ICSE Class 10 Mathematics · Exam Practice

Mathematics Practice Paper — Set 1

Mathematics Practice Paper — Set 1. ICSE Class 10 Mathematics, covering quadratic equations, arithmetic and geometric progressions, matrices, similarity, trigonometric identities, heights and distances, coordinate geometry, probability, mensuration and shares, 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 10 Mathematics chapters on MuskMeadow: quadratic equations, arithmetic and geometric progressions, matrices, similarity, trigonometric identities, heights and distances, coordinate geometry, probability, mensuration and shares.
  • 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. The roots of x² − 5x + 6 = 0 are

A. 2 and 3B. −2 and −3C. 1 and 6D. −1 and 6

2. The 10th term of the AP 3, 7, 11, … is

A. 39B. 43C. 40D. 35

3. The sum of the first 10 terms of an AP with a = 2 and d = 3 is

A. 155B. 145C. 300D. 31

4. The common ratio of the GP 2, 6, 18, … is

A. 2B. 3C. 4D. 6

5. sin²θ + cos²θ =

A. 0B. 1C. 2D. sin 2θ

6. The determinant of the matrix [[1, 2], [3, 4]] is

A. −2B. 2C. 10D. −10

7. Two similar triangles have corresponding sides in the ratio 2 : 3. The ratio of their areas is

A. 2 : 3B. 4 : 9C. 8 : 27D. 3 : 2

8. The slope of the line through (1, 2) and (3, 6) is

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

9. A tower casts a shadow equal to its height. The angle of elevation of the Sun is

A. 30°B. 45°C. 60°D. 90°

10. The probability of getting a prime number on a single throw of a fair die is

A. 1/6B. 1/3C. 1/2D. 2/3
8 MARKS

Section B — Fill in the Blanks & True / False

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

11. The discriminant of ax² + bx + c = 0 is ______.

12. Every quadratic equation has two distinct real roots. (   )

13. The 5th term of the GP 3, 6, 12, … is ______.

14. A tangent to a circle is perpendicular to the radius at the point of contact. (   )

15. The mid-point of (2, 4) and (8, 10) is ______.

16. The volume of a cone with r = 3 cm and h = 4 cm is ______ cm³.

17. Dividend on a share is calculated on its face (nominal) value. (   )

18. The slope of the x-axis is ______.

16 MARKS

Section C — Short Answer Questions

Show your working. (2 marks each)

19. Solve x² − 7x + 12 = 0.

20. Find the 15th term of the AP 5, 8, 11, …

21. Find A + B if A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 5]].

22. Simplify (1 − cos²θ) cosec θ.

23. Find the equation of the line with slope 2 and y-intercept 3.

24. Find the cost of 50 shares of face value ₹100 bought at a premium of ₹20 each.

25. Find the surface area of a sphere of radius 7 cm. (π = 22/7)

26. A bag has 3 red and 5 blue balls. One ball is drawn at random. Find the probability that it is red.

16 MARKS

Section D — Problem Solving

Show all steps. (4 marks each)

27. The product of two consecutive positive integers is 132. Form a quadratic equation and find the integers.

28. From a point 60 m from the foot of a tower, the angle of elevation of its top is 30°. Find (a) the height of the tower, and (b) the distance at which the angle of elevation becomes 60°. (Take √3 = 1.73.)

29. Find the sum of the first 25 terms of the AP 4, 9, 14, … and verify using the last term.

30. The areas of two similar triangles are 36 cm² and 100 cm². If a side of the smaller triangle is 6 cm, find the corresponding side of the larger triangle.

ICSE Class 10 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 and 3

x² − 5x + 6 = (x − 2)(x − 3) = 0, so x = 2 or x = 3.

Q2. A. 39

aₙ = a + (n − 1)d = 3 + 9 × 4 = 39.

Q3. A. 155

Sₙ = n/2 [2a + (n − 1)d] = 5 × (4 + 27) = 155.

Q4. B. 3

r = 6 ÷ 2 = 3.

Q5. B. 1

This is a basic trigonometric identity.

Q6. A. −2

1 × 4 − 2 × 3 = 4 − 6 = −2.

Q7. B. 4 : 9

The ratio of areas equals the square of the ratio of sides: 4 : 9.

Q8. B. 2

m = (6 − 2)/(3 − 1) = 4/2 = 2.

Q9. B. 45°

tan θ = height/shadow = 1, so θ = 45°.

Q10. C. 1/2

Primes on a die are 2, 3, 5: three outcomes out of six, so 3/6 = 1/2.

Section B — Fill in the Blanks & True / False (8 marks)
Q11. b² − 4ac

The nature of the roots depends on D = b² − 4ac.

Q12. False

If the discriminant is zero the roots are equal, and if it is negative there are no real roots.

Q13. 48

aₙ = arⁿ⁻¹ = 3 × 2⁴ = 48.

Q14. True

This is a standard circle theorem.

Q15. (5, 7)

((2 + 8)/2, (4 + 10)/2) = (5, 7).

Q16. 12π

V = ⅓πr²h = ⅓ × π × 9 × 4 = 12π.

Q17. True

Dividend = rate % × nominal value × number of shares.

Q18. 0

The x-axis is horizontal, so its slope is 0.

Section C — Short Answer Questions (16 marks)
Q19. x = 3 or x = 4
  1. Factorise: x² − 3x − 4x + 12 = x(x − 3) − 4(x − 3) = (x − 3)(x − 4).
  2. So x = 3 or x = 4.
Q20. 47
  1. a = 5, d = 3, n = 15.
  2. a₁₅ = 5 + 14 × 3 = 47.
Q21. [[3, 2], [4, 9]]
  1. Add corresponding elements.
  2. Row 1: 1 + 2 = 3, 2 + 0 = 2. Row 2: 3 + 1 = 4, 4 + 5 = 9.
Q22. sin θ
  1. 1 − cos²θ = sin²θ.
  2. sin²θ × (1/sin θ) = sin θ.
Q23. y = 2x + 3
  1. Use y = mx + c with m = 2 and c = 3.
  2. So y = 2x + 3.
Q24. ₹6,000
  1. Market value of 1 share = 100 + 20 = ₹120.
  2. Cost of 50 shares = 50 × 120 = ₹6,000.
Q25. 616 cm²
  1. Surface area = 4πr².
  2. 4 × 22/7 × 49 = 616 cm².
Q26. 3/8
  1. Total outcomes = 3 + 5 = 8.
  2. Favourable outcomes = 3, so P(red) = 3/8.
Section D — Problem Solving (16 marks)
Q27. 11 and 12
  1. Let the integers be x and x + 1: x(x + 1) = 132, so x² + x − 132 = 0.
  2. Factorise: (x + 12)(x − 11) = 0, so x = 11 (x = −12 is rejected as the integers are positive).
  3. The integers are 11 and 12. Check: 11 × 12 = 132 ✓.
Q28. (a) ≈ 34.6 m (b) 20 m
  1. (a) tan 30° = h/60, so h = 60/√3 = 20√3 ≈ 20 × 1.73 = 34.6 m.
  2. (b) tan 60° = h/d, so d = 20√3/√3 = 20 m.
Q29. 1600
  1. a = 4, d = 5, n = 25.
  2. S₂₅ = 25/2 × [2 × 4 + 24 × 5] = 25/2 × 128 = 1600.
  3. Last term = 4 + 24 × 5 = 124; S = 25/2 × (4 + 124) = 1600 ✓.
Q30. 10 cm
  1. Ratio of areas = (ratio of sides)², so ratio of sides = √(36/100) = 6/10.
  2. Let the larger side be x: 6/x = 6/10.
  3. x = 10 cm.
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