CBSE Class 10 Mathematics · Exam Practice

Mathematics Practice Paper — Set 2

Mathematics Practice Paper — Set 2. CBSE Class 10 Mathematics, covering real numbers, polynomials, pair of linear equations, quadratic equations, arithmetic progressions, coordinate geometry, trigonometry, circles and areas, surface areas and volumes, statistics and probability, 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 CBSE Class 10 Mathematics chapters on MuskMeadow: real numbers, polynomials, pair of linear equations, quadratic equations, arithmetic progressions, coordinate geometry, trigonometry, circles and areas, surface areas and volumes, statistics and probability.
  • 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 CBSE 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 HCF of 12 and 18 is

A. 3B. 6C. 12D. 36

2. The sum of the zeros of x² − 5x + 6 is

A. −5B. 5C. 6D. −6

3. If x + y = 5 and x − y = 1, then x =

A. 2B. 3C. 4D. 1

4. The discriminant of x² − 4x + 4 = 0 is

A. 0B. 4C. 8D. 16

5. The 10th term of the AP 2, 5, 8, … is

A. 26B. 29C. 32D. 30

6. The distance of the point (3, 4) from the origin is

A. 3B. 4C. 5D. 7

7. The value of tan 60° is

A. 1/√3B. 1C. √3D. √3/2

8. The probability of drawing an ace from a well-shuffled pack of 52 cards is

A. 1/4B. 1/13C. 1/52D. 4/13

9. The area of a sector of radius 6 cm and angle 60° is

A. 6π cm²B. 12π cm²C. 36π cm²D. 3π cm²

10. The mode of 2, 3, 3, 5, 3, 7 is

A. 2B. 3C. 5D. 7
8 MARKS

Section B — Fill in the Blanks & True / False

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

11. For two positive integers a and b, HCF × LCM = ______.

12. A quadratic polynomial has at most ______ zeros.

13. A tangent to a circle is perpendicular to the radius through the point of contact. (   )

14. The sum of the first n natural numbers is n(n + 1)/2. (   )

15. The total surface area of a solid cylinder is ______.

16. The class mark of the class 10–20 is ______.

17. The probability of an event can be 1.5. (   )

18. The distance between (1, 2) and (4, 6) is ______.

16 MARKS

Section C — Short Answer Questions

Show your working. (2 marks each)

19. Find the HCF and LCM of 12 and 18 and verify that HCF × LCM = product.

20. Find the zeros of x² − 7x + 12.

21. Solve: 2x + y = 7 and x − y = 2.

22. Find the sum of the first 10 terms of the AP 2, 5, 8, …

23. Find the mid-point of the line segment joining (2, 3) and (8, 7).

24. Find the length of the arc of a sector of radius 21 cm and angle 60°. (π = 22/7)

25. Find the probability of getting a prime number when a die is thrown once.

26. Evaluate sin 30° cos 60° + sin 60° cos 30°.

16 MARKS

Section D — Problem Solving

Show all steps. (4 marks each)

27. The cost of 3 notebooks and 2 pens is ₹70, and of 2 notebooks and 3 pens is ₹65. Find the cost of one notebook and one pen.

28. Two numbers differ by 3 and their product is 130. Find the numbers.

29. A 10 m ladder leans against a wall making an angle of 60° with the ground. Find (a) how high up the wall it reaches and (b) how far the foot is from the wall. (c) What would the height be at 30°? (Take √3 = 1.732.)

30. A solid cylinder has radius 7 cm and height 20 cm. (π = 22/7) Find (a) its curved surface area, (b) its total surface area and (c) its volume.

CBSE Class 10 Mathematics · Mathematics Practice Paper — Set 2 · 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. B. 6

12 = 2² × 3 and 18 = 2 × 3²; HCF = 2 × 3 = 6.

Q2. B. 5

Sum of zeros = −b/a = 5 (the zeros are 2 and 3).

Q3. B. 3

Adding the equations gives 2x = 6, so x = 3 (and y = 2).

Q4. A. 0

D = b² − 4ac = 16 − 16 = 0; the roots are real and equal.

Q5. B. 29

a₁₀ = 2 + 9 × 3 = 29.

Q6. C. 5

√(3² + 4²) = 5.

Q7. C. √3

From the table of standard angles, tan 60° = √3.

Q8. B. 1/13

There are 4 aces in 52 cards: 4/52 = 1/13.

Q9. A. 6π cm²

Area = (θ/360) × πr² = (1/6) × 36π = 6π cm².

Q10. B. 3

3 occurs most often (three times).

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

The product of two numbers equals the product of their HCF and LCM.

Q12. 2

The degree of the polynomial bounds the number of zeros.

Q13. True

This is a standard theorem.

Q14. True

For example, 1 + 2 + 3 + 4 = 10 = 4 × 5/2.

Q15. 2πr(r + h)

Curved surface 2πrh plus two circular ends 2πr².

Q16. 15

(10 + 20)/2 = 15.

Q17. False

Probability always lies between 0 and 1.

Q18. 5

√(3² + 4²) = 5.

Section C — Short Answer Questions (16 marks)
Q19. HCF 6, LCM 36
  1. 12 = 2² × 3, 18 = 2 × 3²: HCF = 6, LCM = 2² × 3² = 36.
  2. Check: 6 × 36 = 216 = 12 × 18 ✓.
Q20. 3 and 4
  1. x² − 3x − 4x + 12 = x(x − 3) − 4(x − 3) = (x − 3)(x − 4).
  2. The zeros are 3 and 4.
Q21. x = 3, y = 1
  1. Add the equations: 3x = 9, so x = 3.
  2. From x − y = 2: y = 1. Check: 2 × 3 + 1 = 7 ✓.
Q22. 155
  1. a = 2, d = 3, n = 10.
  2. S₁₀ = (10/2)(2 × 2 + 9 × 3) = 5 × 31 = 155.
Q23. (5, 5)
  1. Mid-point = ((2 + 8)/2, (3 + 7)/2).
  2. = (5, 5).
Q24. 22 cm
  1. Arc length = (θ/360) × 2πr.
  2. = (1/6) × 2 × 22/7 × 21 = 22 cm.
Q25. 1/2
  1. Primes on a die: 2, 3, 5 — three outcomes out of six.
  2. P = 3/6 = 1/2.
Q26. 1
  1. sin 30° cos 60° = 1/2 × 1/2 = 1/4.
  2. sin 60° cos 30° = √3/2 × √3/2 = 3/4. Sum = 1.
Section D — Problem Solving (16 marks)
Q27. Notebook ₹16, pen ₹11
  1. Let notebook = ₹a, pen = ₹b: 3a + 2b = 70 and 2a + 3b = 65.
  2. Multiply by 3 and 2: 9a + 6b = 210 and 4a + 6b = 130. Subtract: 5a = 80, so a = 16.
  3. Then 2b = 70 − 48 = 22, so b = 11. Check: 2 × 16 + 3 × 11 = 65 ✓.
Q28. 10 and 13
  1. Let the smaller be x: x(x + 3) = 130, so x² + 3x − 130 = 0.
  2. (x + 13)(x − 10) = 0, so x = 10 or x = −13.
  3. Taking the positive numbers, they are 10 and 13 (check: 10 × 13 = 130 ✓).
Q29. (a) ≈ 8.66 m (b) 5 m (c) 5 m
  1. (a) Height = 10 sin 60° = 10 × √3/2 = 5√3 ≈ 8.66 m.
  2. (b) Distance = 10 cos 60° = 10 × 1/2 = 5 m.
  3. (c) At 30°: height = 10 sin 30° = 5 m.
Q30. (a) 880 cm² (b) 1188 cm² (c) 3080 cm³
  1. (a) CSA = 2πrh = 2 × 22/7 × 7 × 20 = 880 cm².
  2. (b) TSA = 2πr(r + h) = 2 × 22/7 × 7 × 27 = 1188 cm².
  3. (c) Volume = πr²h = 22/7 × 49 × 20 = 3080 cm³.
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