Are you a Class 9 CBSE student who has already solved Set 1 and Set 2 of our Mathematics papers? At Dhingra Classes, we believe that mastery comes from solving fresh, varied problems. This is Question Paper Set 3 — featuring completely new questions with answers and zero duplicates from our previous papers.

This paper covers nine crucial chapters from your new NCERT Ganita Manjari textbook: Orienting Yourself: The Use of Coordinates, Introduction to Linear Polynomials, Exploring Algebraic Identities, I’m Up and Down, Round and Round, Measuring Space: Perimeter and Area, The Mathematics of Mayhem: Introduction to Probability, Predicting What Comes Next: Exploring Sequences and Progressions, Sets, and Coordinate Geometry.

📋 CBSE Class 9 Mathematics Exam Pattern — 80 Marks (Set 3)

Time Allowed: 3 Hours
Maximum Marks: 80

📝 SECTION A: Multiple Choice Questions (20 × 1 = 20 Marks)

Q1. The x-coordinate of a point is also known as:

(a) Ordinate
(b) Abscissa
(c) Origin
(d) Quadrant

Answer: (b) Abscissa

Q2. If a point lies on the x-axis, its y-coordinate is:

(a) 1
(b) -1
(c) 0
(d) Any number

Answer: (c) 0

Q3. The point (7, -2) lies in which quadrant?

(a) I
(b) II
(c) III
(d) IV

Answer: (d) IV

Q4. Which of the following is a linear polynomial?

(a) x² + 3x + 2
(b) 5x – 7
(c) x³ + 1
(d) 2x² + 5

Answer: (b) 5x – 7

Q5. If f(x) = 3x + 4, then f(-2) equals:

(a) -2
(b) 2
(c) -10
(d) 10

Answer: (a) -2

Q6. The zero of the polynomial f(x) = 7x – 21 is:

(a) 7
(b) -3
(c) 3
(d) -7

Answer: (c) 3

Q7. The expansion of (x + y)³ is:

(a) x³ + y³
(b) x³ + 3x²y + 3xy² + y³
(c) x³ – 3x²y + 3xy² – y³
(d) x³ + y³ + 3xy

Answer: (b) x³ + 3x²y + 3xy² + y³

Q8. Using the identity (a + b)(a – b) = a² – b², the value of 55² – 45² is:

(a) 100
(b) 500
(c) 1000
(d) 10000

Answer: (c) 1000

Q9. The perpendicular from the centre of a circle to a chord:

(a) Bisects the chord
(b) Trisects the chord
(c) Is parallel to the chord
(d) Is equal to the chord

Answer: (a) Bisects the chord

Q10. The angle in a semicircle is:

(a) 45°
(b) 60°
(c) 90°
(d) 180°

Answer: (c) 90°

Q11. The area of a circle with diameter 28 cm is (Take π = 22/7):

(a) 308 cm²
(b) 616 cm²
(c) 1232 cm²
(d) 2464 cm²

Answer: (b) 616 cm²

Q12. The perimeter of a regular hexagon with side 9 cm is:

(a) 45 cm
(b) 54 cm
(c) 63 cm
(d) 72 cm

Answer: (b) 54 cm

Q13. The total surface area of a cube with edge 4 cm is:

(a) 64 cm²
(b) 96 cm²
(c) 48 cm²
(d) 16 cm²

Answer: (b) 96 cm²

Q14. When two coins are tossed simultaneously, the total number of outcomes is:

(a) 2
(b) 3
(c) 4
(d) 8

Answer: (c) 4

Q15. The probability of getting at least one head when two coins are tossed is:

(a) 1/4
(b) 1/2
(c) 3/4
(d) 1

Answer: (c) 3/4

Q16. The next term in the sequence 1, 4, 9, 16, 25, … is:

(a) 30
(b) 36
(c) 42
(d) 49

Answer: (b) 36

Q17. The sum of the first 10 natural numbers is:

(a) 45
(b) 50
(c) 55
(d) 60

Answer: (c) 55

Q18. If A = {a, b, c} and B = {b, c, d}, then A ∩ B is:

(a) {a}
(b) {d}
(c) {b, c}
(d) {a, b, c, d}

Answer: (c) {b, c}

Q19. The power set of an empty set has how many elements?

(a) 0
(b) 1
(c) 2
(d) Infinite

Answer: (b) 1

Q20. The distance between the points A(0, 0) and B(3, 4) is:

(a) 3 units
(b) 4 units
(c) 5 units
(d) 7 units

Answer: (c) 5 units

📝 SECTION B: Very Short Answer Questions (5 × 2 = 10 Marks)

Q21. Write the coordinates of a point whose ordinate is 6 and which lies on the y-axis. (2 marks)

Answer:
For a point on the y-axis, the x-coordinate is 0.
Coordinates = (0, 6)

Q22. Find the value of the polynomial f(x) = x² – 4x + 5 at x = 3. (2 marks)

Answer:
f(3) = (3)² – 4(3) + 5
= 9 – 12 + 5
= 2

Q23. Expand (3x + 2)(3x – 5) using a suitable identity. (2 marks)

Answer:
(3x + 2)(3x – 5) = (3x)² + (2 + (-5))(3x) + (2)(-5)
= 9x² + (-3)(3x) – 10
= 9x² – 9x – 10

Q24. A card is drawn from a well-shuffled deck of 52 playing cards. Find the probability of getting a king. (2 marks)

Answer:
Number of kings = 4
Total cards = 52
P(king) = 4/52 = 1/13

Q25. Find the sum of the first 12 terms of the AP: 4, 9, 14, 19, … (2 marks)

Answer:
Given: a = 4, d = 5, n = 12
Sₙ = n/2 [2a + (n – 1)d]
S₁₂ = 12/2 [2(4) + (12 – 1)(5)]
= 6 [8 + 55]
= 6 × 63
= 378

📝 SECTION C: Short Answer Questions (6 × 3 = 18 Marks)

Q26. Plot the points A(3, 4), B(-3, 4), C(-3, -4), and D(3, -4) on a Cartesian plane. Name the figure formed and find its perimeter. (3 marks)

Answer:
The figure formed is a rectangle.

Dimensions:

• Length = 6 units (from -3 to 3)

• Breadth = 8 units (from -4 to 4)

Perimeter = 2(Length + Breadth) = 2(6 + 8) = 2 × 14 = 28 units

Q27. If g(x) = 5x² – 3x + 2, find g(0), g(1), and g(-1) . (3 marks)

Answer:
g(0) = 5(0)² – 3(0) + 2 = 2

g(1) = 5(1)² – 3(1) + 2 = 5 – 3 + 2 = 4

g(-1) = 5(-1)² – 3(-1) + 2 = 5 + 3 + 2 = 10

Q28. Using the identity (a + b)³ = a³ + 3a²b + 3ab² + b³, evaluate (101)³. (3 marks)

Answer:
101³ = (100 + 1)³
= (100)³ + 3(100)²(1) + 3(100)(1)² + (1)³
= 1000000 + 30000 + 300 + 1
= 1030301

Q29. In a circle of radius 25 cm, a chord is at a distance of 7 cm from the centre. Find the length of the chord. (3 marks)

Answer:
Using the formula: Chord length = 2√(r² – d²)
= 2√(25² – 7²)
= 2√(625 – 49)
= 2√576
= 2 × 24
= 48 cm

Q30. Find the circumference and area of a circle with radius 14 cm. Also find the area of a semicircle with the same radius. (Take π = 22/7) (3 marks)

Answer:
Circumference = 2πr = 2 × (22/7) × 14 = 88 cm

Area = πr² = (22/7) × 14 × 14 = 616 cm²

Area of semicircle = (1/2) × πr² = (1/2) × 616 = 308 cm²

Q31. A bag contains 6 red, 4 blue, and 8 green balls. One ball is drawn at random. Find the probability of getting:
(a) a blue ball
(b) a red or green ball (3 marks)

Answer:
Total balls = 6 + 4 + 8 = 18

(a) P(blue ball) = 4/18 = 2/9

(b) P(red or green ball) = (6 + 8)/18 = 14/18 = 7/9

📝 SECTION D: Long Answer Questions (4 × 5 = 20 Marks)

Q32. (a) State the identity for a³ + b³.
(b) Using this identity, factorise x³ + 27. (5 marks)

Answer:

(a) a³ + b³ = (a + b)(a² – ab + b²)

(b) x³ + 27 = (x)³ + (3)³
= (x + 3)(x² – 3x + 9)

Q33. (a) What is an arithmetic progression?
(b) Find the sum of the first 25 terms of the AP: 7, 11, 15, 19, … (5 marks)

Answer:

(a) An arithmetic progression is a sequence in which the difference between consecutive terms remains constant. This fixed difference is called the common difference (d).

(b) Given: a = 7, d = 4, n = 25
Sₙ = n/2 [2a + (n – 1)d]
S₂₅ = 25/2 [2(7) + (25 – 1)(4)]
= 25/2 [14 + 96]
= 25/2 × 110
= 25 × 55
= 1375

Q34. (a) What is the difference between a subset and a proper subset?
(b) If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, and C = {5, 6, 7, 8}, find A ∪ B, A ∩ B, and (A ∪ B) ∩ C. (5 marks)

Answer:

(a)

• A subset is a set in which all elements are contained in another set.

• A proper subset is a subset that is not equal to the original set.

(b)
A ∪ B = {1, 2, 3, 4, 5, 6}
A ∩ B = {3, 4}
(A ∪ B) ∩ C = {1, 2, 3, 4, 5, 6} ∩ {5, 6, 7, 8} = {5, 6}

Q35. A point R(-4, -5) is given. (5 marks)
(a) In which quadrant does R lie?
(b) Find its distance from the x-axis and y-axis.
(c) If R is reflected across the origin, find the coordinates of the new point.

Answer:

(a) R(-4, -5) lies in Quadrant III (both x and y are negative).

(b) Distance from x-axis = |-5| = 5 units
Distance from y-axis = |-4| = 4 units

(c) Reflecting across the origin changes the sign of both coordinates:
New point = (4, 5)

📝 SECTION E: Case Study Questions (3 × 4 = 12 Marks)

Q36. Read the passage and answer the questions below:

A school survey was conducted to find the favourite sport of students. The probability that a randomly selected student likes cricket is 0.4, football is 0.3, and tennis is 0.2.

(a) What is the probability that a student likes none of these sports? (2 marks)

Answer:
P(none) = 1 – (P(cricket) + P(football) + P(tennis))
= 1 – (0.4 + 0.3 + 0.2)
= 1 – 0.9
= 0.1

(b) What is the probability that a student likes cricket or football? (2 marks)

Answer:
P(cricket or football) = P(cricket) + P(football)
= 0.4 + 0.3
= 0.7

Q37. Read the passage and answer the questions below:

A circular flower bed has a radius of 14 m. The gardener wants to fence it and also plant flowers inside. (Take π = 22/7)

(a) Find the circumference of the flower bed. (1 mark)

Answer:
Circumference = 2πr = 2 × (22/7) × 14 = 88 m

(b) Find the area of the flower bed. (1 mark)

Answer:
Area = πr² = (22/7) × 14 × 14 = 616 m²

(c) If the cost of fencing is ₹25 per metre, find the total cost of fencing. (2 marks)

Answer:
Total cost = Circumference × Rate
= 88 × 25
= ₹2200

Q38. Read the passage and answer the questions below:

A fitness tracker records the number of steps walked each day. The step counts follow the pattern: 2000, 2500, 3000, 3500, … This follows an arithmetic progression.

(a) Find the common difference of this AP. (1 mark)

Answer:
d = 2500 – 2000 = 500

(b) Find the nth term formula for this AP. (1 mark)

Answer:
aₙ = a + (n – 1)d
aₙ = 2000 + (n – 1)(500)
= 2000 + 500n – 500
= 500n + 1500

(c) How many steps will be walked on the 15th day? (2 marks)

Answer:
a₁₅ = 500(15) + 1500
= 7500 + 1500
= 9000 steps

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🎯 Exam Tips for CBSE Class 9 Mathematics Students

1. Practise MCQs daily — they carry 20 marks in Section A

2. Memorise all algebraic identities — including (a + b)³ and a³ + b³

3. Draw neat diagrams for coordinate geometry and circle problems

4. Show step-by-step calculations in long answer questions

5. Link concepts to real-life examples — case study questions test application