CBSE Class 9 Mathematics Sample Paper Set 3 — Free PDF
Comprehensive mathematics sample paper covering number systems, algebra, geometry, and statistics. Strengthen problem-solving skills with diverse question
TL;DR: Comprehensive mathematics sample paper covering number systems, algebra, geometry, and statistics. Strengthen problem-solving skills with diverse ques…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Comprehensive mathematics sample paper covering number systems, algebra, geometry, and statistics. Strengthen problem-solving skills with diverse question types and detailed solutions. This is a shortened practice set: 39 questions worth 68 marks, following the 80-mark CBSE paper pattern. Use it for timed practice, not as a full-length mock.
Board: CBSE · Class: Class 9 · Subject: Mathematics · Total: 68 marks · Time: 3 hours
Section A - Very Short Answer Questions — 20 marks
Attempt all questions. Each question carries 1 mark.
Q1. What is the decimal form of 1/8? (1 mark)
Answer: 0.125
Q2. Is 2 a rational or irrational number? (1 mark)
Answer: Irrational
Q3. Find the value of (2^3)^2. (1 mark)
Answer: 64
Q4. Simplify: (x + 2)(x - 2). (1 mark)
Answer: x^2 - 4
Q5. What is the value of a^0 for any non-zero a? (1 mark)
Answer: 1
Q6. Find the remainder when x^2 + 2x + 1 is divided by x + 1. (1 mark)
Answer: 0
Q7. What is the sum of angles in a quadrilateral? (1 mark)
Answer: 360 degrees
Q8. Define a median in a triangle. (1 mark)
Answer: Line segment from vertex to midpoint of opposite side
Q9. How many lines of symmetry does a square have? (1 mark)
Answer: 4
Q10. What is the area of a circle with radius r? (1 mark)
Answer: pi*r^2
Q11. Find the value of sin 30 degrees. (1 mark)
Answer: 1/2
Q12. What is the distance formula for two points? (1 mark)
Answer: sqrt((x2-x1)^2 + (y2-y1)^2)
Q13. Find mode of data: 5, 3, 5, 2, 5, 4. (1 mark)
Answer: 5
Q14. What is the probability of getting a head when tossing a coin? (1 mark)
Answer: 1/2
Q15. Simplify: sqrt(50). (1 mark)
Answer: 5*sqrt(2)
Q16. Write the standard form of 0.00045. (1 mark)
Answer: 4.5 x 10^-4
Q17. Find the value of x in 2x + 5 = 11. (1 mark)
Answer: 3
Q18. What is the formula for volume of a cylinder? (1 mark)
Answer: pi*r^2*h
Q19. If a pair of linear equations has no solution, lines are? (1 mark)
Answer: Parallel
Q20. What is the HCF of 18 and 24? (1 mark)
Answer: 6
Section B - Short Answer Questions — 25 marks
Attempt all questions. Each question carries 2 or 3 marks.
Q1. Prove that sqrt(3) is irrational. (2 marks)
Answer: Assume sqrt(3) = p/q in lowest terms, then 3 = p^2/q^2, so 3q^2 = p^2, leading to contradiction
Q2. Find the product using algebraic identity: (a + b)(a - b). (2 marks)
Answer: a^2 - b^2
Q3. Factorize: x^2 + 5x + 6. (2 marks)
Answer: (x + 2)(x + 3)
Q4. Solve the linear equation: 3x - 2 = 10. (2 marks)
Answer: x = 4
Q5. Plot points A(2, 3) and B(4, 1) on a graph. Find AB. (2 marks)
Answer: AB = sqrt(8) = 2*sqrt(2)
Q6. In triangle ABC, AB = AC and angle A = 60 degrees. Find angles B and C. (2 marks)
Answer: B = C = 60 degrees (equilateral triangle)
Q7. Find the area of a triangle with sides 3, 4, 5. (2 marks)
Answer: 6 square units
Q8. Construct an angle of 75 degrees using compass and ruler. (3 marks)
Answer: Construct 45 + 30 degrees or bisect 150 degrees angle
Q9. Find the median of data: 2, 4, 6, 8, 10. (2 marks)
Answer: 6
Q10. From a pack of 52 cards, find probability of drawing a red card. (2 marks)
Answer: 26/52 = 1/2
Q11. Two adjacent angles on a straight line sum to? (2 marks)
Answer: 180 degrees
Q12. Find the length of tangent from external point to circle with radius 5 and distance 13 from center. (2 marks)
Answer: 12 units
Section C - Long Answer Questions — 23 marks
Attempt all questions. Each question carries 3 or 4 marks.
Q1. Solve the pair of linear equations 2x + 3y = 8 and x - 2y = 1 using elimination method. (3 marks)
Answer: x = 19/7, y = 2/7
Q2. Find the roots of quadratic equation x^2 - 5x + 6 = 0 using factorization. (3 marks)
Answer: x = 2 or x = 3
Q3. In circle with center O and radius 10 cm, if chord AB = 16 cm, find distance from center to chord. (3 marks)
Answer: 6 cm
Q4. Prove that angle in semicircle is a right angle. (4 marks)
Answer: Using inscribed angle theorem, angle subtended by diameter is 90 degrees
Q5. A cone has base radius 7 cm and height 24 cm. Find slant height, volume, and curved surface area. (4 marks)
Answer: Slant height = 25 cm, Volume = 1232 cm^3, Curved surface area = 550 cm^2
Q6. Three numbers are in ratio 2:3:5. If their sum is 100, find the numbers. (3 marks)
Answer: 20, 30, 50
Q7. Draw graph of y = 2x - 1 and find intercepts. (3 marks)
Answer: y-intercept = -1, x-intercept = 0.5, straight line passing through these points
FAQs
What topics are covered in Class 9 Mathematics?
Number systems, Polynomials, Pair of Linear Equations, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Trigonometry, Circles, and Statistics.
What is the exam pattern?
80 marks with 3 hours duration, covering very short answer (20 marks), short answer (30 marks), and long answer (30 marks) questions.
Which chapters should I focus on for scoring well?
Focus on Linear Equations, Triangles, Circles, Areas, and Trigonometry basics as they carry significant marks.
All sample papers → · Previous-year questions → · Chapter-wise MCQs →