CBSE Class 9 Mathematics · Exam Practice

Mathematics Practice Paper — Set 2

Mathematics Practice Paper — Set 2. CBSE Class 9 Mathematics, covering number systems, algebraic identities, linear polynomials, coordinates, sequences and progressions, perimeter and area, 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 9 Mathematics chapters on MuskMeadow: number systems, algebraic identities, linear polynomials, coordinates, sequences and progressions, perimeter and area, 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. (x + 3)(x − 3) =

A. x² + 9B. x² − 9C. x² − 6x + 9D. x² + 6x + 9

2. The point (−3, 4) lies in the

A. first quadrantB. second quadrantC. third quadrantD. fourth quadrant

3. The probability of getting a head when a fair coin is tossed once is

A. 0B. 1/2C. 1D. 2

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

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

5. The perimeter of a rectangle of length 12 cm and breadth 5 cm is

A. 17 cmB. 34 cmC. 60 cmD. 30 cm

6. The area of a circle of radius 7 cm (π = 22/7) is

A. 44 cm²B. 154 cm²C. 49 cm²D. 22 cm²

7. Which of these is a rational number?

A. 0.25B. √5C. πD. √7

8. The value of 2³ × 2⁴ is

A. 2⁷B. 2¹²C. 4⁷D. 2¹

9. The zero of the polynomial 2x − 6 is

A. −3B. 3C. 6D. 12

10. The value of 99² is

A. 9801B. 9999C. 9601D. 9901
8 MARKS

Section B — Fill in the Blanks & True / False

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

11. The point (0, 4) lies on the ______-axis.

12. The sum of the probabilities of all the outcomes of an experiment is ______.

13. Every integer is a rational number. (   )

14. (a − b)² = a² − b². (   )

15. The common difference of the AP 5, 8, 11, … is ______.

16. The circumference of a circle is 2π times its ______.

17. A linear polynomial has exactly one zero. (   )

18. The area of a triangle is ½ × base × ______.

16 MARKS

Section C — Short Answer Questions

Show your working. (2 marks each)

19. Expand (2x + 3)².

20. Find the zero of p(x) = 3x − 9.

21. A bag has 3 red and 5 blue balls. Find the probability of drawing a red ball.

22. Find the 15th term of the AP 2, 5, 8, …

23. Find the perimeter and area of a rectangle 9 cm by 4 cm.

24. Write the coordinates of the reflection of (3, −2) in the x-axis.

25. Evaluate 2⁵ ÷ 2².

26. Factorise x² − 16.

16 MARKS

Section D — Problem Solving

Show all steps. (4 marks each)

27. Using suitable identities, find (a) 102 × 98, (b) 103² and (c) 97².

28. For the AP 5, 9, 13, … find (a) the common difference, (b) the 20th term and (c) the sum of the first 20 terms.

29. A circular park has radius 14 m. (π = 22/7) Find (a) its area, (b) its circumference and (c) the cost of fencing it at ₹20 per metre.

30. A fair die is rolled once. Find the probability of getting (a) an even number, (b) a prime number, (c) a number greater than 4 and (d) the number 7.

CBSE Class 9 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. x² − 9

Using (a + b)(a − b) = a² − b²: x² − 9.

Q2. B. second quadrant

x is negative and y is positive, which is the second quadrant.

Q3. B. 1/2

One favourable outcome out of two equally likely outcomes.

Q4. B. 39

a₁₀ = a + 9d = 3 + 9 × 4 = 39.

Q5. B. 34 cm

Perimeter = 2(l + b) = 2 × 17 = 34 cm.

Q6. B. 154 cm²

Area = πr² = 22/7 × 49 = 154 cm².

Q7. A. 0.25

0.25 = 1/4, so it is rational. √5, π and √7 are irrational.

Q8. A. 2⁷

Add the exponents: 2³⁺⁴ = 2⁷ = 128.

Q9. B. 3

2x − 6 = 0 ⇒ x = 3.

Q10. A. 9801

99² = (100 − 1)² = 10000 − 200 + 1 = 9801.

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

Its x-coordinate is 0, so it lies on the y-axis.

Q12. 1

Some outcome must occur.

Q13. True

An integer n can be written as n/1.

Q14. False

The correct identity is (a − b)² = a² − 2ab + b².

Q15. 3

d = 8 − 5 = 3.

Q16. radius

C = 2πr.

Q17. True

ax + b = 0 gives the single zero x = −b/a (a ≠ 0).

Q18. height

The height is the perpendicular distance to the base.

Section C — Short Answer Questions (16 marks)
Q19. 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.
Q20. 3
  1. Put p(x) = 0: 3x − 9 = 0.
  2. x = 9/3 = 3.
Q21. 3/8
  1. Total outcomes = 3 + 5 = 8.
  2. P(red) = 3/8.
Q22. 44
  1. a = 2, d = 3, n = 15.
  2. a₁₅ = a + 14d = 2 + 14 × 3 = 44.
Q23. Perimeter 26 cm; area 36 cm²
  1. Perimeter = 2(9 + 4) = 26 cm.
  2. Area = 9 × 4 = 36 cm².
Q24. (3, 2)
  1. Reflection in the x-axis keeps x and changes the sign of y.
  2. So (3, −2) becomes (3, 2).
Q25. 8
  1. Subtract the exponents: 2⁵⁻² = 2³.
  2. 2³ = 8.
Q26. (x + 4)(x − 4)
  1. x² − 16 = x² − 4².
  2. Using a² − b² = (a + b)(a − b): (x + 4)(x − 4).
Section D — Problem Solving (16 marks)
Q27. (a) 9996 (b) 10609 (c) 9409
  1. (a) (100 + 2)(100 − 2) = 100² − 2² = 10000 − 4 = 9996.
  2. (b) (100 + 3)² = 10000 + 600 + 9 = 10609.
  3. (c) (100 − 3)² = 10000 − 600 + 9 = 9409.
Q28. (a) 4 (b) 81 (c) 860
  1. (a) d = 9 − 5 = 4.
  2. (b) a₂₀ = 5 + 19 × 4 = 81.
  3. (c) S₂₀ = (20/2)(2 × 5 + 19 × 4) = 10 × 86 = 860. Check: 20/2 × (5 + 81) = 860 ✓.
Q29. (a) 616 m² (b) 88 m (c) ₹1760
  1. (a) Area = πr² = 22/7 × 196 = 616 m².
  2. (b) Circumference = 2πr = 2 × 22/7 × 14 = 88 m.
  3. (c) Cost = 88 × 20 = ₹1760.
Q30. (a) 1/2 (b) 1/2 (c) 1/3 (d) 0
  1. Sample space {1, 2, 3, 4, 5, 6}: 6 outcomes.
  2. (a) Even: 2, 4, 6 → 3/6 = 1/2. (b) Prime: 2, 3, 5 → 3/6 = 1/2.
  3. (c) Greater than 4: 5, 6 → 2/6 = 1/3.
  4. (d) 7 cannot occur, so the probability is 0 (an impossible event).
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