting the first arc at R. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/10.png Step 5: The ray AR is drawn, which bisects angle BAC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/11.png Diagram showing triangles APR and AQR formed during angle bisector construction. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/12.png Step 1: A line segment AB of length 5 cm is drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/13.png Step 2: An arc is drawn from point A with a radius of 5 cm. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/14.png Step 3: A second arc is drawn from B with the same radius, intersecting the first arc at C. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/15.png Step 4: The points A, B, and C are joined to form the equilateral triangle ABC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/16.png Diagram showing triangle ABC with side lengths based on construction https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/17.png Step 1: A line segment AD of length 4 cm is drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/18.png Step 2: The line segment AD is extended to E such that AD=DE, making AE=8cm. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/19.png Step 3: An arc of radius 5 cm is drawn from point A. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/20.png Step 4: An arc of radius 6 cm from E intersects the arc from A at point B. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/21.png Step 5: Points A and E are joined to B, forming triangle ABE. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/22.png Step 6: BD is extended to C such that BD=DC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/23.png Step 7: AC is joined to complete the required triangle ABC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/24.png Diagram showing triangle ABC with median AD and related parallelogram ABEC https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/25.png Step 1: A line l is drawn with a point D on it. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/26.png Step 2: A perpendicular DX is constructed at point D on line l. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/27.png Step 3: A point A is marked on ray DX such that AD = 4.5 cm. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/28.png Step 4: An angle DAB of 30 degrees is constructed. The ray intersects line l at B. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/29.png Step 5: An angle DAC of 45 degrees is constructed on the other side. The ray intersects line l at C. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/30.png Step 6: The completed triangle ABC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/31.png Step 1: A line segment AB of length 3 cm is drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/32.png Step 2: A perpendicular ray BX is drawn at point B, making a 90-degree angle with AB. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/33.png Step 3: An arc from A with a 5 cm radius intersects the perpendicular ray BX at point C. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/34.png Step 4: The points A and C are joined to complete the right-angled triangle ABC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/35.png Step 1: A line segment QR of length 5 cm is drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/36.png Step 2: An arc with a 6 cm radius is drawn from point Q. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/37.png Step 3: A second arc with a 6 cm radius from R intersects the first arc at point P. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/38.png Step 4: Points P, Q, and R are joined to form the isosceles triangle. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/39.png Diagram showing triangle PQR with base QR and sides PQ, PR https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/40.png Step 1: A line segment BC of length 7 cm is drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/41.png Step 2: A ray BX is drawn at B making a 75-degree angle with BC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/42.png Step 3: A point D is marked on ray BX such that BD = 13 cm. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/43.png Step 4: The points D and C are joined. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/44.png Step 5: The perpendicular bisector of DC is drawn, which intersects BD at point A. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/45.png Step 6: A and C are joined to form the required triangle ABC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/46.png Diagram of triangle ABC constructed, showing point D on ray BX, and perpendicular bisector of DC passing through A https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/47.png Step 1: A line segment BC of length 8 cm is drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/48.png Step 2: A ray BX is drawn at B, making a 45-degree angle with BC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/49.png Step 3: A point D is marked on ray BX such that BD = 3.5 cm. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/50.png Step 4: The points D and C are joined to form segment DC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/51.png Step 5: The perpendicular bisector of DC is drawn, intersecting ray BX at point A. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/52.png Step 6: A and C are joined to form the required triangle ABC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/53.png Step 1: A line segment BC of length 6 cm is drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/54.png Step 2: A ray BX is drawn at B, making a 60-degree angle with BC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/55.png Step 3: Ray BX is extended backwards and a point D is marked such that BD = 2 cm. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/56.png Step 4: The points D and C are joined to form segment DC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/57.png Step 5: The perpendicular bisector of DC is drawn, intersecting ray BX at point A. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/58.png Step 6: A and C are joined to form the required triangle ABC. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/59.png Step 1: A line segment PQ of length 11 cm is drawn. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/60.png Step 2: An angle of 60 degrees is constructed at point P. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/61.png Step 3: An angle of 45 degrees is constructed at point Q. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/62.png Step 4: The bisectors of the angles at P and Q are drawn, intersecting at point A. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/63.png Step 5: The perpendicular bisector of AP is drawn, intersecting PQ at B. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/64.png Step 6: The perpendicular bisector of AQ is drawn, intersecting PQ at C. https://learningspot.co/maths/concepts-class-9/ch-11-constructions%20Images/65.png Step 7: AB and AC are joined to form the required triangle ABC. https://learningspot.co/maths/concepts-class-9/ch-12-herons-formula.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_herons_derivation.jpg Triangle ABC with sides a, b, c, altitude h from A to BC, and foot of perpendicular D on BC. BD=x, DC=a-x. https://learningspot.co/maths/concepts-class-9/placeholder_area_equilateral.jpg Equilateral triangle with side length a and height h https://learningspot.co/maths/concepts-class-9/placeholder_area_isosceles.jpg Isosceles triangle with equal sides a and base b. Altitude h shown. https://learningspot.co/maths/concepts-class-9/placeholder_quad_diag.jpg Quadrilateral ABCD divided into two triangles ABC and ADC by diagonal AC https://learningspot.co/maths/concepts-class-9/placeholder_example_12_1.jpg Quadrilateral ABCD with sides AB=9m, BC=12m, CD=5m, AD=8m, and angle C = 90 degrees https://learningspot.co/maths/concepts-class-9/placeholder_example_12_1_diag.jpg Quadrilateral ABCD with diagonal BD drawn, dividing it into right triangle BCD and triangle ABD https://learningspot.co/maths/concepts-class-9/ch-13-surface-areas-and-volumes.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_solid_figures_intro.jpg Examples of solid figures: cube, cuboid, cylinder, cone, sphere https://learningspot.co/maths/concepts-class-9/placeholder_3d_dimensions.jpg Diagram showing a 3D object with length, breadth, and height indicated https://learningspot.co/maths/concepts-class-9/placeholder_cuboid.jpg Diagram of a cuboid showing its rectangular faces, edges, and vertices https://learningspot.co/maths/concepts-class-9/placeholder_cube.jpg Diagram of a cube showing its square faces, edges, and vertices, with side length 'a' https://learningspot.co/maths/concepts-class-9/placeholder_cylinder.jpg Diagram of a cylinder showing its circular bases and curved lateral surface, with radius r and height h https://learningspot.co/maths/concepts-class-9/placeholder_cone.jpg Diagram of a cone showing its circular base, curved surface, and apex, with radius r, height h, and slant height l https://learningspot.co/maths/concepts-class-9/placeholder_sphere.jpg Diagram of a sphere showing its curved surface and radius r https://learningspot.co/maths/concepts-class-9/placeholder_cuboid_faces.jpg Diagram of a cuboid showing pairs of identical faces: top/bottom (lb), front/back (lh), left/right (bh) https://learningspot.co/maths/concepts-class-9/placeholder_cylinder_net.jpg Diagram showing the net of a cylinder, with two circles and a rectangle (unrolled curved surface) https://learningspot.co/maths/concepts-class-9/placeholder_cone_net.jpg Diagram showing the net of a cone, with a circle (base) and a sector of a circle (unrolled curved surface) https://learningspot.co/maths/concepts-class-9/placeholder_hemisphere.jpg Diagram of a hemisphere showing radius r and flat circular base https://learningspot.co/maths/concepts-class-9/placeholder_cuboid_volume.jpg Diagram of a cuboid showing length l, breadth b, and height h https://learningspot.co/maths/concepts-class-9/ch-14-statistics.html 2026-03-28T11:41:35+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-9/placeholder_bar_graph.png Example of a Bar Graph showing categories on X-axis and frequencies on Y-axis https://learningspot.co/maths/concepts-class-9/placeholder_histogram.png Example of a Histogram showing class intervals on X-axis and frequencies on Y-axis with adjacent bars https://learningspot.co/maths/concepts-class-9/placeholder_frequency_polygon.png Example of a Frequency Polygon formed by connecting midpoints of histogram tops https://learningspot.co/maths/concepts-class-9/placeholder_symmetrical_dist.jpg Graph of a symmetrical distribution where Mean, Median, and Mode are at the same central point https://learningspot.co/maths/concepts-class-9/placeholder_positive_skew.jpg Graph of a positively skewed distribution where Mode < Median < Mean https://learningspot.co/maths/concepts-class-9/placeholder_negative_skew.jpg Graph of a negatively skewed distribution where Mean < Median < Mode https://learningspot.co/maths/concepts-class-10/ch-6-triangles.html 2026-03-28T11:41:51+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-10/placeholder_similar_triangles_def.jpg Two triangles ABC and PQR, showing angle correspondences (A=P, B=Q, C=R) and side proportionality (AB/PQ = BC/QR = CA/RP) https://learningspot.co/maths/concepts-class-10/placeholder_aaa_similarity.jpg Diagram showing two triangles ABC and PQR with equal corresponding angles marked https://learningspot.co/maths/concepts-class-10/placeholder_aa_similarity.jpg Diagram showing two triangles ABC and PQR with two pairs of equal corresponding angles marked https://learningspot.co/maths/concepts-class-10/placeholder_sss_similarity.jpg Diagram showing two triangles ABC and PQR with corresponding sides labelled to show proportionality https://learningspot.co/maths/concepts-class-10/placeholder_sas_similarity.jpg Diagram showing two triangles ABC and PQR with one pair of equal angles and proportional including sides https://learningspot.co/maths/concepts-class-10/ch-7-coordinate-geometry.html 2026-03-28T11:41:51+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-10/placeholder_cartesian_plane.jpg Diagram of the Cartesian plane showing x and y axes, origin (0,0), and the four quadrants with signs of coordinates https://learningspot.co/maths/concepts-class-10/placeholder_plot_points_example1.png Cartesian plane with points (3,2), (-2,4), (-4,-3), (5,-1) plotted and labelled with quadrant names https://learningspot.co/maths/concepts-class-10/placeholder_distance_formula_derivation.jpg Diagram showing points P(x1,y1) and Q(x2,y2) on a Cartesian plane, with lines parallel to axes forming a right triangle PQR where R is (x2,y1). PQ is the hypotenuse. https://learningspot.co/maths/concepts-class-10/placeholder_section_formula_diagram.jpg Diagram showing points A(x1,y1), B(x2,y2) and point P(x,y) dividing AB internally in ratio m1:m2 https://learningspot.co/maths/concepts-class-10/placeholder_section_formula_derivation.jpg Diagram for Section Formula derivation showing points A, P, B, and their projections on axes, forming similar triangles https://learningspot.co/maths/concepts-class-10/placeholder_section_formula_similar_triangles.jpg Diagram for Section Formula derivation using similar triangles formed by projecting points onto horizontal lines https://learningspot.co/maths/concepts-class-10/placeholder_area_triangle_derivation.jpg Diagram showing a triangle ABC with vertices projected onto the x-axis forming trapezoids https://learningspot.co/maths/concepts-class-10/ch-8-introduction-to-trigonometry.html 2026-03-28T11:41:51+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-10/placeholder_right_triangle_sides_theta.jpg Right triangle ABC, right-angled at B. Angle C is theta. Sides are labelled hypotenuse, opposite to theta, adjacent to theta. https://learningspot.co/maths/concepts-class-10/placeholder_right_triangle_sides_phi.jpg Right triangle ABC, right-angled at B. Angle A is phi. Sides are labelled hypotenuse, opposite to phi, adjacent to phi. https://learningspot.co/maths/concepts-class-10/placeholder_trigonometric_ratios_diagram.jpg Right triangle ABC, right-angled at B. Angle C is theta. Sides labelled AB (Opposite), BC (Adjacent), AC (Hypotenuse). https://learningspot.co/maths/concepts-class-10/placeholder_trig_ratios_example1.jpg Right triangle ABC, right-angled at B, with AB=5, BC=12. https://learningspot.co/maths/concepts-class-10/placeholder_complementary_angles_diagram.jpg Right triangle ABC, right-angled at B. Angle C is theta, Angle A is 90-theta. Sides labelled P, B, H relative to theta. https://learningspot.co/maths/concepts-class-10/placeholder_45_degree_triangle.jpg Isosceles right triangle ABC at B, AB=BC=a, angles A and C are 45 degrees, hypotenuse AC. https://learningspot.co/maths/concepts-class-10/placeholder_30_60_triangle.jpg Equilateral triangle ABC with altitude AD. Triangle ABD is a right triangle with angles 30, 60, 90 degrees and sides a, sqrt(3)a, 2a. https://learningspot.co/maths/concepts-class-10/placeholder_unit_circle_0_90.jpg Unit circle with points (1,0) for 0 degrees and (0,1) for 90 degrees https://learningspot.co/maths/concepts-class-10/placeholder_trigonometric_identity_diagram.jpg Right triangle ABC at B. Angle C is theta. Sides labelled AB (Opposite), BC (Adjacent), AC (Hypotenuse). https://learningspot.co/maths/concepts-class-10/ch-9-some-applications-of-trigonometry.html 2026-03-28T11:41:51+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-10/placeholder_line_of_sight.jpg Diagram showing an observer looking at an object, with the line of sight drawn from the eye to the object https://learningspot.co/maths/concepts-class-10/placeholder_angle_of_elevation.jpg Diagram showing angle of elevation. Observer's eye at A, looking at object at B above horizontal line AC. Angle BAC is the angle of elevation. https://learningspot.co/maths/concepts-class-10/placeholder_angle_of_depression.jpg Diagram showing angle of depression. Observer's eye at A (at a height), looking at object at B below horizontal line AC. Angle BAC is the angle of depression. https://learningspot.co/maths/concepts-class-10/placeholder_heights_distances_example1.jpg Diagram for example 1: Right triangle ABC, B at foot of tower, A at observer, C at top. AB=15m, angle CAB=60 degrees. BC is height (h). https://learningspot.co/maths/concepts-class-10/placeholder_heights_distances_example2.jpg Diagram for example 2: Rectangle ABEC representing observer and distance. Chimney EF. Angle of elevation from A to F is 45 degrees. AC=BE=28.5m. EC=AB=1.5m. CF=CE+EF is chimney height. https://learningspot.co/maths/concepts-class-10/ch-10-circles.html 2026-03-28T11:41:51+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-10/placeholder_line_circle_positions.jpg Diagram showing three positions of a line relative to a circle: non-intersecting, intersecting at two points (secant), intersecting at one point (tangent) https://learningspot.co/maths/concepts-class-10/placeholder_secant.jpg Diagram of a circle intersected by a secant line at two points A and B https://learningspot.co/maths/concepts-class-10/placeholder_tangent.jpg Diagram of a circle with a tangent line touching at one point P https://learningspot.co/maths/concepts-class-10/placeholder_tangent_as_limit_of_secant.jpg Diagram showing a secant AB rotating as A approaches B, becoming a tangent at B in the limit https://learningspot.co/maths/concepts-class-10/placeholder_tangents_from_inside_point.jpg Diagram showing a point inside a circle and lines passing through it, none of which is a tangent. https://learningspot.co/maths/concepts-class-10/placeholder_tangent_at_point_on_circle.jpg Diagram showing a point on a circle and the unique tangent at that point. https://learningspot.co/maths/concepts-class-10/placeholder_tangents_from_external_point.jpg Diagram showing a point outside a circle and the two tangents drawn from the point to the circle. https://learningspot.co/maths/concepts-class-10/ch-11-constructions.html 2026-03-28T11:41:51+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/1.png Step 1: A line segment AB of length 7.6 cm is drawn. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/2.png Step 2: A ray AX is drawn from point A, making an acute angle with AB. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/3.png Step 3: 13 equally spaced points are marked on the ray AX. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/4.png Step 4: The last point A13 is joined to point B. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/5.png Step 5: A line parallel to A13B is drawn from A5, intersecting AB at point C. This is the final construction. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/6.png Step 1: The original triangle ABC is constructed with sides 4 cm, 5 cm, and 6 cm. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/7.png Step 2: A ray BX is drawn from vertex B. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/8.png Step 3: Three equally spaced points B1, B2, B3 are marked on ray BX. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/9.png Step 4: The point B3 is joined to C. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/10.png Step 5: A line parallel to CB3 is drawn from B2, intersecting BC at C'. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/11.png Step 6: A line parallel to AC is drawn from C', intersecting AB at A'. The required triangle A'BC' is formed. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/12.png Step 1: The original triangle ABC is constructed. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/13.png Step 2: Sides BA and BC are extended, and a ray BX is drawn. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/14.png Step 3: Five equally spaced points are marked on ray BX. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/15.png Step 4: The point B3 is joined to C. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/16.png Step 5: A line parallel to CB3 is drawn from B5, intersecting the extended side BC at C'. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/17.png Step 6: A line parallel to AC is drawn from C', intersecting the extended side BA at A'. The required triangle A'BC' is formed. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/18.png Step 1: A circle with center O, radius 6 cm, and an external point P, 10 cm away, are drawn. The line segment OP is also drawn. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/19.png Step 2: The perpendicular bisector of OP is constructed, and its midpoint M is found. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/20.png Step 3: A second circle is drawn with center M and radius MO, passing through O and P. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/21.png Step 4: The intersection points of the two circles are marked as A and B. These are the points of contact. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/23.png Step 5: The final construction showing the two tangents PA and PB from point P to the circle. https://learningspot.co/maths/concepts-class-10/ch-11-constructions%20Images/22.png Diagram for justification, showing the radius OA and the line segment PA forming a right angle. https://learningspot.co/maths/concepts-class-10/ch-12-areas-related-to-circles.html 2026-03-28T11:41:51+00:00 daily 0.9500 https://learningspot.co/maths/placeholder_circle_radius_d.jpg Diagram of a circle with center O, radius r, and diameter d https://learningspot.co/maths/placeholder_circle_area.jpg Diagram of a circle with radius r, highlighting the enclosed area https://learningspot.co/maths/placeholder_circle_derivation.jpg Diagram showing a circle being cut into sectors and rearranged into a rectangle to derive its area https://learningspot.co/maths/placeholder_annulus.jpg Diagram of two concentric circles with radii R and r, showing the area of the annulus between them https://learningspot.co/maths/placeholder_sector_diagram.jpg Diagram showing a sector of a circle with radius r and central angle theta https://learningspot.co/maths/placeholder_segment_diagram.jpg Diagram showing a minor segment (shaded) and the corresponding major segment of a circle https://learningspot.co/maths/placeholder_area_combinations_example1.jpg Diagram for example 1: An equilateral triangle OAB with a circle centered at O. The shaded region is the union of the triangle and the circle. https://learningspot.co/maths/placeholder_area_combinations_example2.jpg Diagram for example 2: A square with nine identical circles arranged in a 3x3 grid inside it. The shaded region is the area of the square outside the circles. https://learningspot.co/maths/placeholder_area_combinations_example3.jpg Diagram for example 3: A racing track with two straight sections and two semicircular ends. Dimensions are shown for calculating perimeter and area. https://learningspot.co/maths/concepts-class-10/ch-13-surface-areas-and-volumes.html 2026-03-28T11:41:51+00:00 daily 0.9500 https://learningspot.co/maths/placeholder_cone.jpg Diagram of a cone showing radius r, height h, and slant height l https://learningspot.co/maths/placeholder_cone_derivation.jpg Diagram showing a cone being unrolled into a sector of a circle to derive its curved surface area. https://learningspot.co/maths/placeholder_sphere.jpg Diagram of a sphere showing radius r https://learningspot.co/maths/placeholder_sphere_cylinder.jpg Diagram showing a sphere perfectly enclosed by a cylinder. The cylinder's radius is r and its height is 2r. https://learningspot.co/maths/placeholder_hemisphere.jpg Diagram of a hemisphere showing radius r and flat circular base https://learningspot.co/maths/placeholder_combination_surface_area_example1.jpg Diagram of a toy formed by a cone mounted on a hemisphere. Diameter 10cm, cone height 12cm. https://learningspot.co/maths/placeholder_combination_surface_area_example2.jpg Diagram of a capsule, which is a cylinder with hemispherical ends. Total length 14mm, diameter 5mm. https://learningspot.co/maths/placeholder_combination_volume_example1.jpg Diagram of a solid formed by a cone on a hemisphere, with equal radius and cone height equals radius. https://learningspot.co/maths/placeholder_combination_volume_example2.jpg Diagram of a Gulab Jamun, shaped like a cylinder with hemispherical ends. Total length 5cm, diameter 2.8cm. https://learningspot.co/maths/placeholder_solid_conversion.jpg Diagram showing a sphere being melted and reshaped into a cylinder, illustrating volume conservation https://learningspot.co/maths/placeholder_frustum_cone_diagram.jpg Diagram of a frustum of a cone showing large radius R at the base, small radius r at the top, height h, and slant height l. https://learningspot.co/maths/placeholder_frustum_derivation.jpg Diagram showing how a frustum is formed by subtracting a small cone from a large cone, illustrating the similar triangles used for derivation. https://learningspot.co/maths/concepts-class-10/ch-14-statistics.html 2026-03-28T11:41:51+00:00 daily 0.9500 https://learningspot.co/maths/placeholder_mode_derivation.jpg Histogram showing the modal class and adjacent classes. Similar triangles are used to derive the mode formula. https://learningspot.co/maths/placeholder_median_derivation.jpg A 'less than' ogive curve showing the median class and the similar triangles used for deriving the median formula. https://learningspot.co/maths/placeholder_symmetrical_distribution.jpg Graph of a symmetrical distribution where Mean, Median, and Mode coincide https://learningspot.co/maths/placeholder_positive_skew.jpg Graph of a positively skewed distribution where Mode < Median < Mean https://learningspot.co/maths/placeholder_negative_skew.jpg Graph of a negatively skewed distribution where Mean < Median < Mode https://learningspot.co/maths/placeholder_ogives_intersection.png Graph showing both 'less than' and 'more than' ogives intersecting. A perpendicular from the intersection point to the x-axis indicates the median. https://learningspot.co/maths/placeholder_less_than_ogive_median.png A 'less than' ogive for student weights. A line from N/2 on the y-axis intersects the curve, and a perpendicular from there gives the median on the x-axis. https://learningspot.co/maths/concepts-class-10/ch-15-probability.html 2026-03-28T11:41:51+00:00 daily 0.9500 https://learningspot.co/maths/placeholder_deck_of_cards.jpg An image showing the layout of a full 52-card deck, organized by suits and ranks. https://learningspot.co/maths/concepts-class-11/ch-1-sets.html 2026-03-28T11:44:15+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/26.png Complete revision infographic for Basics of Sets covering definition, well-defined collections, distinct elements, and notation symbols. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/27.png Comprehensive summary chart of set representation methods including rules for Roster form and symbols for standard number sets. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/28.png A comprehensive summary table showing all types of sets, their symbols, and one example for each. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/29.png A summary table showing different sets (Empty, Singleton, Finite) and their corresponding cardinal numbers. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/31.png Tree diagram showing the classification of the number system from Complex numbers down to Natural numbers, including surds, transcendentals, and imaginary parts. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/30.png Euler diagram illustrating the nested relationship of number sets, showing how Natural numbers are contained within Whole, Integers, Rationals, Reals, and Complex numbers. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/3.png Number line showing an open interval from a to b with hollow circles at both ends. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/4.png Number line showing a closed interval from a to b with filled circles at both ends. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/1.png Number line showing an interval from a to b with a filled circle at a and a hollow circle at b. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/2.png Number line showing an interval from a to b with a hollow circle at a and a filled circle at b. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/5.png Number line with a hollow circle at 'a' and an arrow extending to the right towards infinity. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/6.png Number line with a filled circle at 'a' and an arrow extending to the right towards infinity. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/7.png Number line with an arrow extending from negative infinity to a hollow circle at 'b'. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/8.png Number line with an arrow extending from negative infinity to a filled circle at 'b'. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/9.png The entire number line highlighted, with arrows pointing to both positive and negative infinity. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/32.png Consolidated revision map for set relations including Power Set formulas and Subset properties. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/10.png Venn diagram showing a single circle representing set A, enclosed within a rectangle representing the universal set U. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/11.png Venn diagram where circle A is drawn completely inside circle B, which is within the rectangle U. This illustrates that A is a subset of B. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/12.png Venn diagram showing two overlapping circles, A and B, within the universal set U. The overlapping area represents the intersection of A and B. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/13.png Venn diagram showing two separate, non-overlapping circles, A and B, within the universal set U, representing that they are disjoint sets. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/33.png Comprehensive Venn Diagram summary sheet with notation and corresponding shaded images. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/14.png Venn diagram showing two overlapping circles A and B within a rectangle U, with both circles shaded, representing A union B https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/15.png Venn diagram showing two overlapping circles A and B within a rectangle U, with only the overlapping region shaded, representing A intersection B https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/16.png Venn diagram showing two overlapping circles A and B within a rectangle U, with only the part of circle A outside B shaded, representing A minus B https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/17.png Venn diagram showing two overlapping circles A and B within a rectangle U, with only the part of circle B outside A shaded, representing B minus A https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/18.png Venn diagram showing a circle A inside a rectangle U, with the region inside the rectangle but outside the circle shaded, representing the complement of A https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/19.png Venn diagram showing two overlapping circles A and B within a rectangle U, with the parts of A outside B and the parts of B outside A shaded, representing A symmetric difference B https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/34.png Concept map of set operations showing Union, Intersection, Difference, and Complement with symbols and logical keywords. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/20.png Venn diagram showing two overlapping circles A and B within a rectangle U, partitioned into regions A only, B only, and A intersection B https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/37.png Venn diagram with three overlapping circles A, B, and C showing the different intersection regions and the Inclusion-Exclusion formula for n(A ∪ B ∪ C). https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/35.png Complete revision guide for Cardinality of Sets with 2-set and 3-set formulas. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/21.png Venn diagram showing two overlapping circles A and B. The entire area covered by both circles is shaded to represent A union B. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/22.png Venn diagram showing the area outside of the two circles A and B, but within the rectangle U, shaded. This represents the complement of A union B. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/23.png Venn diagram with the area outside circle A shaded, representing A'. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/24.png Venn diagram with the area outside circle B shaded, representing B'. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/25.png Venn diagram where the region that is outside both circle A and circle B is shaded. This represents the intersection of A' and B'. https://learningspot.co/maths/concepts-class-11/ch-1-sets-images/36.png A comprehensive summary table of all laws in the algebra of sets for quick revision. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions.html 2026-03-28T11:44:15+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/14.png Comparison table between a set {a, b} where order is not important and an ordered pair (a, b) where order is crucial. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/15.png A coordinate plane showing points (2, 3) and (3, 2) in different locations to demonstrate that order matters. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/13.png Cheat sheet for Ordered Pairs including the definition, equality rule, and a coordinate graph example. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/16.png Arrow diagram showing elements of set A connecting to all elements of set B to form ordered pairs. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/17.png A table/grid representation of Cartesian product where rows represent set A and columns represent set B. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/19.png Tree diagram showing the systematic branching out of elements from three different sets to form triples. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/18.png The Cartesian coordinate system showing x and y axes as the product of two real number lines. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/20.png Comprehensive summary of Cartesian Product including symbolic definition, example pairs, and the cardinality formula. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/21.png A mapping diagram showing two sets A and B with only specific arrows connecting elements to represent a relation. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/23.png Formula breakdown: n(A)=p, n(B)=q. n(AxB)=pq. Total Relations = 2 to the power of pq. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/24.png Comprehensive summary table of all special types of relations and their mathematical conditions. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/22.png A comparison chart showing Reflexive (a,a), Symmetric (a,b) implies (b,a), and Transitive (a,b) and (b,c) implies (a,c) with examples. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/1.png Arrow diagram showing a relation from set A = {1, 2, 3} to set B = {x, y} with arrows from 1 to x, 1 to y, and 2 to x https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/26.png Comparison showing the same relation as a list of pairs, a math rule, and an arrow diagram. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/25.png Concept map showing Roster form, Set-builder form, Arrow diagrams, and Relation Matrices. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/2.png An arrow diagram showing a relation from set A to set B. Set A contains elements {1, 2, 3, 4} and Set B contains {a, b, c, d, e}. Arrows connect 1 to a, 2 to c, and 4 to c. Element 3 in A and elements b, d, e in B are not part of the relation. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/27.png Table comparing Domain, Range, and Codomain definitions with the mathematical subset relationship: Range ⊆ Codomain. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/28.png Flowchart showing the steps: 1. List ordered pairs, 2. Pick first elements for Domain, 3. Pick second elements for Range. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/3.png Arrow diagram for the example relation. Two ovals, both labeled A and containing numbers 1 to 6. Arrows are drawn from 1 to 2, 2 to 3, 3 to 4, 4 to 5, and 5 to 6. Element 6 in the first oval has no outgoing arrow, and element 1 in the second oval has no incoming arrow. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/29.png Complete infographic summarizing definitions, symbolic notation, and a visual example of Domain, Codomain, and Range. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/30.png A diagram of a machine labeled 'f(x)'. Input x enters the machine, and output f(x) comes out. This illustrates the input-process-output nature of functions. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/4.png An arrow diagram showing a valid function. Arrows go from 1 to a, 2 to b, and 3 to c. Every element in A has exactly one outgoing arrow. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/5.png An arrow diagram where element 3 in set A has no outgoing arrow. This is not a function. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/6.png An arrow diagram where element 1 in set A has two outgoing arrows, one to 'a' and one to 'b'. This is not a function. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/7.png An arrow diagram showing a valid many-to-one function. Arrows go from 1 to a, 2 to a, and 3 to b. Each input has only one output. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/32.png A flowchart starting with a relation and asking: 1. Is every x used? 2. Does any x have two y's? Leading to the conclusion: Function or Not a Function. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/8.png A parabola opening upwards. A vertical line is shown intersecting the curve at only one point. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/9.png A circle. A vertical line is shown intersecting the circle at two points. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/33.png Illustration showing sets A and B, explaining the 'exactly one' rule through real-world mapping examples. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/10.png https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/31.png A mind map showing the definition of functions, types of relations, and the concepts of Domain, Codomain, and Range. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/11.png An arrow diagram illustrating preimages. An element 'y1' in B has one preimage 'x1' in A. An element 'y2' in B has two preimages 'x2' and 'x3'. An element 'y3' in B has zero preimages. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/34.png Two graphs side by side: one showing y=x^2 for all real numbers (continuous curve) and one showing y=x^2 only for natural numbers (discrete dots). They look different because the domains differ. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/35.png A Venn diagram showing: 1. Input is Real (Function of Real Variable), 2. Output is Real (Real-Valued Function), and the overlap where both are Real (Real Function). https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/36.png A function machine illustrating a Real Function: a real number x goes in, and a real number f(x) comes out. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/37.png A mapping diagram where the Domain contains names (Alice, Bob) and the Codomain contains numbers (165, 178). This illustrates a real-valued function. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/38.png A diagram showing numbers on the left (Domain) mapping to ordered pairs on the right (Codomain). https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/39.png A standard Cartesian coordinate system with a curve, showing that both axes are real number lines. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/40.png A diagram showing a fraction P(x)/Q(x) with a large 'Not Equal to Zero' sign on the denominator Q(x). https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/41.png A comparison table showing that even roots require the inside to be ≥ 0, while odd roots allow positive, negative, and zero values. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/42.png https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/43.png https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/44.png A summary chart showing the range of basic parent functions: x-squared (y ≥ 0), Absolute value (y ≥ 0), Square root (y ≥ 0). https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/45.png A step-by-step procedural flowchart: 1. Set y = f(x), 2. Solve for x, 3. Find restrictions on y to determine the Range. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/12.png Graph of the function f(x) = sqrt(x-4), showing a curve starting at the point (4,0) and passing through points (5,1), (8,2), and (13,3). https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/46.png A coordinate plane showing a graph and its horizontal projection onto the X-axis (Domain) and vertical projection onto the Y-axis (Range). https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/47.png A mind map branching into the three methods: Reasoning about powers, solving for x in terms of y, and using graphs. https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/51.png https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/48.png Graph of the identity function y=x https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/49.png Graph of a constant function showing a horizontal line parallel to the x-axis https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/50.png Linear graph showing the relationship y=mx+c with highlighted slope and intercept https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/52.png Symmetric U-shaped parabola of y=x^2 showing points like (1,1) and (2,4) https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/53.png S-shaped graph of f(x)=x^3 https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/54.png Mnemonic showing arm positions for odd and even degree polynomials https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/55.png V-shaped graph of the modulus function y=|x| https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/56.png Graph of the signum function showing horizontal lines at 1 and -1 with an isolated point at origin https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/57.png Staircase graph of the greatest integer function showing jumps at every integer https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/58.png Staircase graph of the Ceiling Function with open circles on the left and closed on the right https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/59.png Sawtooth wave graph of the fractional part function showing jumps at integers https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/60.png Graph of y=1/x showing two separate branches in 1st and 3rd quadrants https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/61.png Graph showing a curve rising from left to right passing through (0,1) https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/62.png https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/63.png Graph of y=log_a(x) for 0 < a < 1 https://learningspot.co/maths/concepts-class-11/ch-2-relations-and-functions-images/64.png Mind map of Operations on Real Functions branching into Addition, Subtraction, Multiplication, Scalar Multiplication, and Division with their formulas and domain rules. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions.html 2026-03-28T11:44:15+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/1.png A diagram showing the formation of an angle. Ray OA is the initial side, ray OB is the terminal side, and O is the vertex. An arc with an arrow shows the direction of rotation. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/2.png Two diagrams side-by-side. The left shows a positive angle with an anti-clockwise arrow. The right shows a negative angle with a clockwise arrow. Both start from the same initial side. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/3.png The Cartesian plane with an angle in standard position. The vertex is at the origin, the initial side is on the positive x-axis, and the terminal side is in Quadrant II. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/4.png The Cartesian plane showing the four quadrants labeled I, II, III, and IV, with the corresponding angle ranges for each. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/5.png A circle in the Cartesian plane showing the measurement of angles in degrees. A full circle is 360 degrees, a straight line is 180 degrees, and a right angle is 90 degrees. The four quadrantal angles are marked. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/6.png Diagram defining 1 radian as the angle subtended by an arc equal to the radius https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/7.png A circle showing that a full rotation equals 360 degrees and 2*pi radians, and a half rotation equals 180 degrees and pi radians. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/8.png Diagram showing the conversion path: Degrees to Radians (multiply by pi/180) and Radians to Degrees (multiply by 180/pi). https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/9.png Graphic showing the mnemonic: To get radians, multiply by pi over 180. To get degrees, multiply by 180 over pi. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/10.png A diagram of a circular sector. The circle has its center at O. Two radii, OA and OB, form the sector. The radius is labeled 'r'. The angle AOB at the center is labeled 'θ'. The curved line from A to B is the arc, and its length is labeled 'l'. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/11.png Unit circle with point P(x,y) on its circumference, showing the angle theta from the positive x-axis to the radius OP, and the coordinates (x,y) https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/12.png The four quadrants of the Cartesian plane. Quadrant I (top right), Quadrant II (top left), Quadrant III (bottom left), Quadrant IV (bottom right). https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/13.png A unit circle showing an angle theta in Quadrant I. The point P(x,y) on the circle has a positive x-coordinate and a positive y-coordinate. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/14.png A unit circle showing an angle theta in Quadrant II. The point P(x,y) on the circle has a negative x-coordinate and a positive y-coordinate. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/15.png A unit circle showing an angle theta in Quadrant III. The point P(x,y) on the circle has a negative x-coordinate and a negative y-coordinate. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/16.png A unit circle showing an angle theta in Quadrant IV. The point P(x,y) on the circle has a positive x-coordinate and a negative y-coordinate. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/17.png https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/18.png Unit circle showing theta and theta plus 2pi reaching the same point https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/19.png A unit circle showing an angle theta pointing to P(x,y) and an angle theta + pi pointing to the diametrically opposite point P'(-x,-y), illustrating the pi periodicity of tangent. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/20.png Unit circle showing reflection of point P(x,y) to P'(x,-y) for negative angles https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/21.png Graph of y = sin x https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/22.png Graph of y = cos x https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/23.png Graph of y = tan x showing multiple branches and asymptotes https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/24.png Graph of y = cosec x showing U-shaped branches and asymptotes https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/25.png Graph of y = sec x showing alternating branches and vertical asymptotes https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/26.png Graph of y = cot x showing multiple decreasing branches and asymptotes at multiples of pi https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/27.png Trigonometric Functions Graph Summary https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/28.png Geometric diagram showing triangles for sin(x+y) derivation https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/29.png Unit circle showing points P1, P2, P3 and P4 for derivation https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/30.png Consolidated table of Sine, Cosine, Tangent, and Cotangent sum and difference formulas for quick revision. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/31.png Flowchart showing Sum and Difference formulas branching into Double Angle formulas (by setting y=x) and Product-to-Sum formulas (by adding/subtracting equations). It then shows Product-to-Sum formulas leading to Sum-to-Product formulas through variable substitution of C and D. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/32.png Mind map summarizing Allied Angles: pi/2 and 3pi/2 branching to 'Ratio Changes', and pi and 2pi branching to 'Ratio Remains Same', with sign rules noted for each. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/33.png A sine wave showing its periodic nature. The line y=0.5 intersects the sine wave at infinitely many points, illustrating the infinite solutions to sin(x)=0.5. https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/34.png Unit circle showing two angles, y and (pi - y), that have the same sine value. This illustrates the basis for the general solution of sin(x) = sin(y). https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/35.png Unit circle showing two angles, y and -y, that have the same cosine value. This illustrates the basis for the general solution of cos(x) = cos(y). https://learningspot.co/maths/concepts-class-11/ch-3-trigonometric-functions-images/36.png Unit circle showing two angles, y and (pi + y), that are diametrically opposite and have the same tangent value. This illustrates the basis for the general solution of tan(x) = tan(y). https://learningspot.co/maths/concepts-class-11/ch-4-principle-of-mathematical-induction.html 2026-03-28T11:44:15+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-11/ch-4-principle-of-mathematical-induction-images/1.png A flowchart starting with a sentence. Step 1: Is it precise? Step 2: Can it be definitively True or False? If yes to both, it is a Mathematical Statement. If it is an opinion or a question, it is not. https://learningspot.co/maths/concepts-class-11/ch-4-principle-of-mathematical-induction-images/2.png A diagram showing Deductive Reasoning as an upside-down triangle (General Truths narrowing down to a Specific Conclusion) and Inductive Reasoning as a right-side-up triangle (Specific Observations expanding into a General Conclusion). https://learningspot.co/maths/concepts-class-11/ch-4-principle-of-mathematical-induction-images/3.png A conceptual image showing a bridge labeled 'Conjecture' crossing a gap between 'Observations' and 'Proven Theorem'. A construction worker labeled 'Induction' is building it, but a 'Deductive Proof' sign is needed to make it safe to cross. https://learningspot.co/maths/concepts-class-11/ch-4-principle-of-mathematical-induction-images/4.png A diagram showing a machine labeled P(n). When n=1 is put in, it outputs the statement P(1). When n=k is put in, it outputs P(k). It highlights that P is the name of the property and n is the input variable. https://learningspot.co/maths/concepts-class-11/ch-4-principle-of-mathematical-induction-images/5.png Mnemonic graphic: P.V.S. — Proposition (the name), Variable (the 'n'), Substitution (plugging in numbers to check truth). https://learningspot.co/maths/concepts-class-11/ch-4-principle-of-mathematical-induction-images/6.png An infinitely long row of standing dominoes, with the first one starting to fall and hitting the second one. https://learningspot.co/maths/concepts-class-11/ch-4-principle-of-mathematical-induction-images/7.png A diagram showing P(k) as a solid platform. A bridge is being built from P(k) to P(k+1). The text 'Assume this' is over P(k) and 'Prove this' is over P(k+1). https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations.html 2026-03-28T11:44:15+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/1.png A diagram labeling z = a + bi. 'a' is labeled as the Real Part, 'bi' is the Imaginary Term, and 'b' is specifically highlighted as the Imaginary Part (a real number). https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/2.png A diagram of nested sets, showing the Natural Numbers inside the Integers, which are inside the Rational Numbers, which are inside the Real Numbers, which are finally inside the Complex Numbers. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/3.png A flowchart starting with the equation a+bi = c+di. Branch 1: Set Real parts equal (a=c). Branch 2: Set Imaginary parts equal (b=d). Result: Solve the resulting system of equations. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/4.png A mind map with 'Complex Numbers' at the center. Branches include: Property (i^2 = -1), Standard Form (a+bi), Real Numbers (b=0), and Purely Imaginary Numbers (a=0). https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/5.png A color-coded diagram showing (a + bi) + (c + di). Arrows connect 'a' and 'c' into one box labeled 'Real Sum', and arrows connect 'b' and 'd' into another box labeled 'Imaginary Sum'. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/6.png A mind map with 'Addition Properties' at the center. Five branches: 1. Closure (Result is Complex), 2. Commutative (Order doesn't matter), 3. Associative (Grouping doesn't matter), 4. Identity (Adding 0+0i), 5. Inverse (Adding -a-bi). https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/7.png https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/8.png A FOIL diagram for (a + bi)(c + di). Arrows show First (ac), Outer (adi), Inner (bci), and Last (bdi^2). A highlight shows bdi^2 changing to -bd, which is then grouped with the real part 'ac'. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/9.png A mind map with 'Multiplication Properties' at the center. Branches include: Closure, Commutative, Associative, Unit Identity (1+0i), and the Distributive Law. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/10.png A flowchart for division: 1. Identify denominator conjugate. 2. Multiply top and bottom. 3. Simplify denominator to a^2 + b^2. 4. Split result into real and imaginary parts. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/11.png A diagram showing 1/z. It follows the division path: multiply 1 by (a-bi) and the bottom by (a-bi), resulting in the standard reciprocal formula. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/12.png A summary table. Addition: Real+Real, Imag+Imag. Subtraction: Real-Real, Imag-Imag. Multiplication: FOIL + i^2 rule. Division: Conjugate multiplication. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/13.png A circular clock-like diagram showing the four values: i, -1, -i, and 1. Arrows show the rotation: i to the power of 1 is i, squared is -1, cubed is -i, and to the power of 4 is 1. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/14.png https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/15.png A colorful table mapping remainders to values. Remainder 0 maps to 1; Remainder 1 maps to i; Remainder 2 maps to -1; Remainder 3 maps to -i. It includes the note: Just check the last two digits for division by 4! https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/16.png A concept map for negative powers. Path A: Use 1 / i^n and then rationalize. Path B: Find a multiple of 4 larger than the number to make the exponent positive. Both lead to the same result. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/17.png A comparative table. Column 1: Addition (Identity is 0, Inverse is -z). Column 2: Multiplication (Identity is 1, Inverse is 1/z). It highlights that the Inverse leads back to the Identity. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/18.png An algebraic diagram showing z1 (z2 + z3). Arrows (rainbow arcs) point from z1 to z2 and from z1 to z3, resulting in z1z2 + z1z3. A similar diagram shows the right distributive law (z1+z2)z3. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/19.png A list of formulas on a card: (z1+z2)^2, (z1-z2)^2, (z1+z2)^3, (z1-z2)^3, and the difference of squares. A footer note says: 'Works just like real algebra!' https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/20.png Argand plane showing the horizontal real axis and vertical imaginary axis. Several points are plotted: z1=4+2i, the real number 3 (at 3,0), and the imaginary number -2i (at 0,-2). https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/21.png Argand plane showing the complex number z=a+bi as a position vector originating from (0,0) and ending at the point P(a,b). https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/22.png Argand plane showing complex numbers z1 and z2 as vectors from the origin. Their sum z1+z2 is shown as the resultant vector, which is the diagonal of the parallelogram formed by z1 and z2. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/23.png Argand plane showing the subtraction z1 - z2. The vector for z2 is shown, along with its opposite vector -z2. The sum of z1 and -z2 is then found using the parallelogram law. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/24.png A vector z in the first quadrant is rotated 90 degrees counter-clockwise to a new position, iz, in the second quadrant. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/25.png Argand plane showing a point z=a+bi in the first quadrant and its conjugate z-bar = a-bi in the fourth quadrant, indicating reflection across the real axis https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/26.png A right-angled triangle in the Argand plane. The horizontal side is the real part 'a', the vertical side is the imaginary part 'b', and the hypotenuse is the modulus |z|. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/27.png Argand plane showing point P(a,b), the origin O, the distance r from O to P, and the angle theta between the positive real axis and the line segment OP. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/28.png A circular diagram showing rotation from the positive real axis. Counter-clockwise rotation from 0 to pi is positive. Clockwise rotation from 0 to -pi is negative. A bold line marks the 'cut' at -pi. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/29.png A vector in Quadrant I of the Argand plane. The principal argument theta is equal to the reference angle alpha. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/30.png A vector in Quadrant II. The principal argument theta is calculated as pi minus the reference angle alpha. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/31.png A vector in Quadrant III. The principal argument theta is calculated as the negative of (pi minus the reference angle alpha). https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/32.png A vector in Quadrant IV. The principal argument theta is equal to the negative of the reference angle alpha. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/33.png The real and imaginary axes showing points and their principal arguments: a point on the positive real axis has angle 0, positive imaginary has pi/2, negative real has pi, and negative imaginary has -pi/2. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/34.png A diagram illustrating the polar form of a complex number. It shows a point P(a,b) in the Argand plane, with a right triangle demonstrating that a = r cos(theta) and b = r sin(theta). https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/35.png Argand plane showing the complex number z = a + bi as a point P(a,b). A right-angled triangle is formed with the origin, showing sides of length a and b, and the hypotenuse of length |z|. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/36.png Argand plane showing points for z, z-bar, and -z. All three points lie on a circle centered at the origin, illustrating that they have the same modulus. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/37.png A triangle in the Argand plane with sides representing the vectors z1, z2, and z1+z2. The lengths of the sides are |z1|, |z2|, and |z1+z2|, illustrating the triangle inequality. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/38.png A mind map with '|z| Properties' at the center. Branches include: 1. Product rule (|z1z2|=|z1||z2|), 2. Quotient rule (|z1/z2|=|z1|/|z2|), 3. Conjugate relationship (z*z-bar = |z|^2), and 4. Power rule (|z^n|=|z|^n). https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/39.png Argand plane showing a complex number z = a + bi and its conjugate z-bar = a - bi. The point for z-bar is a reflection of the point for z across the real axis. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/40.png A mind map with 'z-bar Properties' at the center. Branches show: 1. The 'Double-Flip' (conjugate of a conjugate is z). 2. Addition/Subtraction (The bar splits). 3. Multiplication/Division (The bar splits). 4. Powers (The bar moves inside the exponent). https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/41.png A flowchart for finding the square root: 1. Find the modulus |z|. 2. Create the system: x^2 + y^2 = |z| and x^2 - y^2 = a. 3. Solve for x and y. 4. Use the sign of b to pair them. https://learningspot.co/maths/concepts-class-11/ch-5-complex-numbers-and-quadratic-equations-images/42.png https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities.html 2026-03-28T11:44:15+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/1.png A concept map linking Linear Expressions, Inequality Symbols, Replacement Sets, and Solution Sets. https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/2.png A summary table showing that addition, subtraction, and multiplication/division by positive numbers keep the sign same, while multiplication/division by negative numbers reverses it. https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/3.png A detailed flowchart showing the steps: Simplify, Clear Fractions, Isolate Variables, and the final check for negative coefficients. https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/4.png A summary table mapping inequality symbols to their graph types (open/closed circles) and interval notation (parentheses/brackets). https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/5.png Number line with a closed circle at -3 and shading extending infinitely to the left, representing x <= -3 https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/6.png https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/7.png https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/8.png Number line with a closed circle at -11/3 and another closed circle at 5. The line segment between these two points is shaded. https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/9.png A number line showing two separate inequalities and a third line showing only the overlapping region as the final solution. https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/10.png https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/11.png https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/12.png Number line showing an open circle at -2 with shading to the right, and an open circle at 7/3 with shading to the left. The overlapping region is between -2 and 7/3. https://learningspot.co/maths/concepts-class-11/ch-6-linear-inequalities-images/13.png Number line showing a closed circle at 4 with shading to the right, and an open circle at 1 with shading to the left. There is no overlap between the two shaded regions. https://learningspot.co/maths/concepts-class-11/ch-8-binomial-theorem.html 2026-03-28T11:44:15+00:00 daily 0.9500 https://learningspot.co/Mathematics/BinomialTheorem/pascal_triangle_diagram.jpg Diagram showing the construction of Pascal's Triangle https://learningspot.co/Mathematics/BinomialTheorem/pascal_row_sum.jpg Visual representation of row sums in Pascal's Triangle https://learningspot.co/maths/concepts-class-11/ch-10-straight-lines.html 2026-03-28T11:44:15+00:00 daily 0.9500 https://learningspot.co/Mathematics/Images/angle_between_lines.jpg Two intersecting lines showing inclinations and the angle between them https://learningspot.co/maths/concepts-class-11/ch-11-conic-sections.html 2026-03-28T11:44:15+00:00 daily 0.9500 https://learningspot.co/Mathematics/Images/circle_diameter_form.jpg A circle with diameter endpoints A and B and a point P forming a right angle at the circumference https://learningspot.co/Mathematics/Images/parabola_right.jpg Graph of y^2 = 4ax opening to the right https://learningspot.co/Mathematics/Images/parabola_left.jpg Graph of y^2 = -4ax opening to the left https://learningspot.co/Mathematics/Images/parabola_upward.jpg Graph of x^2 = 4ay opening upwards https://learningspot.co/Mathematics/Images/parabola_downward.jpg Graph of x^2 = -4ay opening downwards https://learningspot.co/Mathematics/Conics_Images/circle_right_triangle.jpg Circle passing through (0,0), (8,0), and (0,6) https://learningspot.co/maths/concepts-class-11/ch-15-statistics.html 2026-03-28T11:44:15+00:00 daily 0.9500 https://learningspot.co/Mathematics/Statistics/arjun_plot.jpg Dot plot for Arjun showing scores tightly packed around 70 https://learningspot.co/Mathematics/Statistics/vijay_plot.jpg Dot plot for Vijay showing scores scattered from 40 to 100 https://learningspot.co/maths/concepts-class-12/ch-1-relations-and-functions.html 2026-03-28T11:44:26+00:00 daily 0.9500 https://learningspot.co/Mathematics/Functions/composition_flow.jpg Arrow diagram showing elements from A mapping to B and then to C https://learningspot.co/maths/concepts-class-12/ch-6-application-of-derivatives.html 2026-03-28T11:44:26+00:00 daily 0.9500 https://learningspot.co/Mathematics/Calculus/Tangents_and_Normals/horizontal_tangent.jpg Tangent parallel to X-axis https://learningspot.co/maths/concepts-class-12/ch-7-integrals.html 2026-03-28T11:44:26+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-12/placeholder_antiderivatives.png Family of antiderivatives for f(x)=2x, showing y=x^2+C for different C https://learningspot.co/maths/concepts-class-12/ch-8-application-of-integrals.html 2026-03-28T11:44:26+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-12/placeholder_area_above_x.png Area under a curve above x-axis from x=a to x=b https://learningspot.co/maths/concepts-class-12/placeholder_area_below_x.png Area under a curve below x-axis from x=a to x=b https://learningspot.co/maths/concepts-class-12/placeholder_area_mixed.png Area under a curve with positive and negative parts https://learningspot.co/maths/concepts-class-12/placeholder_area_right_y.png Area to the right of y-axis bounded by x=g(y) from y=c to y=d https://learningspot.co/maths/concepts-class-12/placeholder_area_left_y.png Area to the left of y-axis bounded by x=g(y) from y=c to y=d https://learningspot.co/maths/concepts-class-12/placeholder_area_ex1.png Sketch of region bounded by y=x^2, x-axis, x=0, x=2 https://learningspot.co/maths/concepts-class-12/placeholder_area_ex2_chap8.png Sketch of region bounded by y^2=4x, y-axis, and y=2 https://learningspot.co/maths/concepts-class-12/placeholder_area_between_f_g.png Area between two curves y=f(x) and y=g(x) from x=a to x=b https://learningspot.co/maths/concepts-class-12/placeholder_area_between_right_left.png Area between two curves x=g(y) and x=h(y) from y=c to y=d https://learningspot.co/maths/concepts-class-12/placeholder_area_ex1_chap8_sec2.png Sketch of region between y^2=x and x^2=y https://learningspot.co/maths/concepts-class-12/placeholder_area_ex2_chap8_sec2.png Sketch of region bounded by ellipse x^2/9+y^2/4=1 in first quadrant https://learningspot.co/maths/concepts-class-12/ch-10-vector-algebra.html 2026-03-28T11:44:26+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-12/placeholder_vector_representation.png Vector representation as a directed line segment from A to B https://learningspot.co/maths/concepts-class-12/placeholder_triangle_law.png Triangle Law of Vector Addition showing a+b=c https://learningspot.co/maths/concepts-class-12/placeholder_parallelogram_law.png Parallelogram Law of Vector Addition showing a+b=c https://learningspot.co/maths/concepts-class-12/placeholder_vector_subtraction.png Vector subtraction a-b https://learningspot.co/maths/concepts-class-12/placeholder_vector_components_2d.png Vector components in 2D showing r=xi+yj https://learningspot.co/maths/concepts-class-12/placeholder_vector_magnitude_2d.png Magnitude of a vector in 2D using Pythagorean theorem https://learningspot.co/maths/concepts-class-12/placeholder_vector_components_3d.png Vector components in 3D showing r=xi+yj+zk https://learningspot.co/maths/concepts-class-12/placeholder_section_internal.png Internal Section Formula showing point P dividing AB internally in ratio m:n https://learningspot.co/maths/concepts-class-12/placeholder_section_external.png External Section Formula showing point P dividing AB externally in ratio m:n https://learningspot.co/maths/concepts-class-12/placeholder_area_parallelogram.png Area of parallelogram from cross product https://learningspot.co/maths/concepts-class-12/placeholder_ijk_cross_product_cycle.png Cyclic representation for cross products of i, j, k https://learningspot.co/maths/concepts-class-12/scalar_triple_product_parallelepiped.png Volume of parallelepiped from scalar triple product https://learningspot.co/maths/concepts-class-12/ch-11-three-dimensional-geometry.html 2026-03-28T11:44:26+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-12/placeholder_3d_coords.png 3D coordinate system showing X, Y, Z axes and a point P(x,y,z) https://learningspot.co/maths/concepts-class-12/placeholder_line_point_parallel_vector.png Line through point A parallel to vector b showing vectors OA, OP, and AP https://learningspot.co/maths/concepts-class-12/placeholder_plane_point_normal_vector.png Plane through point A with normal vector N showing vectors OA, OP, and AP https://learningspot.co/maths/concepts-class-12/ch-12-linear-programming.html 2026-03-28T11:44:26+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-12/placeholder_lpp_graph_ex1.png Graph showing constraint lines and feasible region for the LPP example. https://learningspot.co/maths/concepts-class-12/ch-13-probability.html 2026-03-28T11:44:26+00:00 daily 0.9500 https://learningspot.co/maths/concepts-class-12/placeholder_partition_sample_space.png Diagram showing sample space S divided into disjoint events E1, E2, ..., En that cover S.