CBSE Class 10 Mathematics Sample Paper 2024

CBSE Class 10 Mathematics Sample Paper 2024

Time allowed: 3 hours Maximum Marks: 80

General Instructions:

1. This question paper contains 38 questions. All questions are compulsory.
2. The question paper consists of 5 sections A, B, C, D and E.
3. Section A: Questions 1 to 18 are MCQs of 1 mark each.
4. Section B: Questions 19 to 24 are short answer questions of 2 marks each.
5. Section C: Questions 25 to 30 are short answer questions of 3 marks each.
6. Section D: Questions 31 to 36 are long answer questions of 5 marks each.
7. Section E: Questions 37 to 38 are case study based questions of 4 marks each.

SECTION A (Multiple Choice Questions)

1. The decimal expansion of 17/8 is: (a) Terminating (b) Non-terminating repeating (c) Non-terminating non-repeating (d) None of these

2. If α and β are zeros of polynomial x² - 6x + 9, then α + β is: (a) 6 (b) 9 (c) -6 (d) -9

3. The pair of equations x + 2y = 5 and 3x + 6y = 15 has: (a) Unique solution (b) No solution (c) Infinitely many solutions (d) Two solutions

4. The discriminant of equation 2x² - 4x + 3 = 0 is: (a) 4 (b) -8 (c) 8 (d) -4

[Questions 5-18 continue...]

SECTION B (Short Answer Questions - 2 marks)

1. Find the HCF of 96 and 404 by prime factorization method.

2. Find the zeros of polynomial p(x) = x² - 2x - 8.

3. Solve the pair of linear equations: 2x + 3y = 11 2x - 4y = -24

[Questions 22-24 continue...]

SECTION C (Short Answer Questions - 3 marks)

1. Prove that √5 is an irrational number.

2. Find the values of k for which the system of equations: kx + 2y = 5 3x + y = 1 has (i) unique solution (ii) no solution

[Questions 27-30 continue...]

SECTION D (Long Answer Questions - 5 marks)

1. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

[Questions 32-36 continue...]

SECTION E (Case Study Questions - 4 marks each)

1. Case Study: A school playground is in the shape of a rectangle with semicircular ends...

MARKING SCHEME AND SOLUTIONS PROVIDED