CBSE Class 10 Mathematics Sample Paper Set 3 — Free PDF
This sample paper follows the latest CBSE Class 10 Mathematics curriculum with a balanced mix of algebra, geometry, trigonometry, and statistics. Practice
TL;DR: This sample paper follows the latest CBSE Class 10 Mathematics curriculum with a balanced mix of algebra, geometry, trigonometry, and statistics. Prac…
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This sample paper follows the latest CBSE Class 10 Mathematics curriculum with a balanced mix of algebra, geometry, trigonometry, and statistics. Practice real exam-pattern questions covering all chapters with detailed solutions. This is a shortened practice set: 41 questions worth 75 marks, following the 80-mark CBSE paper pattern. Use it for timed practice, not as a full-length mock.
Board: CBSE · Class: Class 10 · Subject: Mathematics · Total: 75 marks · Time: 3 hours
Section A - Very Short Answer — 20 marks
Attempt all questions. Each question carries 1 mark.
Q1. Find the HCF of 24 and 36. (1 mark)
Answer: 12
Q2. If the pair of linear equations has unique solution, then the lines are called? (1 mark)
Answer: Intersecting lines
Q3. What is the discriminant of quadratic equation x^2 + 2x + 1 = 0? (1 mark)
Answer: 0
Q4. Find the sum of first 10 natural numbers. (1 mark)
Answer: 55
Q5. In a circle, if angle at center is 60 degrees, what is the angle at circumference subtended by same arc? (1 mark)
Answer: 30 degrees
Q6. Find the value of sin 45 degrees. (1 mark)
Answer: 1/sqrt(2) or sqrt(2)/2
Q7. What is the formula for volume of sphere? (1 mark)
Answer: 4/3 * pi * r^3
Q8. If P(A) = 0.5 and P(B) = 0.3, find P(not A)? (1 mark)
Answer: 0.5
Q9. Find the mode of data: 2, 3, 3, 4, 5, 5, 5, 6. (1 mark)
Answer: 5
Q10. Write the distance formula between two points (x1, y1) and (x2, y2). (1 mark)
Answer: sqrt((x2-x1)^2 + (y2-y1)^2)
Q11. A quadratic polynomial having zeros 2 and 3 is? (1 mark)
Answer: x^2 - 5x + 6
Q12. Find the common difference of AP: 5, 10, 15, 20. (1 mark)
Answer: 5
Q13. If tan A = 3/4, find sin A. (1 mark)
Answer: 3/5
Q14. What is the surface area of cube with side a? (1 mark)
Answer: 6a^2
Q15. Find the mean of 10, 20, 30, 40, 50. (1 mark)
Answer: 30
Q16. Two lines are parallel if their slopes are? (1 mark)
Answer: Equal
Q17. Find the LCM of 12 and 18. (1 mark)
Answer: 36
Q18. A tangent to a circle is perpendicular to the radius at the point of? (1 mark)
Answer: Contact
Q19. If a = 2, b = 3, then (a + b)^2 equals? (1 mark)
Answer: 25
Q20. The probability of an impossible event is? (1 mark)
Answer: 0
Section B - Short Answer — 24 marks
Attempt all questions. Each question carries 2 marks.
Q1. Solve 2x + 3y = 5 and 3x - 2y = 4 using substitution method. (2 marks)
Answer: x = 2, y = 1/3
Q2. Find the roots of quadratic equation 2x^2 - 7x + 3 = 0 using factorization. (2 marks)
Answer: x = 3/2 or x = 1
Q3. If an AP has first term 5 and common difference 2, find the 10th term. (2 marks)
Answer: 23
Q4. Prove that sqrt(2) is irrational. (2 marks)
Answer: Assume sqrt(2) = p/q, then 2q^2 = p^2, showing 2 divides both p and q, contradicting coprimality
Q5. In triangle ABC, angle A = 60 degrees, angle B = 80 degrees, find angle C. (2 marks)
Answer: 40 degrees
Q6. If two chords are equal, prove they are equidistant from the center. (2 marks)
Answer: Using perpendicular from center bisects equal chords equally
Q7. Find the area of a sector with radius 7 cm and central angle 60 degrees. (2 marks)
Answer: 49pi/6 cm^2 or approximately 25.67 cm^2
Q8. Two dice are thrown together. Find probability of getting sum 7. (2 marks)
Answer: 6/36 = 1/6
Q9. Find the median of 12, 15, 18, 22, 25. (2 marks)
Answer: 18
Q10. If cos A = 5/13, find all trigonometric ratios of A. (2 marks)
Answer: sin A = 12/13, tan A = 12/5, cot A = 5/12, sec A = 13/5, cosec A = 13/12
Q11. Find the distance between parallel lines 3x + 4y + 5 = 0 and 3x + 4y - 10 = 0. (2 marks)
Answer: 3 units
Q12. A circle passes through (0,0), (4,0), (0,3). Find its center and radius. (2 marks)
Answer: Center: (2, 1.5), Radius: 2.5
Section C - Long Answer — 31 marks
Attempt all questions. Each question carries 3 or 4 marks.
Q1. Two pillars of equal height are 100 m apart. From a point between them on the ground, the angles of elevation to the tops are 30 and 60 degrees. Find height of pillars. (4 marks)
Answer: Height = 25*sqrt(3) meters or approximately 43.3 meters
Q2. A bag contains 5 red and 3 blue balls. Two balls are drawn without replacement. Find probability of getting one red and one blue ball. (3 marks)
Answer: 15/56
Q3. If the sum of n terms of an AP is 3n^2 + 5n, find the 12th term and common difference. (3 marks)
Answer: 12th term = 77, common difference = 6
Q4. Construct a triangle ABC with sides 5 cm, 6 cm, 7 cm and then construct a triangle similar to it with scale factor 2/3. (4 marks)
Answer: Construction steps: Draw triangle ABC, then construct similar triangle AB'C' with sides in ratio 2/3
Q5. A cone has base radius 7 cm and height 24 cm. Find total surface area and volume. (4 marks)
Answer: Volume = 1232 cm^3, Total surface area = 704 cm^2
Q6. Solve the pair of equations graphically: x + y = 6 and x - y = 2. (3 marks)
Answer: x = 4, y = 2 (intersection point)
Q7. Find the sum of first 20 terms of AP with first term 3 and last term 61. (3 marks)
Answer: 640
Q8. Prove that the tangent at any point of a circle is perpendicular to the radius through that point. (3 marks)
Answer: By contradiction using definition of tangent and properties of circles
Q9. Two towers stand 100 m apart. From a point on the ground between them, angles of elevation are 45 and 30 degrees. Find heights if both are equal. (4 marks)
Answer: Height = 50*(sqrt(3)-1) meters
FAQs
What is the exam pattern for CBSE Class 10 Mathematics?
The exam is of 80 marks with 3 hours duration. It includes MCQ (20 marks), short answer (24 marks), and long answer (36 marks) questions covering all chapters.
How many chapters are in Class 10 Mathematics syllabus?
There are 15 chapters including Number Systems, Polynomials, Linear Equations, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Trigonometry, Circles, Areas Related to Circles, Surface Areas and Volumes, Statistics, and Probability.
What is the best way to prepare for Class 10 Mathematics?
Practice previous year papers and sample papers regularly, understand concepts thoroughly, solve all textbook exercises, and focus on problem-solving techniques and formula applications.
All sample papers → · Previous-year questions → · Chapter-wise MCQs →