CBSE Class 9 Mathematics Sample Paper 2026 Set 2 (with Solutions) — Free PDF
This comprehensive sample paper tests your knowledge of Class 9 Maths including number systems, geometry, and statistics. Practice regularly to strengthen
TL;DR: This comprehensive sample paper tests your knowledge of Class 9 Maths including number systems, geometry, and statistics. Practice regularly to streng…
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This comprehensive sample paper tests your knowledge of Class 9 Maths including number systems, geometry, and statistics. Practice regularly to strengthen your foundation for higher classes. This set is longer than the board paper: 110 marks against the 80-mark CBSE pattern, so treat it as extended practice rather than a timed board rehearsal.
Board: CBSE · Class: Class 9 · Subject: Mathematics · Total: 110 marks · Time: 4 hours
Section A: Multiple Choice — 20 marks
Choose the correct option for each of the 20 questions.
Q1. sqrt(144) = ? (a) 12 (b) 14 (c) 11 (d) 13 (1 mark)
Answer: (a) 12
Q2. The value of pi to two decimal places is: (a) 3.12 (b) 3.14 (c) 3.16 (d) 3.18 (1 mark)
Answer: (b) 3.14
Q3. A quadrilateral with all sides equal and all angles 90 is: (a) Rectangle (b) Square (c) Rhombus (d) Trapezoid (1 mark)
Answer: (b) Square
Q4. The sum of interior angles of a triangle is: (a) 90 (b) 180 (c) 270 (d) 360 (1 mark)
Answer: (b) 180
Q5. Area of a rectangle with length 5 cm and width 3 cm is: (a) 8 (b) 15 (c) 16 (d) 10 (1 mark)
Answer: (b) 15
Q6. Which is a perfect cube? (a) 8 (b) 12 (c) 18 (d) 20 (1 mark)
Answer: (a) 8
Q7. The average of 10, 20, 30 is: (a) 15 (b) 20 (c) 25 (d) 30 (1 mark)
Answer: (b) 20
Q8. If x + 5 = 12, then x = ? (a) 5 (b) 6 (c) 7 (d) 8 (1 mark)
Answer: (c) 7
Q9. Circumference of a circle with radius 7 cm: (a) 22 cm (b) 44 cm (c) 154 cm (d) 77 cm (1 mark)
Answer: (b) 44 cm
Q10. Probability of getting heads in a coin toss: (a) 0 (b) 0.5 (c) 1 (d) 2 (1 mark)
Answer: (b) 0.5
Q11. 3^3 = ? (a) 9 (b) 18 (c) 27 (d) 81 (1 mark)
Answer: (c) 27
Q12. HCF of 12 and 18 is: (a) 2 (b) 3 (c) 6 (d) 12 (1 mark)
Answer: (c) 6
Q13. Area of a circle with radius 5 cm: (a) 78.5 (b) 31.4 (c) 25 (d) 50 (1 mark)
Answer: (a) 78.5
Q14. Perimeter of a square with side 6 cm: (a) 12 (b) 18 (c) 24 (d) 36 (1 mark)
Answer: (c) 24
Q15. LCM of 4 and 6 is: (a) 2 (b) 12 (c) 24 (d) 6 (1 mark)
Answer: (b) 12
Q16. 2.5 + 3.7 = ? (a) 5.2 (b) 6.2 (c) 6.1 (d) 6.3 (1 mark)
Answer: (b) 6.2
Q17. The number of sides in a hexagon: (a) 4 (b) 5 (c) 6 (d) 7 (1 mark)
Answer: (c) 6
Q18. If 2x = 10, then x = ? (a) 4 (b) 5 (c) 6 (d) 7 (1 mark)
Answer: (b) 5
Q19. Median of 5, 8, 12, 15, 20: (a) 8 (b) 12 (c) 15 (d) 20 (1 mark)
Answer: (b) 12
Q20. Volume of a cube with side 3 cm: (a) 9 (b) 18 (c) 27 (d) 81 (1 mark)
Answer: (c) 27
Section B: Short Answer — 30 marks
Answer any 10 questions briefly with working.
Q1. Find the value of 2^5 + 3^2. (2 marks)
Answer: 2^5 = 32, 3^2 = 9. Sum = 32 + 9 = 41
Q2. Solve: 3x - 7 = 14 (2 marks)
Answer: 3x = 21. x = 7
Q3. Find the area of a triangle with base 10 cm and height 6 cm. (2 marks)
Answer: Area = (1/2) * base * height = (1/2) * 10 * 6 = 30 cm^2
Q4. Express 0.75 as a fraction in simplest form. (2 marks)
Answer: 0.75 = 75/100 = 3/4
Q5. Find the distance between (0, 0) and (5, 12) using distance formula. (2 marks)
Answer: Distance = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13
Q6. If a + b = 10 and a - b = 2, find a and b. (2 marks)
Answer: Adding: 2a = 12, a = 6. From first: b = 4. Answer: a = 6, b = 4
Q7. Find the perimeter of a rectangle with length 8 cm and width 5 cm. (2 marks)
Answer: Perimeter = 2(length + width) = 2(8 + 5) = 2(13) = 26 cm
Q8. Calculate 15% of 200. (2 marks)
Answer: (15/100) * 200 = 0.15 * 200 = 30
Q9. Find two consecutive integers whose sum is 25. (2 marks)
Answer: Let integers be x and x+1. x + (x+1) = 25. 2x + 1 = 25. x = 12. Integers are 12 and 13
Q10. Find the mode of 2, 3, 3, 5, 5, 5, 7. (2 marks)
Answer: Mode = 5 (appears 3 times)
Q11. Expand (a + b)(a - b). (2 marks)
Answer: (a + b)(a - b) = a^2 - b^2
Q12. Find the sum of first 5 natural numbers. (2 marks)
Answer: 1 + 2 + 3 + 4 + 5 = 15 or (5*6)/2 = 15
Q13. If a rectangle has area 48 cm^2 and length 8 cm, find width. (2 marks)
Answer: Area = length * width. 48 = 8 * width. width = 6 cm
Q14. Convert 2/5 to decimal. (2 marks)
Answer: 2/5 = 0.4
Q15. Find the LCM and HCF of 12 and 15. (2 marks)
Answer: HCF(12, 15) = 3. LCM(12, 15) = 60
Section C: Long Answer — 60 marks
Answer any 10 questions with detailed working.
Q1. A quadrilateral ABCD has angles A = 80, B = 100, C = 85. Find angle D. Explain your method. (4 marks)
Answer: Sum of angles in quadrilateral = 360 degrees. A + B + C + D = 360. 80 + 100 + 85 + D = 360. D = 360 - 265 = 95 degrees
Q2. Prove that (a + b)^2 = a^2 + 2ab + b^2 algebraically. (4 marks)
Answer: (a + b)^2 = (a + b)(a + b) = a(a + b) + b(a + b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2
Q3. A store offers 25% discount on items. If original price is 800, find selling price. (4 marks)
Answer: Discount = 25% of 800 = (25/100) * 800 = 200. Selling price = 800 - 200 = 600
Q4. Construct a triangle with sides 5 cm, 6 cm, and 7 cm. (4 marks)
Answer: Using compass: Draw base 6 cm. From one end, arc of radius 5 cm. From other end, arc of radius 7 cm. Join intersection point to both ends.
Q5. A number is 5 more than another. Their product is 66. Find the numbers. (4 marks)
Answer: Let numbers be x and x+5. x(x+5) = 66. x^2 + 5x - 66 = 0. (x + 11)(x - 6) = 0. x = 6 or x = -11. Numbers are 6 and 11 or -11 and -6
Q6. Find the area and perimeter of a circle with radius 7 cm. (4 marks)
Answer: Area = πr^2 = π(7)^2 = 49π = 153.86 cm^2 (approx). Perimeter = 2πr = 2π(7) = 14π = 43.96 cm (approx)
Q7. Explain the difference between rational and irrational numbers with examples. (4 marks)
Answer: Rational: can be expressed as p/q (p, q integers, q not 0). Examples: 1/2, 3, -5/4. Irrational: cannot be expressed as p/q, non-terminating non-repeating decimals. Examples: sqrt(2), pi, e
Q8. A triangle has angles in ratio 1:2:3. Find all three angles. (4 marks)
Answer: Let angles be x, 2x, 3x. Sum = 180. x + 2x + 3x = 180. 6x = 180. x = 30. Angles are 30, 60, 90 degrees
Q9. Solve the pair of equations: 2x + y = 7 and x - y = 2. Find x and y. (4 marks)
Answer: Adding equations: 3x = 9, x = 3. From second: 3 - y = 2, y = 1. Solution: x = 3, y = 1
Q10. A trapezoid has parallel sides 8 cm and 12 cm, height 5 cm. Find area. (4 marks)
Answer: Area = (1/2)(sum of parallel sides)(height) = (1/2)(8 + 12)(5) = (1/2)(20)(5) = 50 cm^2
Q11. Find the sum of all even numbers from 1 to 50. (4 marks)
Answer: Even numbers: 2, 4, 6, ..., 50 form an AP with a=2, d=2, l=50. n = (50-2)/2 + 1 = 25. Sum = (25/2)(2+50) = (25/2)(52) = 650
Q12. Explain how to construct perpendicular bisector of a line segment. (4 marks)
Answer: Using compass: Place compass on one end, open more than half length, draw arcs above and below line. From other end, draw arcs same radius intersecting first arcs. Line through intersection points is perpendicular bisector.
Q13. A cylinder has radius 5 cm and height 10 cm. Find its volume. (4 marks)
Answer: Volume = πr^2h = π(5)^2(10) = 250π = 785.4 cm^3 (approx)
Q14. Simplify: (3a^2 + 2a - 5) / (a - 1) (4 marks)
Answer: Factor numerator: 3a^2 + 2a - 5 = (3a + 5)(a - 1). Simplify: (3a + 5)(a - 1)/(a - 1) = 3a + 5
Q15. Find three consecutive odd numbers whose sum is 51. (4 marks)
Answer: Let numbers be x, x+2, x+4. Sum = 51. x + x+2 + x+4 = 51. 3x + 6 = 51. x = 15. Numbers are 15, 17, 19
FAQs
What topics are most important for CBSE Class 9 Maths?
Number systems, polynomials, linear equations, geometry (triangles, circles), statistics and probability are key topics with high weightage.
How can I improve my speed in solving Maths problems?
Practice regularly with sample papers, memorize formulas, identify patterns, and attempt to solve mentally for simple calculations.
Is calculator allowed in Class 9 Maths exam?
No, calculators are not allowed. All calculations must be done by hand using mathematical methods and formulas.
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