Sample Math Paper for Class 10 by CBSE in 2024: You can get the sample test and scoring scheme for the CBSE Class 10 Math (Standard) Board Exam 2024 by downloading them. You can also get a sample paper from the CBSE Board that has questions at a higher level of difficulty for the CBSE Class 10 Maths Exam 2024.

**CBSE Class 10 Maths Sample Paper 2023–24:** CBSE sample papers are the best way to prepare for the yearly CBSE board exams because they use the same type of questions and grade distribution. The board also releases marking scheme cum solutions that show the correct way to write an answer or solution and how the marks are given out. The CBSE Class 10 Mathematics (Standard) Sample Paper 2023–24 is in this article. This sample question will really help you get ready for the end-of-year board exam in the right way.

The CBSE Class 10 Maths Marking Scheme helps students learn how to answer questions on the sample paper and how their answers will be graded on board tests. It shows the steps that will be taken to solve each question. CBSE provided both a sample paper and a practice paper for Class 10 Maths (Standard). The practice paper has more competency-based questions, which is in line with the CBSE’s new exam pattern for the 2023–24 school year. Check out the details of the practice test and download it along with the answer key at the end of this piece.

The CBSE Class 10 Maths Board Exam 2024 will be worth 80 marks, and you will have 3 hours to finish it. For more information on how the question paper should be prepared, see the PDFs below that contain a full sample paper and a marking system.

## CBSE Class 10 Maths (Standard) Sample Paper 2024 PDF

### General Instructions

- There are 5 parts to this question paper: A, B, C, D, and E.
- Part A has 20 multiple-choice questions (MCQs) worth one point each. Part B has five questions worth two points each.
- Section C has six questions, and each one is worth three points.
- Section D has four questions, and each one is worth five points.
- Section E has three case-based integrated assessment units, each worth four marks and made up of three parts worth one point, one point, and two points.
- All questions must be answered. There is, however, an internal decision with two questions worth five marks, two questions worth three marks, and two questions worth two marks. For the two-mark problems in Section E, there is an internal choice.
- If you need to, draw neat figures. If it’s not stated, use π =22/7 wherever it’s needed.

**SECTION A**

*Section A consists of 20 questions of 1 mark each.*

1. If two positive integers a and b are written as a = x^{3}y^{2}and b = xy^{3}, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is

(a) xy (b) xy^{2} (c) x^{3}y^{3} (d) x^{2}y^{2}

2.

The given linear polynomial y = f(x) has

(a) 2 zeros

(b) 1 zero and the zero is ‘3’

(c) 1 zero and the zero is ‘4’

(d) No zero

3. The given pair of linear equations is non-intersecting.

Which of the following statements is true?

4. Write the nature of roots of the quadratic equation 9x^{2}– 6x – 2 = 0.

(a) No real roots

(b) 2 equal real roots

(c) 2 distinct real roots

(d) More than 2 real roots

5. Two APs have the same common difference. The first term of one of these is –1 and that of the other is

– 8. Then the difference between their 4th terms is

(a) 1

(b) -7

(c) 7

(d) 9

6. Find the ratio in which the line segment joining (2,-3) and (5, 6) is divided by x-axis.

(a) 1:2

(b) 2:1

(c) 2:5

(d) 5:2

7. (x,y) is 5 unit from the origin. How many such points lie in the third quadrant?

(a) 0

(b) 1

(c) 2

(d) infinitely many

8. In In △ABC, DE ‖ AB. If AB = a, DE = x, BE = b and EC = c.

Express x in terms of a, b and c.

(a) ac/b

(b) ac/(b+c)

(c) ab/c

(d) ab/(b+c)

9. If O is centre of a circle and Chord PQ makes an angle 50° with the tangent PR at the point of contact P, find the angle made by the chord at the centre.

(a) 130°

(b) 100°

(c) 50°

(d) 30°

10. A Quadrilateral PQRS is drawn to circumscribe a circle. If PQ = 12 cm, QR = 15 cm and RS = 14 cm, find the length of SP.

(a) 15 cm (b) 14 cm (c) 12 cm (d) 11 cm

11. Given that sin θ = a/b, find cos θ.

12. (sec A + tan A) (1 – sin A) =

(a) sec A

(b) sin A

(c) cosec A

(d) cos A

13. A pole 6 m high casts a shadow 2 √3m long on the ground, then the Sun’s elevation is

(a) 60°

(b) 45°

(c) 30°

(d) 90°

14. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

(a) 2 units

(b) π units

(c) 4 units

(d) 7 units

15. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park is

(a) 10m

(b) 15m

(c) 20m

(d) 24m

16. There is a green square board of side ‘2a’ unit circumscribing a red circle. Jayadev is asked to keep a dot on the above said board. Find the probability that he keeps the dot on the green region.

17. 2 cards of hearts and 4 cards of spades are missing from a pack of 52 cards. What is the probability of getting a black card from the remaining pack?

(a)22/52

(b)22/46

(c)24/52

(d)24/46

18. Find the upper limit of the modal class from the given distribution.

Height[in cm] | Below 140 | Below 145 | Below 150 | Below 155 | Below 160 | Below 165 |

Number ofgirls | 4 | 11 | 29 | 40 | 46 | 51 |

(a) 165

(b) 160

(c) 155

(d) 150

19. DIRECTION: In the question number 19 and 20, a statement of assertion (A) is followed by a statement of Reason (R).

Choose the correct option

Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.

Statement R( Reason) : Top is obtained by fixing the plane surfaces of the hemisphere and cone together.

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

20. Statement A (Assertion): -5, −5/2, 0, 5/2, …. is in Arithmetic Progression.

Statement R (Reason) : The terms of an Arithmetic Progression cannot have both positive and negative rational numbers.

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

To check all questions, download the full sample paper and its marking scheme from the links given below:

### CBSE Class 10 Maths Sample Paper PDF

CBSE Class 10 Maths (Standard) Sample Paper for Board Exam 2024 (PDF) |

CBSE Class 10 Maths (Standard) Sample Paper 2024 Marking Scheme (PDF) |

## Extra CBSE Practice Questions or a CBSE Practice Paper for Class 10 Standard Math

More practice questions for the CBSE Class 10 Maths Board Exam 2024 were released by the Central Board of Secondary Education (CBSE). There are more practice questions in this resource than in the CBSE sample papers. It is a type of practice paper. But the questions on this sample test are a bit harder. They require you to think more critically and analytically. This means that students will get more questions based on their skills, which is what the new CBSE exam plan calls for.

The questions below are from the CBSE Class 10 Maths Practice Paper. They will help you figure out what kind of questions you can expect on the CBSE Board Exam 2024:

Q. Kimaya and Heena started walking from the point P at the same moment in opposite directions on an 800 m long circular path as shown below. Kimaya walked to the club house at an average speed of 100 m/min and Heena walked to the badminton court at an average speed of 80 m/min. The length of the circular track between the clubhouse and the badminton court is 180 m.

If Heena took 1 minute more than Kimaya to each her destination, find the time taken by Heena to reach the badminton court. Show your work. (2 marks)

Q. ABCD is a rhombus with side 3 cm. Two arcs are drawn from points A and C respectively such that the radius equals the side of the rhombus. The figure is shown below.

If BD is a line of symmetry for the figure, then find the area of the shaded part of the figure in terms of 𝜋. Show your work. (2 marks)

Q. Prime factorisation of three numbers A, B and C is given below: (3 marks)

A = (2^{r} × 3^{p} × 5^{q})

B = (2^{p} × 3^{r} × 5^{p})

C = (2^{q} × 3^{q} × 5^{p}) such that, p < q < r and p, q, & r are natural numbers.

♦ The largest number that divides A, B and C without leaving a remainder is 30.

♦ The smallest number that leaves a remainder of 2 when divided by each of A, B and C is 5402. Find A, B and C. Show your work.

Check all questions and their answers by downloading the practice paper and its marking scheme from the respective links given below: