ICSE Class 8 Mathematics · Exam Practice

Practice Paper — Set 1

ICSE Class 8 Mathematics, covering rational numbers, exponents, squares & cubes, percentage, profit & loss, interest, algebra, and geometry, with a full answer key and worked solutions.

🎯 Full Marks: 50 ⏱️ Time: 1½ Hours 📝 Questions: 30
SectionType of questionsQsMarks
AMultiple Choice Questions1010
BFill in the Blanks & True / False88
CShort Answer Questions816
DProblem Solving416
Total3050
Before you start
  • This paper samples across ICSE Class 8 chapters on MuskMeadow: Rational Numbers, Exponents, Squares & Square Roots, Cubes & Cube Roots, Percent & Percentage, Profit, Loss & Discount, Interest, Direct & Inverse Variations, Sets, Factorisation, Linear Equations & Inequations, Identities, Special Quadrilaterals, Understanding Shapes, Data Handling, Probability, and Surface Area, Volume & Capacity.
  • Attempt the paper first, without looking at the answer key at the bottom of the page.
  • Show your working for Sections C and D — method marks are given even if the final answer is wrong.
10 MARKS

Section A — Multiple Choice Questions

Choose the correct option. (1 mark each)

1. The rational number equivalent to −3/4 with denominator 20 is

A. −15/20B. 15/20C. −12/20D. −20/15

2. The value of 2⁻³ is

A. −8B. 8C. −1/8D. 1/8

3. √225 =

A. 25B. 15C. 12D. 45

4. The cube root of 216 is

A. 4B. 8C. 36D. 6

5. 35% of 240 is

A. 84B. 70C. 75D. 90

6. A table bought for ₹800 is sold for ₹920. The gain per cent is

A. 10%B. 15%C. 20%D. 12%

7. The simple interest on ₹5,000 for 2 years at 8% per annum is

A. ₹400B. ₹1,000C. ₹800D. ₹880

8. If y varies directly as x, and y = 15 when x = 5, then y when x = 8 is

A. 18B. 20C. 27D. 24

9. (x + 5)² =

A. x² + 10x + 25B. x² + 5x + 25C. x² + 25D. x² + 10x + 10

10. The sum of the interior angles of a hexagon is

A. 540°B. 720°C. 900°D. 360°
8 MARKS

Section B — Fill in the Blanks & True / False

Fill in each blank, or write True / False. (1 mark each)

11. The additive inverse of 5/8 is ______.

12. If 3x − 7 = 11, then x = ______.

13. A rhombus is a special type of parallelogram. (   )

14. The probability of an impossible event is 1. (   )

15. The two factors of x² − 9 are ______ and ______.

16. If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = ______.

17. In a cuboid, all six faces are rectangles. (   )

18. The mean of 4, 7, 9, 12 and 13 is ______.

16 MARKS

Section C — Short Answer Questions

Show your working. (2 marks each)

19. Simplify: (2x + 3y) − (x − 5y).

20. Solve for x: 2x + 5 = 3x − 4.

21. Factorise: 5x² − 20.

22. Find the cube root of 512 by prime factorisation.

23. Solve the inequation 3x − 4 < 11, where x is a natural number, and list the solution set.

24. Find the compound interest on ₹4,000 for 2 years at 5% per annum, compounded annually.

25. In a survey of 50 students, 30 like tea and 20 like coffee, and 8 like both. How many students like neither?

26. The angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6. Find all four angles.

16 MARKS

Section D — Problem Solving

Write the complete solution. (4 marks each)

27. A shopkeeper buys a table for ₹2,400 and sells it at a loss of 10%.

  1. Find the loss amount.
  2. Find the selling price.

28. Rahul invests ₹15,000 in a scheme offering simple interest at 6% per annum.

  1. Find the interest after 3 years.
  2. Find the total amount he receives.

29. Factorise completely: 2x² + 7x + 3.

30. The volume of a cuboid is 480 cm³. Its length is 10 cm and its breadth is 8 cm.

  1. Find its height. [2]
  2. Find its total surface area. [2]

ICSE 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 — Multiple Choice Questions (10 marks)
Q1. A. −15/20

To keep the value the same, multiply numerator and denominator by the same number: −3/4 = (−3 × 5)/(4 × 5) = −15/20.

Tempting wrong answer: 15/20 — this drops the negative sign. −3/4 is negative, so its equivalent fraction must be negative too.

Q2. D. 1/8

A negative exponent means "reciprocal": 2⁻³ = 1/2³ = 1/8.

Tempting wrong answer: −8 — students treat the negative sign in the exponent as if it makes the whole answer negative, but it only means "take the reciprocal."

Q3. B. 15

15 × 15 = 225, so √225 = 15.

Tempting wrong answer: 25 — a common mix-up confusing 225 with a "near" perfect square.

Q4. D. 6

6 × 6 × 6 = 216, so the cube root of 216 is 6.

Tempting wrong answer: 8 — that is the cube root of 512, a different number; students sometimes mix up which cube they've memorised.

Q5. A. 84

35% of 240 = 35/100 × 240 = 0.35 × 240 = 84.

Tempting wrong answer: 90 — comes from rounding 35% or miscounting a zero while multiplying.

Q6. B. 15%

Gain = SP − CP = 920 − 800 = 120. Gain% = (Gain/CP) × 100 = (120/800) × 100 = 15%.

Tempting wrong answer: 12% — comes from dividing the gain by the selling price instead of the cost price; gain % is always calculated on the cost price.

Q7. C. ₹800

SI = (P × R × T)/100 = (5,000 × 8 × 2)/100 = 80,000/100 = ₹800.

Tempting wrong answer: ₹880 — a simple multiplication slip, not derived from any sensible alternate method.

Q8. D. 24

Direct variation means y = kx. From y = 15 when x = 5: k = 15/5 = 3. When x = 8: y = 3 × 8 = 24.

Tempting wrong answer: 18 — comes from adding the difference in x (3) to y instead of multiplying by the constant of variation.

Q9. A. x² + 10x + 25

(x + 5)² = x² + 2(x)(5) + 5² = x² + 10x + 25, using the identity (a + b)² = a² + 2ab + b².

Tempting wrong answer: x² + 25 — this forgets the middle "cross term" 2ab entirely, a very common identity mistake.

Q10. B. 720°

Sum of interior angles of a polygon = (n − 2) × 180°. For a hexagon, n = 6, so (6 − 2) × 180° = 4 × 180° = 720°.

Tempting wrong answer: 540° — that is the correct total for a pentagon (n = 5), not a hexagon.

Section B — Fill in the Blanks & True / False (8 marks)
Q11. −5/8

The additive inverse is the number that adds to give 0: 5/8 + (−5/8) = 0.

Q12. 6

3x − 7 = 11 → 3x = 18 → x = 6.

Q13. True

A rhombus has all the properties of a parallelogram (opposite sides parallel and equal), plus all four sides equal.

Q14. False

The probability of an impossible event is 0, not 1. A probability of 1 means the event is certain.

Q15. (x − 3) and (x + 3)

x² − 9 is a difference of squares: x² − 3² = (x − 3)(x + 3).

Q16. {2, 3}

A ∩ B (intersection) contains the elements common to both sets: 2 and 3 appear in both A and B.

Q17. True

Every face of a cuboid is a rectangle (a cube is a special cuboid where every face is a square, which is also a rectangle).

Q18. 9

Sum = 4 + 7 + 9 + 12 + 13 = 45. Mean = 45 ÷ 5 = 9.

Section C — Short Answer Questions (16 marks)
Q19. x + 8y
  1. Remove the brackets, changing the sign of every term in the second bracket: 2x + 3y − x + 5y.
  2. Collect like terms: (2x − x) + (3y + 5y) = x + 8y.
Q20. x = 9
  1. Bring the x-terms to one side: 2x − 3x = −4 − 5.
  2. −x = −9, so x = 9.
Q21. 5(x − 2)(x + 2)
  1. Take out the common factor 5: 5x² − 20 = 5(x² − 4).
  2. x² − 4 is a difference of squares: x² − 2² = (x − 2)(x + 2).
  3. So 5x² − 20 = 5(x − 2)(x + 2).
Q22. 8
  1. 512 = 2⁹ (2 multiplied by itself 9 times).
  2. Group the prime factors in threes: (2×2×2) × (2×2×2) × (2×2×2).
  3. Take one factor from each group: cube root of 512 = 2 × 2 × 2 = 8.
Q23. x < 5, so the solution set is {1, 2, 3, 4}
  1. 3x − 4 < 11 → 3x < 15 → x < 5.
  2. Since x must be a natural number less than 5, the solution set is {1, 2, 3, 4}.
Q24. ₹410
  1. Amount after 2 years = P(1 + R/100)ⁿ = 4,000 × (1.05)² = 4,000 × 1.1025 = ₹4,410.
  2. Compound interest = Amount − Principal = 4,410 − 4,000 = ₹410.
Q25. 8 students
  1. Students who like at least one drink = (Tea) + (Coffee) − (Both) = 30 + 20 − 8 = 42.
  2. Students who like neither = Total − 42 = 50 − 42 = 8.
Q26. 48°, 72°, 96°, 144°
  1. The angle sum of a quadrilateral is 360°, and the ratio has 2 + 3 + 4 + 6 = 15 parts.
  2. Value of 1 part = 360 ÷ 15 = 24°.
  3. Angles = 2×24, 3×24, 4×24, 6×24 = 48°, 72°, 96°, 144°.
  4. Check: 48+72+96+144 = 360° ✓.
Section D — Problem Solving (16 marks)
Q27. (a) ₹240 loss (b) ₹2,160
  1. Loss = 10% of CP = 10/100 × 2,400 = ₹240.
  2. SP = CP − Loss = 2,400 − 240 = ₹2,160.
Q28. (a) ₹2,700 (b) ₹17,700
  1. SI = (P × R × T)/100 = (15,000 × 6 × 3)/100 = ₹2,700.
  2. Total amount = Principal + Interest = 15,000 + 2,700 = ₹17,700.
Q29. (2x + 1)(x + 3)
  1. Split the middle term: 2x² + 7x + 3 = 2x² + 6x + x + 3 (since 6×1=6 and 6+1=7, matching 2×3=6).
  2. Group and factor: 2x(x + 3) + 1(x + 3).
  3. Take out the common bracket: (2x + 1)(x + 3).
  4. Check: (2x+1)(x+3) = 2x²+6x+x+3 = 2x²+7x+3 ✓.
Q30. (a) 6 cm (b) 376 cm²
  1. Volume = l × b × h → 480 = 10 × 8 × h = 80h → h = 6 cm.
  2. Total surface area = 2(lb + bh + hl) = 2(10×8 + 8×6 + 6×10) = 2(80+48+60) = 2×188 = 376 cm².
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