CBSE Class 8 Mathematics · Exam Practice

Practice Paper — Set 1

CBSE Class 8 Mathematics (Ganita Prakash), covering squares, cubes, exponents, algebra, proportional reasoning, and geometry (area, the Pythagoras theorem), with a full answer key and worked solutions.

🎯 Full Marks: 63 ⏱️ Time: 2½ Hours 📝 Questions: 42
SectionTopicQsMarks
ASquares, Cubes & Exponents1515
BAlgebra & Proportional Reasoning1520
CGeometry — Area & Pythagoras Theorem1228
Total4263
Before you start
  • Attempt the paper first, without looking at the answer key at the bottom of the page.
  • Show your working for Sections B and C — method marks are given even if the final answer is wrong.
15 MARKS

Section A — Squares, Cubes & Exponents

1. Multiple Choice Questions (MCQs) (1 mark each)

1. √169 =

A. 12B. 13C. 14D. 15

2. The cube of 5 is

A. 15B. 25C. 125D. 100

3. 2⁵ =

A. 10B. 16C. 25D. 32

4. Which of the following is a perfect square?

A. 48B. 50C. 64D. 90

5. (−2)³ =

A. −8B. 8C. −6D. 6

6. 10⁻² =

A. −100B. 0.01C. 0.1D. 100

7. The cube root of 27 is

A. 2B. 3C. 9D. 6

8. The smallest perfect square greater than 20 is

A. 21B. 24C. 25D. 16

9. 3⁰ =

A. 0B. 1C. 3D. Undefined

10. √0.04 =

A. 0.02B. 0.2C. 2D. 0.4

2. Fill in the Blanks (1 mark each)

1. 7² = ______.

2. The cube root of 64 is ______.

3. 4³ = ______.

4. √225 = ______.

5. (−3)² = ______.

20 MARKS

Section B — Algebra & Proportional Reasoning

3. True or False (1 mark each)

1. If 3x + 2 = 11, then x = 3. (   )

2. The simple interest formula is (P × R × T) ÷ 100. (   )

3. 25% is the same as 1/4. (   )

4. If a : b = 3 : 5 and b : c = 5 : 8, then a : c = 3 : 8. (   )

5. (−5) × (−5) = −25. (   )

4. Match the Following (1 mark each)

Column A
1.5x − 3 = 12, find x
2.Simple interest on ₹1,000 at 5% for 2 years
3.15% of 200
4.Ratio 4 : 8 in simplest form
5.Profit % when CP = ₹100, SP = ₹120
Column B
a)3
b)₹100
c)30
d)1 : 2
e)20%

5. Very Short Answer Type Questions (2 marks each)

1. Solve for x: 4x + 7 = 23.

2. Find 20% of 350.

3. A number is increased by 25% to get 100. Find the original number.

4. Simplify: 3(x + 4) − 2x.

5. If a : b = 3 : 5 and b = 20, find a.

28 MARKS

Section C — Geometry: Area & Pythagoras Theorem

6. Solve the Following (2 marks each)

1. Find the area of a square with side 12 cm.

2. Find the area of a rectangle 15 cm long and 9 cm wide.

3. A right triangle has legs of 6 cm and 8 cm. Find the hypotenuse.

4. Find the sum of the interior angles of a quadrilateral.

5. Find the area of a triangle with base 10 cm and height 7 cm.

7. Do As Directed (2 marks each)

1. A square has area 81 sq cm. Find its perimeter.

2. A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the other leg.

3. Find the area of a parallelogram with base 12 cm and height 6 cm.

4. What is the measure of each angle of a square?

5. Find the diagonal of a rectangle with length 8 cm and width 6 cm.

8. Think & Solve (Word Problems) (4 marks each)

1. A rectangular garden has length 20 m and width 15 m. Find (a) its area, and (b) if fencing costs ₹25 per metre, the total cost of fencing it.

2. The area of a square field is 625 sq m. Find (a) the side of the field, and (b) the cost of fencing it at ₹40 per metre.

CBSE Class 8 Mathematics · Practice Paper — Set 1 · Answer Key

Answers & Worked Solutions

Mark your own paper, then read the solution for every question you got wrong. For the multiple-choice questions, the note in pink shows the answer most students pick by mistake, and why.

Section A — Squares, Cubes & Exponents (15 marks)
1. Multiple Choice Questions
Q1. B. 13

13 × 13 = 169, so √169 = 13.

Q2. C. 125

5 × 5 × 5 = 125.

Tempting wrong answer: 15 — this comes from multiplying 5 × 3 instead of cubing (5 × 5 × 5).

Q3. D. 32

2⁵ = 2×2×2×2×2 = 32.

Q4. C. 64

64 = 8 × 8, a perfect square. 48, 50, and 90 are not the product of any whole number multiplied by itself.

Q5. A. −8

(−2) × (−2) × (−2) = 4 × (−2) = −8. An odd number of negative factors gives a negative result.

Tempting wrong answer: 8 — forgetting that cubing (an odd power) keeps the negative sign, unlike squaring.

Q6. B. 0.01

A negative exponent means "reciprocal": 10⁻² = 1/10² = 1/100 = 0.01.

Tempting wrong answer: −100 — treating the negative sign in the exponent as if it makes the whole answer negative, instead of meaning "take the reciprocal."

Q7. B. 3

3 × 3 × 3 = 27, so the cube root of 27 is 3.

Q8. C. 25

4² = 16 (less than 20) and 5² = 25 (the next perfect square, greater than 20).

Tempting wrong answer: 21 or 24 — these are close to 20 but not perfect squares at all.

Q9. B. 1

Any non-zero number raised to the power 0 equals 1.

Q10. B. 0.2

0.2 × 0.2 = 0.04, so √0.04 = 0.2.

Tempting wrong answer: 0.02 — a common slip with the decimal point when working with square roots of decimals.

2. Fill in the Blanks
Q1. 49

7 × 7 = 49.

Q2. 4

4 × 4 × 4 = 64.

Q3. 64

4 × 4 × 4 = 64.

Q4. 15

15 × 15 = 225.

Q5. 9

(−3) × (−3) = 9.

Section B — Algebra & Proportional Reasoning (20 marks)
3. True or False
Q1. True

3(3) + 2 = 9 + 2 = 11 ✓.

Q2. True

Simple Interest = (Principal × Rate × Time) ÷ 100.

Q3. True

25% = 25/100 = 1/4.

Q4. True

Since the b-value already matches in both ratios (b = 5 in both), they can be combined directly: a : b : c = 3 : 5 : 8, so a : c = 3 : 8.

Q5. False

(−5) × (−5) = 25, not −25 — a negative times a negative gives a positive.

4. Match the Following
1 → a) 3

5x − 3 = 12 → 5x = 15 → x = 3.

2 → b) ₹100

SI = (1,000 × 5 × 2) ÷ 100 = ₹100.

3 → c) 30

15% of 200 = 0.15 × 200 = 30.

4 → d) 1 : 2

4 : 8 simplifies to 1 : 2 (dividing both by 4).

5 → e) 20%

Profit = 120 − 100 = 20. Profit% = (20 ÷ 100) × 100 = 20%.

5. Very Short Answer Type Questions
Q1. x = 4

4x + 7 = 23 → 4x = 16 → x = 4.

Q2. 70

20% of 350 = 0.20 × 350 = 70.

Q3. 80

original × 1.25 = 100 → original = 100 ÷ 1.25 = 80.

Q4. x + 12

3(x + 4) − 2x = 3x + 12 − 2x = x + 12.

Q5. 12

a : b = 3 : 5, so a = (3 ÷ 5) × 20 = 12.

Section C — Geometry: Area & Pythagoras Theorem (28 marks)
6. Solve the Following
Q1. 144 sq cm

Area of a square = side × side = 12 × 12 = 144 sq cm.

Q2. 135 sq cm

Area = length × width = 15 × 9 = 135 sq cm.

Q3. 10 cm

By the Pythagoras theorem: hypotenuse² = 6² + 8² = 36 + 64 = 100, so hypotenuse = √100 = 10 cm.

Q4. 360°

The interior angles of any quadrilateral always add up to 360°.

Q5. 35 sq cm

Area of a triangle = ½ × base × height = ½ × 10 × 7 = 35 sq cm.

7. Do As Directed
Q1. 36 cm
  1. Side = √81 = 9 cm.
  2. Perimeter = 4 × 9 = 36 cm.
Q2. 12 cm

By the Pythagoras theorem: other leg² = 13² − 5² = 169 − 25 = 144, so other leg = √144 = 12 cm.

Q3. 72 sq cm

Area of a parallelogram = base × height = 12 × 6 = 72 sq cm.

Q4. 90°

Every angle of a square is a right angle, 90°.

Q5. 10 cm

By the Pythagoras theorem: diagonal² = 8² + 6² = 64 + 36 = 100, so diagonal = √100 = 10 cm.

8. Think & Solve (Word Problems)
Q1. (a) 300 sq m (b) ₹1,750
  1. Area = 20 × 15 = 300 sq m.
  2. Perimeter = 2 × (20 + 15) = 70 m.
  3. Cost of fencing = 70 × ₹25 = ₹1,750.
Q2. (a) 25 m (b) ₹4,000
  1. Side = √625 = 25 m.
  2. Perimeter = 4 × 25 = 100 m.
  3. Cost of fencing = 100 × ₹40 = ₹4,000.
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