ICSE Class 9 Mathematics · Exam Practice

Mathematics Practice Paper — Set 1

Mathematics Practice Paper — Set 1. ICSE Class 9 Mathematics, covering rational and irrational numbers, indices, logarithms, expansions and factorisation, simultaneous equations, Pythagoras theorem, trigonometric ratios, distance formula, statistics, compound interest and area, 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 the ICSE Class 9 Mathematics chapters on MuskMeadow: rational and irrational numbers, indices, logarithms, expansions and factorisation, simultaneous equations, Pythagoras theorem, trigonometric ratios, distance formula, statistics, compound interest and area.
  • 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.
  • This is a MuskMeadow practice paper. It is not an official CISCE paper and its mark scheme does not copy the board's exact pattern.
10 MARKS

Section A — Multiple Choice Questions

Choose the correct option. (1 mark each)

1. Which of the following is an irrational number?

A. √2B. 0.75C. −3D. 22/7

2. The value of 2³ × 2⁴ ÷ 2⁵ is

A. 2B. 4C. 8D. 16

3. log₁₀ 1000 =

A. 1B. 2C. 3D. 10

4. (x − 4)² =

A. x² − 16B. x² − 8x + 16C. x² + 8x + 16D. x² − 4x + 16

5. The factors of x² − 16 are

A. (x − 4)(x − 4)B. (x + 8)(x − 2)C. (x + 4)(x − 4)D. (x − 8)(x + 2)

6. The hypotenuse of a right-angled triangle with legs 6 cm and 8 cm is

A. 10 cmB. 14 cmC. 12 cmD. 9 cm

7. sin 30° =

A. √3/2B. 1/2C. 1D. 1/√2

8. The distance between the points (0, 0) and (3, 4) is

A. 7B. 5C. 1D. 12

9. The mean of 4, 6, 8, 10, 12 is

A. 6B. 8C. 10D. 40

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

A. 360°B. 540°C. 720°D. 900°
8 MARKS

Section B — Fill in the Blanks & True / False

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

11. The value of 5⁰ is ______.

12. If 2x + 3y = 12 and x = 3, then y = ______.

13. tan 45° = ______.

14. Every integer is a rational number. (   )

15. log(ab) = log a × log b. (   )

16. The median of 3, 5, 7, 9, 11 is ______.

17. The diagonals of a rectangle are equal. (   )

18. The mid-point of (2, 4) and (6, 8) is ______.

16 MARKS

Section C — Short Answer Questions

Show your working. (2 marks each)

19. Evaluate 16^(3/4).

20. Expand (2x + 3)².

21. Factorise x² + 7x + 12.

22. Solve: 2x − y = 4 and x + y = 5.

23. Find the value of log₂ 32.

24. In a right-angled triangle the hypotenuse is 13 cm and one leg is 5 cm. Find the other leg.

25. Find the distance between the points (1, 2) and (4, 6).

26. Find the median of 12, 7, 9, 15, 10, 8.

16 MARKS

Section D — Problem Solving

Show all steps. (4 marks each)

27. Solve the simultaneous equations 3x + 2y = 16 and 5x − 2y = 16 and verify your answer.

28. A 10 m ladder leans against a wall and makes an angle of 60° with the ground. Find (a) the height it reaches on the wall and (b) the distance of its foot from the wall. (Take √3 = 1.73.)

29. Find the compound interest on ₹8,000 for 2 years at 10% per annum, compounded annually.

30. The sides of a triangle are 13 cm, 14 cm and 15 cm. Using Heron’s formula, find (a) its area and (b) the length of the altitude on the side of 14 cm.

ICSE Class 9 Mathematics · Mathematics Practice Paper — Set 1 · Answer Key

Answers & Worked Solutions

Check your paper, then read the solutions for the questions you missed.

Section A — Multiple Choice Questions (10 marks)
Q1. A. √2

√2 cannot be written as p/q with integers p, q (q ≠ 0), so it is irrational. The others are rational.

Q2. B. 4

2³ × 2⁴ = 2⁷; 2⁷ ÷ 2⁵ = 2² = 4.

Q3. C. 3

1000 = 10³, so log₁₀ 1000 = 3.

Q4. B. x² − 8x + 16

(a − b)² = a² − 2ab + b² gives x² − 8x + 16.

Q5. C. (x + 4)(x − 4)

x² − 16 = x² − 4² = (x + 4)(x − 4), a difference of two squares.

Q6. A. 10 cm

h² = 6² + 8² = 36 + 64 = 100, so h = 10 cm.

Q7. B. 1/2

From the standard table, sin 30° = 1/2.

Q8. B. 5

d = √(3² + 4²) = √25 = 5.

Q9. B. 8

Sum = 40, number of values = 5, mean = 40 ÷ 5 = 8.

Q10. B. 540°

Sum = (n − 2) × 180° = 3 × 180° = 540°.

Section B — Fill in the Blanks & True / False (8 marks)
Q11. 1

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

Q12. 2

6 + 3y = 12 → 3y = 6 → y = 2.

Q13. 1

sin 45° = cos 45°, so tan 45° = 1.

Q14. True

An integer n can be written as n/1, so it is rational.

Q15. False

The correct rule is log(ab) = log a + log b.

Q16. 7

The values are already in order; the middle (3rd) value is 7.

Q17. True

In a rectangle the diagonals are equal in length and bisect each other.

Q18. (4, 6)

((2 + 6)/2, (4 + 8)/2) = (4, 6).

Section C — Short Answer Questions (16 marks)
Q19. 8
  1. 16 = 2⁴, so 16^(3/4) = (2⁴)^(3/4).
  2. Multiply the indices: 2^(4 × 3/4) = 2³ = 8.
Q20. 4x² + 12x + 9
  1. Use (a + b)² = a² + 2ab + b² with a = 2x, b = 3.
  2. (2x)² + 2(2x)(3) + 3² = 4x² + 12x + 9.
Q21. (x + 3)(x + 4)
  1. Find two numbers with product 12 and sum 7: 3 and 4.
  2. x² + 3x + 4x + 12 = x(x + 3) + 4(x + 3) = (x + 3)(x + 4).
Q22. x = 3, y = 2
  1. Add the equations: 3x = 9, so x = 3.
  2. Put x = 3 in x + y = 5: y = 2.
  3. Check: 2(3) − 2 = 4 ✓.
Q23. 5
  1. Write 32 as a power of 2: 32 = 2⁵.
  2. So log₂ 32 = 5.
Q24. 12 cm
  1. Other leg² = 13² − 5² = 169 − 25 = 144.
  2. Other leg = √144 = 12 cm.
Q25. 5 units
  1. d = √[(4 − 1)² + (6 − 2)²] = √(9 + 16).
  2. d = √25 = 5.
Q26. 9.5
  1. Arrange in order: 7, 8, 9, 10, 12, 15 (6 values).
  2. For an even number of values, median = average of the 3rd and 4th = (9 + 10)/2 = 9.5.
Section D — Problem Solving (16 marks)
Q27. x = 4, y = 2
  1. Add the equations to eliminate y: 8x = 32, so x = 4.
  2. Substitute in 3x + 2y = 16: 12 + 2y = 16, so y = 2.
  3. Verify: 5(4) − 2(2) = 20 − 4 = 16 ✓.
Q28. (a) ≈ 8.65 m (b) 5 m
  1. Height = 10 sin 60° = 10 × √3/2 = 5√3.
  2. 5 × 1.73 = 8.65 m (a).
  3. Distance of foot = 10 cos 60° = 10 × 1/2 = 5 m (b).
Q29. ₹1,680
  1. Amount = P(1 + R/100)ⁿ = 8,000 × (1.1)².
  2. (1.1)² = 1.21, so Amount = 8,000 × 1.21 = ₹9,680.
  3. Compound interest = Amount − Principal = 9,680 − 8,000 = ₹1,680.
Q30. (a) 84 cm² (b) 12 cm
  1. s = (13 + 14 + 15)/2 = 21 cm.
  2. Area = √[s(s − a)(s − b)(s − c)] = √(21 × 8 × 7 × 6) = √7056 = 84 cm² (a).
  3. Area = ½ × base × height ⇒ 84 = ½ × 14 × h ⇒ h = 12 cm (b).
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