Are you a Class 9 CBSE student who has already solved Set 1, Set 2, and Set 3 of our Mathematics papers? At Dhingra Classes, we believe that consistent practice with fresh questions sharpens your problem-solving skills. This is Question Paper Set 4 — 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 4)

Time Allowed: 3 Hours
Maximum Marks: 80

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

Q1. The coordinates of the origin are:

(a) (1, 1)
(b) (0, 1)
(c) (1, 0)
(d) (0, 0)

Answer: (d) (0, 0)

Q2. A point lying on the y-axis has coordinates of the form:

(a) (x, 0)
(b) (0, y)
(c) (x, y)
(d) (0, 0)

Answer: (b) (0, y)

Q3. The point (6, -8) lies in which quadrant?

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

Answer: (d) IV

Q4. The degree of the linear polynomial 5x – 9 is:

(a) 0
(b) 1
(c) 2
(d) 3

Answer: (b) 1

Q5. If p(x) = 3x + 7, then p(4) equals:

(a) 12
(b) 19
(c) 21
(d) 28

Answer: (b) 19

Q6. The zero of the polynomial p(x) = 4x – 20 is:

(a) 4
(b) 5
(c) -5
(d) 20

Answer: (b) 5

Q7. The identity (a + b)² – (a – b)² equals:

(a) 2ab
(b) 4ab
(c) a² + b²
(d) 2(a² + b²)

Answer: (b) 4ab

Q8. Using the identity (a – b)² = a² – 2ab + b², the value of 97² is:

(a) 9409
(b) 9419
(c) 9429
(d) 9439

Answer: (a) 9409

Q9. The angle subtended by a diameter at any point on the circle is:

(a) 45°
(b) 60°
(c) 90°
(d) 180°

Answer: (c) 90°

Q10. The perpendicular bisector of a chord of a circle always passes through:

(a) The midpoint of the chord
(b) The centre of the circle
(c) The endpoint of the chord
(d) The tangent point

Answer: (b) The centre of the circle

Q11. The circumference of a circle with radius 21 cm is (Take π = 22/7):

(a) 66 cm
(b) 132 cm
(c) 264 cm
(d) 154 cm

Answer: (b) 132 cm

Q12. The area of a square with perimeter 48 cm is:

(a) 100 cm²
(b) 121 cm²
(c) 144 cm²
(d) 169 cm²

Answer: (c) 144 cm²

Q13. The volume of a cube with edge 6 cm is:

(a) 36 cm³
(b) 108 cm³
(c) 216 cm³
(d) 144 cm³

Answer: (c) 216 cm³

Q14. When a fair die is rolled, the probability of getting an even number is:

(a) 1/6
(b) 1/3
(c) 1/2
(d) 2/3

Answer: (c) 1/2

Q15. If the probability of an event is 0.75, then the probability of its complement is:

(a) 0.15
(b) 0.25
(c) 0.35
(d) 0.50

Answer: (b) 0.25

Q16. The common difference of the AP: 12, 9, 6, 3, … is:

(a) 3
(b) -3
(c) 6
(d) -6

Answer: (b) -3

Q17. The 5th term of the AP: 4, 10, 16, 22, … is:

(a) 26
(b) 28
(c) 30
(d) 32

Answer: (b) 28

Q18. Which of the following is a finite set?

(a) {1, 2, 3, 4, …}
(b) The set of all natural numbers
(c) The set of days in a week
(d) The set of all integers

Answer: (c) The set of days in a week

Q19. If A = {1, 2, 3, 4} and B = {3, 4, 5}, then A – B is:

(a) {1, 2}
(b) {5}
(c) {3, 4}
(d) {1, 2, 3, 4, 5}

Answer: (a) {1, 2}

Q20. The distance between the points P(1, 2) and Q(4, 6) 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 abscissa is -7 and ordinate is 0. (2 marks)

Answer: The coordinates are (-7, 0). This point lies on the x-axis.

Q22. Find the value of the polynomial p(x) = 2x² – 7x + 5 at x = 2. (2 marks)

Answer:
p(2) = 2(2)² – 7(2) + 5
= 8 – 14 + 5
= -1

Q23. Expand (2x + 7)(2x – 3) using the identity (x + a)(x + b) = x² + (a + b)x + ab. (2 marks)

Answer:
(2x + 7)(2x – 3) = (2x)² + (7 + (-3))(2x) + (7)(-3)
= 4x² + (4)(2x) – 21
= 4x² + 8x – 21

Q24. A bag contains 3 red balls, 5 green balls, and 7 blue balls. One ball is drawn at random. Find the probability of getting a green ball. (2 marks)

Answer:
Total balls = 3 + 5 + 7 = 15
Number of green balls = 5
P(green ball) = 5/15 = 1/3

Q25. Find the sum of the first 10 terms of the AP: 3, 7, 11, 15, … (2 marks)

Answer:
Given: a = 3, d = 4, n = 10
Sₙ = n/2 [2a + (n – 1)d]
S₁₀ = 10/2 [2(3) + (10 – 1)(4)]
= 5 [6 + 36]
= 5 × 42
= 210

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

Q26. Plot the points A(2, 5), B(-2, 5), C(-2, -1), and D(2, -1) on a Cartesian plane. Name the figure formed and find its area. (3 marks)

Answer:
The figure formed is a rectangle.

Dimensions:

• Length = 4 units (from -2 to 2)

• Breadth = 6 units (from -1 to 5)

Area = Length × Breadth = 4 × 6 = 24 square units

Q27. If p(x) = x³ – 2x² + 3x – 4, find p(1) and p(-1) . (3 marks)

Answer:
p(1) = (1)³ – 2(1)² + 3(1) – 4
= 1 – 2 + 3 – 4
= -2

p(-1) = (-1)³ – 2(-1)² + 3(-1) – 4
= -1 – 2 – 3 – 4
= -10

Q28. Using a suitable identity, evaluate 105 × 95. (3 marks)

Answer:
105 × 95 = (100 + 5)(100 – 5)
Using identity (a + b)(a – b) = a² – b²:
= (100)² – (5)²
= 10000 – 25
= 9975

Q29. In a circle of radius 15 cm, a chord is at a distance of 9 cm from the centre. Find the length of the chord. (3 marks)

Answer:
Using the formula: Chord length = 2√(r² – d²)
= 2√(15² – 9²)
= 2√(225 – 81)
= 2√144
= 2 × 12
= 24 cm

Q30. Find the area and perimeter of a rectangle with length 16 cm and breadth 12 cm. Also find the length of its diagonal. (3 marks)

Answer:
Area = l × b = 16 × 12 = 192 cm²

Perimeter = 2(l + b) = 2(16 + 12) = 2 × 28 = 56 cm

Diagonal = √(l² + b²) = √(16² + 12²) = √(256 + 144) = √400 = 20 cm

Q31. In a box, there are 10 red marbles, 8 blue marbles, and 6 green marbles. One marble is drawn at random. Find the probability of getting:
(a) a red marble
(b) a blue or green marble (3 marks)

Answer:
Total marbles = 10 + 8 + 6 = 24

(a) P(red marble) = 10/24 = 5/12

(b) P(blue or green marble) = (8 + 6)/24 = 14/24 = 7/12

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

Q32. (a) State the identity for (a + b)³.
(b) Using this identity, expand (2x + 3y)³. (5 marks)

Answer:

(a) (a + b)³ = a³ + 3a²b + 3ab² + b³

(b) (2x + 3y)³
= (2x)³ + 3(2x)²(3y) + 3(2x)(3y)² + (3y)³
= 8x³ + 36x²y + 54xy² + 27y³

Q33. (a) Define an arithmetic progression.
(b) Find the sum of the first 15 terms of the AP: 6, 11, 16, 21, … (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 = 6, d = 5, n = 15
Sₙ = n/2 [2a + (n – 1)d]
S₁₅ = 15/2 [2(6) + (15 – 1)(5)]
= 15/2 [12 + 70]
= 15/2 × 82
= 15 × 41
= 615

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

Q35. A point M(-5, 3) is given. (5 marks)
(a) In which quadrant does M lie?
(b) Find its distance from the x-axis and y-axis.
(c) If M is reflected across the y-axis, find the coordinates of the new point.

Answer:

(a) M(-5, 3) lies in Quadrant II (x is negative, y is positive).

(b) Distance from x-axis = |3| = 3 units
Distance from y-axis = |-5| = 5 units

(c) Reflecting across the y-axis changes the sign of the x-coordinate:
New point = (5, 3)

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

Q36. Read the passage and answer the questions below:

A weather forecast predicts that the probability of rain on Monday is 0.3, on Tuesday is 0.5, and on Wednesday is 0.2.

(a) What is the probability that it rains on at least one of these three days? (2 marks)

Answer:
P(rain on at least one day) = P(Monday) + P(Tuesday) + P(Wednesday)
= 0.3 + 0.5 + 0.2
= 1.0

(b) What is the probability that it does not rain on Tuesday? (2 marks)

Answer:
P(no rain on Tuesday) = 1 – P(rain on Tuesday)
= 1 – 0.5
= 0.5

Q37. Read the passage and answer the questions below:

A circular swimming pool has a radius of 7 m. The owner wants to build a walkway around it. (Take π = 22/7)

(a) Find the circumference of the pool. (1 mark)

Answer:
Circumference = 2πr
= 2 × (22/7) × 7
= 44 m

(b) Find the area of the pool. (1 mark)

Answer:
Area = πr²
= (22/7) × 7 × 7
= 154 m²

(c) If the walkway is 2 m wide, find the area of the walkway. (2 marks)

Answer:
Outer radius = 7 + 2 = 9 m
Area of walkway = π(R² – r²)
= (22/7) × (9² – 7²)
= (22/7) × (81 – 49)
= (22/7) × 32
= 100.57 m² (approximately)

Q38. Read the passage and answer the questions below:

A tree plantation drive records the number of trees planted each day: 15, 20, 25, 30, … This follows an arithmetic progression.

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

Answer:
d = 20 – 15 = 5

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

Answer:
aₙ = a + (n – 1)d
aₙ = 15 + (n – 1)(5)
= 15 + 5n – 5
= 5n + 10

(c) How many trees will be planted on the 12th day? (2 marks)

Answer:
a₁₂ = 5(12) + 10
= 60 + 10
= 70 trees

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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 (a – b)³

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