Class 8 Maths Worksheets (with Answers) - Free PDF Download

Boost your exam preparation with our free Class 8 Maths Worksheets. This page provides a complete set of chapter-wise practice sheets, including answers, designed by expert teachers. All Worksheets are available for free PDF download and are fully aligned with the latest CBSE syllabus for 2025-26. Start practicing topics like Linear Equations, Squares, and Mensuration today.

Our collection of maths worksheets for Class 8 PDF includes practice sheets for all 16 chapters — from Rational Numbers to Introduction to Graphs. Each worksheet includes important questions, word problems, and exam-based exercises to make learning complete.

Class 8 Maths Worksheets – Chapter-wise 

NCERT Solutions for Class 8 Maths Worksheets

Along with practice material, we provide NCERT solutions for class 8 maths worksheets so that students can check step-by-step answers. This helps in quick revision, self-assessment, and error correction.

Features of Our Class 8 Maths Worksheets

• Free PDF Download: Easy to print and use for self-study.
• Topic-Wise Practice: Each worksheet targets one concept at a time.
• Exam Preparation: Includes HOTS, word problems, and application-based sums.
• Teacher-Friendly: Useful for assignments, class tests, and homework.

Why Use Our Class 8 Maths Worksheets?

• NCERT-Based: Worksheets follow the latest CBSE Class 8 Maths syllabus.
• Chapter-Wise PDFs: Get practice material for all 16 chapters in one place.
• Answer Keys Provided: Includes NCERT solutions for Class 8 Maths worksheets for step-by-step guidance.
• Printable PDFs: Free to download and use offline.
• Exam-Ready Practice: Questions are based on the CBSE exam pattern, including HOTS and application-based problems.

Download Class 8 Maths Worksheets PDF

Get chapter-wise maths worksheets for Class 8 PDF free of cost. Whether you need practice for Rational Numbers, Linear Equations, Data Handling, Mensuration, or any other topic, you’ll find well-structured worksheets with answers here.

Class 8 Maths – Important Questions with Step-by-Step Solutions

This page lists two exam-style questions for each of the 16 NCERT Class 8 Maths chapters with clear, step-by-step solutions. You can copy this HTML directly into your CMS. No CSS is used.

1) Rational Numbers

Q1. Evaluate: -5/6 + 7/9 - 1/3

1. Find LCM of denominators 6, 9, 3: LCM = 18.
2. Convert each fraction:
   • -5/6 = -15/18
   • 7/9 = 14/18
   • -1/3 = -6/18
3. Add numerators: (-15) + 14 + (-6) = -7.
4. Result = -7/18.

Answer: -7/18

Q2. Show closure under multiplication by finding (-2/5) × (15/8)

1. Multiply numerators and denominators: (-2 × 15) / (5 × 8) = -30/40.
2. Simplify: -30/40 = -3/4.
3. The product is rational, so closure holds.

Answer: -3/4

2) Linear Equations in One Variable

Q1. Solve: 3(x - 2) + 4 = 2(2x + 1)

1. Expand: 3x - 6 + 4 = 4x + 2 → 3x - 2 = 4x + 2.
2. Rearrange: -2 - 2 = x → x = -4.

Answer: x = -4

Q2. A number is 7 more than half of another. Their sum is 31. Find the numbers.

1. Let numbers be x and y with x = y/2 + 7 and x + y = 31.
2. Substitute: (y/2 + 7) + y = 31 → (3y/2) = 24 → y = 16.
3. Then x = 16/2 + 7 = 8 + 7 = 15.

Answer: 15 and 16

3) Understanding Quadrilaterals

Q1. For a 12-gon, find (i) sum of interior angles (ii) each interior angle if regular.

1. Sum = (n - 2) × 180° = (12 - 2) × 180° = 1800°.
2. Each (regular) = 1800° / 12 = 150°.

Answer: 1800° and 150°

Q2. In parallelogram ABCD, if ∠A = 70°, find ∠B, ∠C, ∠D.

1. Adjacent angles are supplementary, opposite angles are equal.
2. ∠B = 180° - 70° = 110°; ∠C = ∠A = 70°; ∠D = ∠B = 110°.

Answer: ∠B = 110°, ∠C = 70°, ∠D = 110°

4) Practical Geometry

Q1. Construct quadrilateral ABCD given AB = 5 cm, BC = 7 cm, CD = 6 cm, DA = 8 cm, AC = 9 cm. Describe steps.

1. Draw AC = 9 cm.
2. With center A radius 5 cm and center C radius 7 cm, intersect arcs at B; join AB and BC.
3. With center A radius 8 cm and center C radius 6 cm, intersect arcs at D; join AD and CD.
4. ABCD is formed; verify side lengths.

Answer: Construction completed as above.

Q2. Construct quadrilateral PQRS with PQ = 6 cm, QR = 5 cm, RS = 7 cm, ∠Q = 110°, ∠R = 90°.

1. Draw QR = 5 cm.
2. At Q, construct 110° and mark P so that PQ = 6 cm.
3. At R, construct 90° and mark S so that RS = 7 cm.
4. Join PS to obtain PQRS.

Answer: Construction completed as above.

5) Data Handling

Q1. For data 12, 15, 18, 12, 20, 18, 12 find mean, median, and mode.

1. Sum = 12 + 15 + 18 + 12 + 20 + 18 + 12 = 107; n = 7 → Mean = 107 / 7 ≈ 15.29.
2. Ordered data: 12, 12, 12, 15, 18, 18, 20 → Median = 15.
3. Mode = most frequent = 12.

Answer: Mean ≈ 15.29, Median = 15, Mode = 12

Q2. A bag has 5 red, 3 blue, 2 green balls. Find P(red) and P(not red).

1. Total = 5 + 3 + 2 = 10.
2. P(red) = 5/10 = 1/2.
3. P(not red) = 5/10 = 1/2.

Answer: P(red) = 1/2, P(not red) = 1/2

6) Squares and Square Roots

Q1. Find the least number to multiply 396 to make it a perfect square. Also find the square root of the product.

1. Prime factors: 396 = 2^2 × 3^2 × 11.
2. Unpaired factor is 11; multiply by 11: 396 × 11 = 4356.
3. 4356 = 66^2 → square root is 66.

Answer: Multiply by 11; square root = 66

Q2. Find √1296 by prime factorization.

1. 1296 = 2^4 × 3^4 = (2^2 × 3^2)^2 = 36^2.
2. Therefore √1296 = 36.

Answer: 36

7) Cubes and Cube Roots

Q1. Smallest number to multiply 392 to make a perfect cube; also find the cube root.

1. 392 = 2^3 × 7^2.
2. Make powers multiples of 3 → multiply by 7: 392 × 7 = 2744.
3. 2744 = 14^3 → cube root is 14.

Answer: Multiply by 7; cube root = 14

Q2. Smallest number to divide 686 to make a perfect cube; also find the cube root.

1. 686 = 2 × 7^3.
2. Divide by 2: 686 / 2 = 343 = 7^3.
3. Cube root is 7.

Answer: Divide by 2; cube root = 7

8) Comparing Quantities

Q1. An article with MRP Rs. 800 has successive discounts of 20% and 10%. Find the selling price and overall discount.

1. After 20%: 800 × 0.8 = Rs. 640.
2. After 10%: 640 × 0.9 = Rs. 576.
3. Overall discount = 800 - 576 = Rs. 224 = 28%.

Answer: SP = Rs. 576; overall discount = 28%

Q2. Compare SI and CI on Rs. 5000 at 10% p.a. for 2 years.

1. Simple Interest = PRT/100 = 5000 × 10 × 2 / 100 = Rs. 1000.
2. Compound Interest = 5000[(1.10)^2 - 1] = 5000(1.21 - 1) = Rs. 1050.
3. Difference = Rs. 50.

Answer: SI = Rs. 1000; CI = Rs. 1050

9) Algebraic Expressions and Identities

Q1. Find 999^2 using (a - b)^2 identity.

1. 999 = 1000 - 1.
2. (1000 - 1)^2 = 1000^2 - 2(1000)(1) + 1 = 1,000,000 - 2,000 + 1.
3. Result = 998,001.

Answer: 998001

Q2. Factorise: 25x^2 - 30xy + 9y^2

1. Recognize as a perfect square: (5x - 3y)^2.

Answer: (5x - 3y)^2

10) Visualising Solid Shapes

Q1. Verify Euler’s formula V - E + F = 2 for a triangular prism.

1. Vertices V = 6, Edges E = 9, Faces F = 5.
2. Compute: 6 - 9 + 5 = 2.

Answer: Verified (2)

Q2. For a square pyramid, list V, E, F and verify Euler’s relation.

1. V = 5, E = 8, F = 5.
2. Compute: 5 - 8 + 5 = 2.

Answer: Verified (2)

11) Mensuration

Q1. Find the curved surface area of a cylinder with radius 7 cm and height 10 cm. Use pi = 22/7.

1. CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm^2.

Answer: 440 cm^2

Q2. A square garden of side 20 m has a surrounding path of width 1 m. Find the area of the path.

1. Outer side = 20 + 1 + 1 = 22 m.
2. Area of path = 22^2 - 20^2 = 484 - 400 = 84 m^2.

Answer: 84 m^2

12) Exponents and Powers

Q1. Simplify: ((2^-3 × 5^2)^2) / 10^-1

1. (2^-3 × 5^2)^2 = 2^-6 × 5^4.
2. Divide by 10^-1 is multiply by 10^1 = 2^1 × 5^1.
3. Overall = 2^-6 × 5^4 × 2^1 × 5^1 = 2^-5 × 5^5 = (5/2)^5 = 3125/32.

Answer: 3125/32

Q2. Write 0.00056 in standard (scientific) form.

1. 0.00056 = 5.6 × 10^-4.

Answer: 5.6 × 10^-4

13) Direct and Inverse Proportions

Q1. 8 workers finish a job in 15 days. How many workers are needed to finish it in 12 days?

1. Workers × Days = Constant → 8 × 15 = x × 12.
2. x = (8 × 15) / 12 = 10.

Answer: 10 workers

Q2. A car covers 150 km in 3 hours at uniform speed. Find time to cover 220 km.

1. Speed = 150 / 3 = 50 km/h.
2. Time = 220 / 50 = 4.4 h = 4 hours 24 minutes.

Answer: 4 hours 24 minutes

14) Factorisation

Q1. Factorise: 6x^2 - x - 15

1. Product = 6 × (-15) = -90. Split -x as +9x - 10x.
2. 6x^2 + 9x - 10x - 15 = 3x(2x + 3) - 5(2x + 3).
3. Factor by grouping: (2x + 3)(3x - 5).

Answer: (2x + 3)(3x - 5)

Q2. Factorise: x^3 - 8

1. Difference of cubes: x^3 - 2^3 = (x - 2)(x^2 + 2x + 4).

Answer: (x - 2)(x^2 + 2x + 4)

15) Introduction to Graphs

Q1. For y = 2x + 1, make a table for x = -1, 0, 1, 2 and find intercepts.

1. Points:
   • x = -1 → y = -1 → (-1, -1)
   • x = 0 → y = 1 → (0, 1)
   • x = 1 → y = 3 → (1, 3)
   • x = 2 → y = 5 → (2, 5)
2. y-intercept at (0, 1); x-intercept from 2x + 1 = 0 → x = -1/2 → (-1/2, 0).

Answer: Points as listed; intercepts: (0, 1) and (-1/2, 0)

Q2. A distance–time graph passes through (1, 60) and (3, 180). Find the speed.

1. Slope = (180 - 60) / (3 - 1) = 120 / 2 = 60 km/h.

Answer: 60 km/h

16) Playing with Numbers

Q1. For a 3-digit number 3ab (hundreds digit 3), give the condition for divisibility by 9.

1. A number is divisible by 9 if sum of digits is a multiple of 9.
2. Sum = 3 + a + b must be a multiple of 9.

Answer: 3 + a + b is a multiple of 9

Q2. A two-digit number has digit sum 11. The difference between the number and the reversed-number is 27. Find the number.

1. Let tens = x, ones = y. Then x + y = 11.
2. (10x + y) − (10y + x) = 27 → 9(x − y) = 27 → x − y = 3.
3. Solve: add equations → 2x = 14 → x = 7; then y = 4.

Answer: 74