Are you a Class 9 CBSE student preparing for your Mathematics examination with the new NCERT Ganita Manjari textbook? At Dhingra Classes, we understand that the updated syllabus and exam pattern can feel challenging. That’s why we’ve created this 80 Marks Question Paper with Answers covering nine crucial chapters from your new syllabus.
This paper follows the latest CBSE Class 9 exam pattern, including competency-based questions, case study questions, and application-based problems .
📋 CBSE Class 9 Mathematics Exam Pattern — 80 Marks
| Section | Question Type | Marks |
|---|---|---|
| Section A | Multiple Choice Questions (MCQ) | 20 × 1 = 20 |
| Section B | Very Short Answer Questions | 5 × 2 = 10 |
| Section C | Short Answer Questions | 6 × 3 = 18 |
| Section D | Long Answer Questions | 4 × 5 = 20 |
| Section E | Case Study Questions | 3 × 4 = 12 |
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, 0)
(b) (0, 1)
(c) (0, 0)
(d) (1, 1)
Q2. A point lying on the x-axis has coordinates of the form:
(a) (0, y)
(b) (x, 0)
(c) (x, y)
(d) (0, 0)
Q3. In which quadrant does the point (-3, 5) lie?
(a) I
(b) II
(c) III
(d) IV
Q4. The degree of the linear polynomial 3x + 7 is:
(a) 0
(b) 1
(c) 2
(d) 3
Q5. If p(x) = 2x + 5, then p(3) equals:
(a) 6
(b) 11
(c) 10
(d) 15
Q6. The identity (a + b)² equals:
(a) a² + b²
(b) a² + 2ab + b²
(c) a² – 2ab + b²
(d) a² + ab + b²
Q7. Using the identity (a – b)² = a² – 2ab + b², the value of 98² is:
(a) 9604
(b) 9608
(c) 9614
(d) 9704
Q8. The circumcentre of a right-angled triangle lies:
(a) Inside the triangle
(b) Outside the triangle
(c) At the midpoint of the hypotenuse
(d) At the vertex of the right angle
Answer: (c) At the midpoint of the hypotenuse
Q9. The perimeter of a square with side 7 cm is:
(a) 14 cm
(b) 21 cm
(c) 28 cm
(d) 49 cm
Q10. The area of a circle with radius 7 cm is (Take π = 22/7):
(a) 44 cm²
(b) 154 cm²
(c) 308 cm²
(d) 616 cm²
Q11. The total surface area of a cube with side 5 cm is:
(a) 25 cm²
(b) 100 cm²
(c) 125 cm²
(d) 150 cm²
Q12. The volume of a cylinder with radius 7 cm and height 10 cm is (Take π = 22/7):
(a) 1540 cm³
(b) 1440 cm³
(c) 1640 cm³
(d) 1740 cm³
Q13. When a fair coin is tossed once, the probability of getting a head is:
(a) 0
(b) 1/2
(c) 1
(d) 1/4
Q14. If the probability of an event is 0, then the event is:
(a) Certain
(b) Impossible
(c) Likely
(d) Unlikely
Q15. The next term in the sequence 2, 6, 18, 54, … is:
(a) 108
(b) 162
(c) 216
(d) 72
Q16. The 10th term of the arithmetic progression 3, 8, 13, 18, … is:
(a) 43
(b) 48
(c) 53
(d) 58
Q17. Which of the following is a well-defined set?
(a) The set of beautiful flowers
(b) The set of prime numbers less than 20
(c) The set of good students in a class
(d) The set of tasty fruits
Answer: (b) The set of prime numbers less than 20
Q18. If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B is:
(a) {1, 2}
(b) {3}
(c) {4, 5}
(d) {1, 2, 3, 4, 5}
Q19. The abscissa of a point is its distance from the:
(a) x-axis
(b) y-axis
(c) origin
(d) z-axis
Q20. The point (0, -4) lies on the:
(a) x-axis
(b) y-axis
(c) origin
(d) Quadrant IV
📝 SECTION B: Very Short Answer Questions (5 × 2 = 10 Marks)
Q21. Write the coordinates of a point whose abscissa is 4 and ordinate is -3. (2 marks)
Answer: The coordinates are (4, -3).
Q22. Find the value of the polynomial p(x) = x² – 3x + 2 at x = 2. (2 marks)
Answer:
p(2) = (2)² – 3(2) + 2
= 4 – 6 + 2
= 0
Q23. Expand (x + 6)(x + 2) using the identity (x + a)(x + b) = x² + (a + b)x + ab. (2 marks)
Answer:
(x + 6)(x + 2) = x² + (6 + 2)x + (6)(2)
= x² + 8x + 12
Q24. Find the probability of getting a number greater than 4 when a fair die is rolled once. (2 marks)
Answer:
Numbers greater than 4 on a die: 5, 6 (2 favourable outcomes)
Total outcomes = 6
P(greater than 4) = 2/6 = 1/3
Q25. Write the next two terms of the sequence 5, 10, 20, 40, … (2 marks)
Answer:
The sequence doubles each time.
Next two terms: 80, 160
📝 SECTION C: Short Answer Questions (6 × 3 = 18 Marks)
Q26. Plot the points A(2, 3), B(-2, 3), C(-2, -3), and D(2, -3) on a Cartesian plane. Name the quadrilateral formed and find its area. (3 marks)
Answer:
The quadrilateral formed is a rectangle.
Area:
Length = 4 units (from -2 to 2)
Breadth = 6 units (from -3 to 3)
Area = Length × Breadth = 4 × 6 = 24 square units
Q27. Find the zero of the linear polynomial p(x) = 3x – 12. (3 marks)
Answer:
Set p(x) = 0:
3x – 12 = 0
3x = 12
x = 4
The zero of the polynomial is x = 4.
Q28. Using a suitable identity, evaluate 103 × 97. (3 marks)
Answer:
103 × 97 = (100 + 3)(100 – 3)
Using identity (a + b)(a – b) = a² – b²:
= (100)² – (3)²
= 10000 – 9
= 9991
Q29. In a circle of radius 10 cm, a chord is at a distance of 6 cm from the centre. Find the length of the chord. (3 marks)
Answer:
Using the formula: Chord length = 2√(r² – d²)
= 2√(10² – 6²)
= 2√(100 – 36)
= 2√64
= 2 × 8
= 16 cm
Q30. Find the volume and total surface area of a cuboid with dimensions length = 8 cm, breadth = 6 cm, and height = 4 cm. (3 marks)
Answer:
Volume = l × b × h = 8 × 6 × 4 = 192 cm³
Total Surface Area = 2(lb + bh + hl)
= 2(8×6 + 6×4 + 4×8)
= 2(48 + 24 + 32)
= 2(104)
= 208 cm²
Q31. In a bag, there are 5 red balls, 3 blue balls, and 2 green balls. One ball is drawn at random. Find the probability of getting a blue ball. (3 marks)
Answer:
Total balls = 5 + 3 + 2 = 10
Number of blue balls = 3
P(blue ball) = 3/10 = 0.3
📝 SECTION D: Long Answer Questions (4 × 5 = 20 Marks)
Q32. (a) State the identity for (a + b + c)².
(b) Using this identity, expand (2x + 3y + 4z)². (5 marks)
Answer:
(a) (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
(b) (2x + 3y + 4z)²
= (2x)² + (3y)² + (4z)² + 2(2x)(3y) + 2(3y)(4z) + 2(4z)(2x)
= 4x² + 9y² + 16z² + 12xy + 24yz + 16xz
Q33. (a) Define an arithmetic progression.
(b) Find the sum of the first 20 terms of the AP: 5, 9, 13, 17, … (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 = 5, d = 4, n = 20
Sum formula: Sₙ = n/2 [2a + (n – 1)d]
S₂₀ = 20/2 [2(5) + (20 – 1)(4)]
= 10 [10 + 76]
= 10 × 86
= 860
Q34. (a) What is a set? Give an example of a well-defined set.
(b) If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}, find A ∪ B and A ∩ B. (5 marks)
Answer:
(a) A set is a well-defined collection of objects. Example: The set of prime numbers less than 20 = {2, 3, 5, 7, 11, 13, 17, 19}.
(b) A ∪ B = {1, 2, 3, 4, 5, 6, 7}
A ∩ B = {4, 5}
Q35. A point P(-3, 4) is given. (5 marks)
(a) In which quadrant does P lie?
(b) Find its distance from the x-axis and y-axis.
(c) If P is reflected across the y-axis, find the coordinates of the new point.
Answer:
(a) P(-3, 4) lies in Quadrant II (x is negative, y is positive).
(b) Distance from x-axis = |4| = 4 units
Distance from y-axis = |-3| = 3 units
(c) Reflecting across the y-axis changes the sign of the x-coordinate:
New point = (3, 4)
📝 SECTION E: Case Study Questions (3 × 4 = 12 Marks)
Q36. Read the passage and answer the questions below:
A school organizes a lucky draw for its annual function. The draw box contains 50 tickets numbered from 1 to 50. A student draws one ticket at random.
(a) What is the probability of drawing a ticket with a multiple of 5? (2 marks)
Answer:
Multiples of 5 from 1 to 50: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 (10 numbers)
P(multiple of 5) = 10/50 = 1/5 = 0.2
(b) What is the probability of drawing a ticket with a number greater than 40? (2 marks)
Answer:
Numbers greater than 40: 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 (10 numbers)
P(greater than 40) = 10/50 = 1/5 = 0.2
Q37. Read the passage and answer the questions below:
A rectangular garden has length 15 m and breadth 10 m. The gardener wants to build a circular fountain of radius 3.5 m in the middle of the garden. (Take π = 22/7)
(a) Find the perimeter of the rectangular garden. (1 mark)
Answer:
Perimeter = 2(l + b) = 2(15 + 10) = 2 × 25 = 50 m
(b) Find the area of the rectangular garden. (1 mark)
Answer:
Area = l × b = 15 × 10 = 150 m²
(c) Find the area of the circular fountain. (2 marks)
Answer:
Area of circle = πr²
= (22/7) × (3.5)²
= (22/7) × 12.25
= 38.5 m²
Q38. Read the passage and answer the questions below:
A medical representative records the number of sales calls she makes each day: 5, 8, 11, 14, 17, … This follows an arithmetic progression.
(a) Find the common difference of this AP. (1 mark)
(b) Find the nth term formula for this AP. (1 mark)
Answer:
aₙ = a + (n – 1)d
aₙ = 5 + (n – 1)(3) = 5 + 3n – 3 = 3n + 2
(c) How many calls will she make on the 10th day? (2 marks)
Answer:
a₁₀ = 3(10) + 2 = 30 + 2 = 32 calls
📞 Contact Dhingra Classes Today!
📍 Address: Plot No 3, XQ3G+H3M Deacon Homes, 301C, opp. Metro Zone, near Guru Govind Sing, Samarth Nagar, Dnyaneshwar Nagar, Pathardi Phata, Nashik, Maharashtra 422009
📱 Phone: 98230 62106
🌐 Website: https://www.dhingraclassesnashik.com/
📧 Email: dhingraclassesnsk@gmail.com
🎯 Exam Tips for CBSE Class 9 Mathematics Students
Practise MCQs daily — they carry 20 marks in Section A
Memorise all algebraic identities — they are frequently tested
Draw neat diagrams for coordinate geometry and circle problems
Show step-by-step calculations in long answer questions
Link concepts to real-life examples — case study questions test application
Call Us Now