CBSE Class 10 Basic Mathematics Sample Paper, Exams of Mathematics

A sample question paper for cbse class 10 basic mathematics (code: 241). It includes general instructions and is divided into four sections (a, b, c, and d) with a total of 30 compulsory questions. The paper covers various topics in mathematics, such as algebra, geometry, trigonometry, and statistics. It is designed to be completed in 3 hours and is worth a maximum of 80 marks. The use of calculators is not permitted, and students are encouraged to draw diagrams where necessary. This sample paper is useful for students preparing for their class 10 mathematics examination, providing them with an opportunity to practice and assess their understanding of the subject matter. It includes a variety of question types, ranging from simple calculations to more complex problem-solving tasks, covering a wide range of topics within the syllabus. The paper is structured to test students' knowledge, comprehension, and application skills in mathematics.

Typology: Exams

2024/2025

Available from 09/03/2025

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CBSE Class 10 Basic
Mathematics – Sample Paper
(Code: 241)
Time Allowed: 3 Hours
Maximum Marks: 80
General Instructions:
All questions are compulsory.
The question paper consists of 30 questions divided into four sections A,
B, C, and D.
Use of calculator is not permitted.
Draw diagrams wherever necessary.
Section A – (1 mark each)
1. Find the value of (–3) × 7 + 4.
2. Write the standard form of a quadratic equation.
3. Find the HCF of 16 and 20.
4. Write the next term in the AP: 3, 6, 9, __.
5. If the distance between two points is 0, what can you say about the
points?
6. Write the value of sin 90°.
Section B – (2 marks each)
1. Find the roots of the quadratic equation x² - 9 = 0 by factorization.
2. Find the 10th term of the AP: 7, 10, 13, ....
3. From a deck of 52 cards, find the probability of drawing a red card.
4. Find the distance between the points (1, 2) and (4, 6).
5. A cone has radius 3 cm and height 4 cm. Find its volume.
6. Draw a pair of tangents to a circle from a point outside it using ruler and
compass.
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CBSE Class 10 Basic

Mathematics – Sample Paper

(Code: 241)

Time Allowed: 3 Hours Maximum Marks: 80 General Instructions:  All questions are compulsory.  The question paper consists of 30 questions divided into four sections A, B, C, and D.  Use of calculator is not permitted.  Draw diagrams wherever necessary.

Section A – (1 mark each)

  1. Find the value of (–3) × 7 + 4.
  2. Write the standard form of a quadratic equation.
  3. Find the HCF of 16 and 20.
  4. Write the next term in the AP: 3, 6, 9, __.
  5. If the distance between two points is 0, what can you say about the points?
  6. Write the value of sin 90°.

Section B – (2 marks each)

  1. Find the roots of the quadratic equation x² - 9 = 0 by factorization.
  2. Find the 10th term of the AP: 7, 10, 13, ....
  3. From a deck of 52 cards, find the probability of drawing a red card.
  4. Find the distance between the points (1, 2) and (4, 6).
  5. A cone has radius 3 cm and height 4 cm. Find its volume.
  6. Draw a pair of tangents to a circle from a point outside it using ruler and compass.

Section C – (3 marks each)

  1. Find the sum of first 15 terms of the AP: 5, 8, 11, ....
  2. Solve the system of equations: x + y = 7 and x – y = 3.
  3. Find the coordinates of the point which divides the line segment joining (2, 3) and (6, 7) in the ratio 2:1.
  4. A dice is thrown once. Find the probability of getting a number less than
  5. The height of a cone is 24 cm and the radius of its base is 7 cm. Find its slant height.
  6. Find the area of a triangle with vertices at (1,1), (4,1) and (4,5).
  7. Find the mode of the following data: 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6.
  8. Find the angle of elevation if a tower 20 m high casts a shadow of 20√3 m.
  9. Prove that (1 + cot²θ) = cosec²θ.

Section D – (4 marks each)

  1. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the numbers.
  2. A motorboat takes 1 hour more to go 48 km upstream than to return downstream. If the speed of the stream is 4 km/h, find the speed of the boat in still water.
  3. Find the mean of the following data: Class: 0–10, 10–20, 20–30, 30–40, 40– Frequency: 5, 10, 15, 10, 5
  4. From a point on the ground, the angle of elevation of the top of a 20 m tall building is 60°. Find the distance of the point from the foot of the building.
  5. Draw a triangle similar to a given triangle ABC with scale factor 3/4.
  6. Construct a tangent to a circle of radius 4 cm from a point 6 cm away from the center.
  7. A metallic spherical ball of radius 4.2 cm is melted and recast into smaller spherical balls of radius 0.7 cm. Find how many such balls are formed.