Sample Paper Class 10 Maths with Solution 2024 PDF Download

The Central Board of Secondary Education (CBSE) has officially released the Class 10th Maths Sample Paper 2024 with Solution allowing students to better prepare for the half-yearly and final board exams. These CBSE Class 10 Maths Sample Paper 2024-25 help students familiarize themselves with the real exam pattern, the nature of the questions, and many other crucial insights.

Students who are going to appear in the upcoming board exam in 2025, must download and practice the CBSE Class 10th Mathematicatics Sample paper 2024 25 as much as they can. For the convenience of the students, we have shared the direct link to Sample paper class 10 maths with solution 2024 pdf download for basic and standard courses.

CBSE Class 10 Maths Sample Paper 2024-25

Maths is regarded as the most changeling subject due to its complexity. With proper preparation and strategy, one can successfully achieve the highest score in this paper. The Class 10 Maths Sample Paper 2024-25 is created in compliance with the revised syllabus and using the most recent updated test pattern. These maths sample papers are essential study materials for students who want to understand the expected question paper format and typology of questions. These model question papers help students grasp the format of the question paper and the marking scheme.

Check CBSE Class 10 Date Sheet 2025

Pattern of CBSE Class 10 Maths Sample Paper 2024-25

By solving these papers, students get to know the exam structure, sorts of questions, and marking system, because the sample paper pattern is exactly a replicate of the actual CBSE Class 10 Maths Question Paper. Check out the pattern of the CBSE Class 10 Maths Sample Paper 2024-25 discussed below:

1.  This question paper contains 38 questions which are divided into 5 Sections A, B, C, D, and E.
2. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion- Reason based questions of 1 mark each.
3. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks
   each.
4.  In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
5. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
6.  In Section E, Questions no. 36-38 are case study-based questions carrying 4 marks each with
   sub parts of the values of 1, 1 and 2 marks each respectively.
7.  All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of Section C and 2 Questions of Section D have been provided. An internal choice has been provided in all the 2 marks questions of Section E.
8. Draw neat and clean figures wherever required.
9. Take π =22/7 wherever required if not stated.

Sample Paper Class 10 Maths with Solution 2023 PDF Download

Every year, CBSE used to release sample papers for all subjects at the beginning of the academic year. In the below table, we have shared the last two years’ CBSE Class 10 Maths sample paper with solution PDF which is super beneficial for the students as a practice resource. check sample paper class 10 maths with solution 2023 pdf download and sample paper class 10 maths with solution 2022 pdf download links.

Sample Paper Class 10 2024 Maths Standard with Solution

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

1. The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30), (4,-20) and (6,0). The zeroes of the polynomial are
A) – 6,0 B) 4, 6 C) – 30,-20 D) – 6,6

Answer: D) – 6,6

2. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is inconsistent, is
A) -10 B) -5 C) 5 D) 7

Answer:B) -5

3. Which of the following statements is not true?
A) A number of secants can be drawn at any point on the circle.
B) Only one tangent can be drawn at any point on a circle.
C) A chord is a line segment joining two points on the circle
D) From a point inside a circle only two tangents can be drawn.

Answer:D) From a point inside a circle only two tangents can be drawn.

4. If nth term of an A.P. is 7n-4 then the common difference of the A.P. is
A) 7 B) 7n C) – 4 D) 4

Answer:A) 7

5. The radius of the base of a right circular cone and the radius of a sphere are each 5 cm  in length. If the volume of the cone is equal to the volume of the sphere then the height of the cone is
A) 5 cm B) 20 cm C) 10 cm D) 4 cm

Answer: B) 20 cm

6.

Answer: A) 11/9

7. In the given figure, a tangent has been drawn at a point P on the circle centered at O.

If ∠ TPQ= 110𝑂 then ∠POQ is equal to
A) 110º B) 70º C) 140º D)55º

Answer: C) 140º 

8.. A quadratic polynomial having zeroes – √5/2 and √5/2 is
A) 𝑥²− 5√2 x +1 B) 8𝑥²- 20 C) 15𝑥²- 6 D) 𝑥²- 2√5 x -1

Answer: B) 8𝑥²- 20

9. Consider the frequency distribution of 45 observations.

The upper limit of median class is
A) 20 B) 10 C) 30 D) 40

Answer: C) 30

10. O is the point of intersection of two chords AB and CD of a circle.

If ∠𝐵𝑂𝐶 = 80𝑂 and OA = OD then 𝛥𝑂𝐷𝐴 𝑎𝑛𝑑 𝛥𝑂𝐵𝐶 are
A) equilateral and similar B) isosceles and similar
C) isosceles but not similar D) not similar

Answer: B) isosceles and similar

11. The roots of the quadratic equation 𝑥²+x-1 = 0 are
A) Irrational and distinct B) not real
C ) rational and distinct D) real and equal

Answer: A) Irrational and distinct

12. If 𝜃 = 30𝑜 then the value of 3tan𝜃 is
A)1  B) 1/√3  C )3/ √3 (D) not defined

Answer:  C )3/ √3 

13. The volume of a solid hemisphere is 396/7 𝑐𝑚³.The total surface area of the solid hemisphere (in sq. cm) is
A)396/7
B)594/ 7
C)549/7
D) 604/ 7

Answer: B)594/ 7

14. In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is drawn at random. The probability that the drawn ball is white in colour is
𝐴) 1/6
B) 3/8
C ) 11/ 24
D) 5/8

Answer: B) 3/8
15. The point on the x- axis nearest to the point (-4,-5) is
A) (0, 0) B) (-4, 0) C ) (-5, 0) D) (√41, 0)

Answer: B) (-4, 0) 

16. Which of the following gives the middle most observation of the data?
A) Median B) Mean C) Range D) Mode

Answer: A) Median

17. A point on the x-axis divides the line segment joining the points A(2, -3) and B(5, 6) in the ratio 1:2. The point is
A) (4, 0) B) ( 7/2 ,3/2) C) (3, 0) D) (0,3)

Answer: C) (3, 0) 

18. A card is drawn from a well shuffled deck of playing cards. The probability of getting red face card is
𝐴) 3/ 13
B) 1/ 2
C) 3/ 52
D) 3/ 26

Answer: D) 3/ 26

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
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.

19. Assertion (A): HCF of any two consecutive even natural numbers is always 2.
Reason (R): Even natural numbers are divisible by 2.

Answer: (B)

20. Assertion (A): If the radius of the sector of a circle is reduced to half and the angle is doubled then the perimeter of the sector remains the same.

Reason (R): The length of the arc subtending angle θ at the centre of a circle of radius r = 𝛱𝑟𝜃/180.

Answer: (D)

Section B
Section B consists of 5 questions of 2 marks each.

21. (A)Find the H.C.F and L.C.M of 480 and 720 using the Prime factorisation method.

OR
(A) The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of m.

22. (A) Two dice are rolled together bearing numbers 4, 6, 7, 9, 11, 12. Find the probability that the product of numbers obtained is an odd number
OR
(B) How many positive three digit integers have the hundredths digit 8 and unit’s digit 5? Find the probability of selecting one such number out of all three digit numbers.

23.

24. Find the point(s) on the x-axis which is at a distance of √41 units from the point (8, -5).
25. Show that the points A(-5,6), B(3, 0) and C( 9, 8) are the vertices of an isosceles triangle.

Section C
Section C consists of 6 questions of 3 marks each.

26. (A) In 𝛥ABC, D, E and F are midpoints of BC,CA, and AB respectively. Prove that
△ 𝐹𝐵𝐷 ∼ △ DEF and △ DEF ∼ △ ABC

OR
(B) In 𝛥ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Prove that the median AD drawn from A on BC bisects PQ

27. The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers.

28. If 𝛼 and 𝛽 are zeroes of a polynomial 6𝑥²-5x+1 then form a quadratic polynomial whose zeroes are 𝛼²  and 𝛽².

29. If cosθ + sinθ = 1 , then prove that cosθ – sinθ = ±1 3
30. (A) The minute hand of a wall clock is 18 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.
OR
(B) AB is a chord of a circle centered at O such that ∠AOB=60˚. If OA = 14 cm then find the area of the minor segment. (take √3 =1.73)

31. Prove that √3 is an irrational number.

Section D
Section D consists of 4 questions of 5 marks each

32. (A) Solve the following system of linear equations graphically:
x+2y = 3, 2x-3y+8 = 0
OR
(B) Places A and B are 180 km apart on a highway. One car starts from A and another from B at the same time. If the car travels in the same direction at different speeds, they meet in 9 hours. If they travel towards each other with the same speeds as before, they meet in an hour. What are the speeds of the two cars?

33. Prove that the lengths of tangents drawn from an external point to a circle are equal.

Using the above result, find the length BC of 𝛥ABC. Given that, a circle is inscribed in 𝛥ABC touching the sides AB, BC, and CA at R, P, and Q respectively, and AB= 10 cm, AQ= 7cm, CQ= 5cm.

34. A boy whose eye level is 1.35 m from the ground, spots a balloon moving with the wind in a horizontal line at some height from the ground. The angle of elevation of the balloon from the eyes of the boy at an instant is 60º. After 12 seconds, the angle of elevation reduces to 30°. If the speed of the wind is 3m/s then find the height of the balloon from the ground. (Use √3= 1.73)

35. Find the mean and median of the following data:

OR

The monthly expenditure on milk in 200 families of a Housing Society is given below

Find the value of x and also find the mean expenditure.

Section E
Section E consists of 3 case study-based questions of 4 marks each.

36. Ms. Sheela visited a store near her house and found that the glass jars were arranged one above the other in a specific pattern.

On the top layer there are 3 jars. In the next layer there are 6 jars. In the 3rd layer from the top there are 9 jars and so on till the 8th layer. On the basis of the above situation answer the following questions.

(i) Write an A.P whose terms represent the number of jars in different layers starting from top . Also, find the common difference.
(ii) Is it possible to arrange 34 jars in a layer if this pattern is continued? Justify your answer.
(iii) (A) If there are ‘n’ number of rows in a layer then find the expression for finding the total number of jars in terms of n. Hence find 𝑆8 .

OR

(iii) (B) The shopkeeper added 3 jars in each layer. How many jars are there in the 5th
layer from the top?

37.

Triangle is a very popular shape used in interior designing. The picture given above shows a cabinet designed by a famous interior designer. Here the largest triangle is represented by △ ABC and smallest one with shelf is represented by △ DEF. PQ is parallel to EF.

(i) Show that △ DPQ ∼ △ DEF.  (1)
(ii) If DP= 50 cm and PE = 70 cm then find 𝑃𝑄/𝐸𝐹.
(iii) (A) If 2AB = 5DE and △ ABC ∼ △ DEF then show that 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 △𝐴𝐵𝐶/𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 △𝐷𝐸𝐹 is constant.

OR

(iii) (B) If AM and DN are medians of triangles ABC and DEF respectively then prove that △ ABM ∼ △ DEN.

38. Metallic silos are used by farmers for storing grains. Farmer Girdhar has decided to build a new metallic silo to store his harvested grains. It is in the shape of a cylinder mounted by a cone.
Dimensions of the conical part of a silo is as follows:

• Radius of base = 1.5 m
• Height = 2 m
• Dimensions of the cylindrical part of a silo is as follows:
• Radius = 1.5 m
• Height = 7 m

On the basis of the above information answer the following questions.
(i) Calculate the slant height of the conical part of one silo.
(ii) Find the curved surface area of the conical part of one silo.
(iii)(A) Find the cost of the metal sheet used to make the curved cylindrical part of 1 silo at the rate of ₹2000 per 𝑚² .
OR
(iii) (B) Find the total capacity of one silo to store grains

Maths Sample Paper Class 10 2024 25 Answer Key

sample paper class 10 maths with solution pdfs are extremely useful resources for preparation for the CBSE Class 10 examination. The accompanying answer keys contain useful information about the correct responses and can considerably improve your learning. Here’s how to apply them effectively:

• Familiarize Yourself with the Format: Understand the format, question kinds, and marking scheme so that you may prepare accordingly.
• Analyze your performance: Compare your answers to the solutions to identify areas of strength and weakness, and then work on them to improve.
• Identify reoccurring topics: Determine which topics are commonly tested, and concentrate on those.
• Practice different question types: Make sure you’re familiar with MCQs, short answer, and long answer questions.
• Timed Practice: Solve sample papers under exam conditions to mirror the real test experience.
• Practice regularly: Solve sample papers in timed mode to imitate the test setting and improve time management.
• Seek feedback from teachers: Seek expert advice and comments on your performance to identify areas for improvement.
• Consistent practice: Sample papers help to reinforce concepts and enhance problem-solving abilities. Consistent practice, excellent time management, and a positive mindset are crucial for success in the CBSE Class 10 Mathematics exam.

Advantage of Class 10 Maths Sample Paper 2024-25 with Solutions

Using the Class 10 Maths Sample Paper for 2024-25 has several benefits, especially with the updated CBSE exam pattern. Here are some advantages:

Familiarity with Exam Pattern: The sample paper follows the latest CBSE exam pattern, giving students an idea of question types, marking schemes, and difficulty levels, which helps reduce exam anxiety.

Time Management: Practicing with the sample paper allows students to strategize their time for each section, improving speed and accuracy during the actual exam.

Focused Practice: By solving questions similar to those on the actual exam, students can focus on frequently tested concepts, making their study sessions more efficient.

Self-Assessment: The sample paper helps students evaluate their understanding, identify areas of weakness, and work on improving them.

Exposure to Different Question Formats: CBSE sample papers include objective, subjective, case-based, and assertion-reason questions, giving students comprehensive exposure to all possible formats.

Builds Confidence: Consistent practice with sample papers can boost confidence and readiness, as students become more comfortable with the exam structure.

For best results, students should solve the sample paper under timed conditions and review mistakes to avoid similar errors in the actual exam.

How useful is NCERT Previous Year Question Papers Class 10 Maths with Solutions?

NCERT itself does not release specific “previous year question papers” for Class 10 Maths. However, you can access solved previous years’ question papers for Class 10 Mathematics that are based on the NCERT syllabus, especially those from CBSE board exams. Here’s how you can find these:

Books
Reference books like Oswaal Question Banks, Arihant’s All in One, or Educart often include solved previous years’ question papers along with NCERT-style solutions.
Websites
Websites like Adda247 provide PDFs of solved papers.
Search for “Class 10 Maths Previous Year Question Papers PDF” on these sites.
NCERT Exemplar Solutions
NCERT Exemplar books include challenging problems and their solutions, which align with board exam patterns.
Sample Paper Portals
The CBSE website (cbse.gov.in) often releases sample papers that follow NCERT guidelines and past question trends.

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