Important Questions Class 9 Maths 2026-27

Important Questions Class 9 Maths cover coordinates, linear polynomials, numbers, algebraic identities, circles, mensuration, probability and sequences from Ganita Manjari Part I. For CBSE Class 9 Maths 2026-27, students should practise MCQs, short answers, long answers and case-based questions that test reasoning, formulas and application.

Class 9 Maths begins the move from middle-school calculation to secondary-level reasoning. The NCERT Class 9 Maths textbook Ganita Manjari Part I introduces coordinates, algebra, number systems, circles, area, probability and sequences through examples, activities, visual models and application-based problems. The book gives importance to mathematical thinking, problem-solving, explanation and proof, instead of only using procedures. 

These Important Questions Class 9 Maths bring together chapter-wise practice from the full Part I textbook so students can revise concepts, formulas, calculations and reasoning-based answers in one place.

Key Takeaways

• Ganita Manjari Class 9 Maths: Part I has 8 chapters across algebra, geometry, mensuration, probability and sequences.
• Class 9 Maths syllabus focus: The book builds reasoning, visualisation, problem-solving and mathematical communication.
• Question types: Students should practise MCQs, short answers, long answers and case-based questions.
• Formula use: Coordinates, algebraic identities, perimeter, area, circumference and probability formulas need regular practice.

Important Questions Class 9 Maths Exam Pattern Overview

The CBSE Class 9 Maths curriculum for 2026–27 has been redesigned in line with NEP 2020 and NCF-SE 2023, with focus on conceptual understanding, logical reasoning, problem-solving, visualisation, mathematical modelling and communication.

NCERT Class 9 Maths Ganita Manjari Chapters

The uploaded Ganita Manjari Class 9 Maths Part I textbook contains 8 chapters. It starts with coordinate geometry and number systems, then moves to algebra, circles, mensuration, probability and sequences.

Class 9 Maths Formulas for Quick Revision

These formulas are useful across Class 9 Maths practice questions. Students should write the formula before substitution in calculation-based answers.

Class 9 Maths MCQs

These Class 9 Maths MCQs test formulas, definitions and quick concept recall from the main chapters.

Q1. The point (0, 0) is called the:

(a) x-axis
(b) y-axis
(c) origin
(d) quadrant

Answer: (c) origin

The point where the x-axis and y-axis meet is called the origin.

Q2. The degree of the polynomial 7x + 3 is:

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

Answer: (b) 1

The highest power of x is 1, so 7x + 3 is a linear polynomial.

Q3. Which of the following is an irrational number?

(a) 3/5
(b) 0.25
(c) √2
(d) −7

Answer: (c) √2

√2 cannot be written in the form p/q, where p and q are integers and q ≠ 0.

Q4. The identity (a + b)² is equal to:

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

Answer: (c) a² + 2ab + b²

This is a standard algebraic identity.

Q5. If the radius of a circle is 7 cm, its circumference is:

(a) 14π cm
(b) 7π cm
(c) 49π cm
(d) 21π cm

Answer: (a) 14π cm

Circumference = 2πr = 2π × 7 = 14π cm.

Q6. If a coin is tossed once, the probability of getting a head is:

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

Answer: (b) 1/2

There are two equally likely outcomes: head and tail. So, the probability of getting a head is 1/2.

Coordinate Geometry and Number System Questions

These Class 9 Maths important questions test plotting, distance, midpoint and number classification.

Q7. What does plotting a point mean in coordinate geometry?

Plotting a point means marking its exact position on the Cartesian plane using its x-coordinate and y-coordinate.

For example, the point (3, 2) is 3 units to the right of the origin and 2 units above the x-axis.

Q8. Find the distance between A(0, 0) and B(3, 4).

Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]

= √[(3 − 0)² + (4 − 0)²]
= √(9 + 16)
= √25
= 5 units

So, the distance is 5 units.

Q9. Find the midpoint of A(2, 4) and B(6, 8).

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

= ((2 + 6)/2, (4 + 8)/2)
= (8/2, 12/2)
= (4, 6)

So, the midpoint is (4, 6).

Q10. Explain why every integer is a rational number.

A rational number can be written in the form p/q, where p and q are integers and q ≠ 0.

Every integer can be written with denominator 1.
For example, 7 = 7/1 and −5 = −5/1.

So, every integer is a rational number.

Algebra Questions from Class 9 Maths

Algebra questions in Class 9 Maths solutions usually need expansion, factorisation, zeros of polynomials and simplification.

Q11. What is a linear polynomial?

A polynomial of degree 1 is called a linear polynomial.

For example, 3x + 5 is a linear polynomial because the highest power of x is 1.

Q12. Find the zero of the polynomial p(x) = 2x − 8.

To find the zero, put p(x) = 0.

2x − 8 = 0
2x = 8
x = 4

So, the zero of the polynomial is 4.

Q13. Expand (x + 5)².

Using (a + b)² = a² + 2ab + b²,

(x + 5)² = x² + 2(x)(5) + 5²
= x² + 10x + 25

So, the expansion is x² + 10x + 25.

Q14. Expand (2x − 3)².

Using (a − b)² = a² − 2ab + b²,

(2x − 3)² = (2x)² − 2(2x)(3) + 3²
= 4x² − 12x + 9

So, the expansion is 4x² − 12x + 9.

Q15. Factorise x² − 16.

x² − 16 = x² − 4²

Using a² − b² = (a − b)(a + b),

x² − 16 = (x − 4)(x + 4)

Q16. Simplify (a + b)² − (a − b)².

(a + b)² = a² + 2ab + b²
(a − b)² = a² − 2ab + b²

Now,

(a + b)² − (a − b)²
= (a² + 2ab + b²) − (a² − 2ab + b²)
= 4ab

So, the simplified form is 4ab.

Q17. Factorise x² + 7x + 12.

We need two numbers whose product is 12 and sum is 7.

The numbers are 3 and 4.

x² + 7x + 12
= x² + 3x + 4x + 12
= x(x + 3) + 4(x + 3)
= (x + 3)(x + 4)

Geometry Questions from Class 9 Maths

Geometry questions test definitions, diagrams and reasoning. Students should draw rough figures wherever needed.

Q18. What is a chord of a circle?

A chord is a line segment that joins any two points on a circle.

The diameter is the longest chord because it passes through the centre.

Q19. What is the relation between radius and diameter?

The diameter of a circle is twice its radius.

Diameter = 2 × Radius

If radius = r, then diameter = 2r.

Q20. A circle has radius 10 cm. Find its diameter.

Diameter = 2r
= 2 × 10
= 20 cm

So, the diameter is 20 cm.

Q21. Why is the diameter the longest chord of a circle?

A chord joins two points on a circle.

The diameter passes through the centre and covers the maximum possible distance between two points on the circle. Therefore, it is the longest chord.

Q22. What is an arc of a circle?

An arc is a part of the circumference of a circle.

It is formed between two points on the circle.

Mensuration Questions on Perimeter and Area

Mensuration questions need correct formulas and units. Answers for area should use square units such as cm² or m².

Q23. Find the perimeter of a rectangle of length 12 cm and breadth 8 cm.

Perimeter of rectangle = 2(l + b)

= 2(12 + 8)
= 2 × 20
= 40 cm

So, the perimeter is 40 cm.

Q24. Find the area of a triangle with base 10 cm and height 6 cm.

Area of triangle = 1/2 × base × height

= 1/2 × 10 × 6
= 30 cm²

So, the area is 30 cm².

Q25. Find the area of a circle with radius 7 cm.

Area of circle = πr²

= π × 7²
= 49π cm²

Using π = 22/7,

Area = 49 × 22/7
= 154 cm²

So, the area is 154 cm².

Q26. A square has side 9 cm. Find its perimeter and area.

Perimeter of square = 4 × side
= 4 × 9
= 36 cm

Area of square = side²
= 9²
= 81 cm²

So, the perimeter is 36 cm and the area is 81 cm².

Probability and Sequences Questions

Probability and sequences test pattern recognition, logical listing of outcomes and formula use.

Q27. A die is rolled once. Find the probability of getting an even number.

Possible outcomes = {1, 2, 3, 4, 5, 6}

Even outcomes = {2, 4, 6}

Number of even outcomes = 3
Total outcomes = 6

Probability = 3/6 = 1/2

So, the probability is 1/2.

Q28. A bag has 3 red balls and 2 blue balls. One ball is drawn at random. Find the probability of getting a blue ball.

Total balls = 3 + 2 = 5
Blue balls = 2

Probability of blue ball = 2/5

So, the probability is 2/5.

Q29. Find the next three terms of the sequence: 4, 8, 12, 16, …

The sequence increases by 4 each time.

Next three terms are:

20, 24, 28

Q30. Find the 10th term of the arithmetic progression 3, 7, 11, 15, …

First term, a = 3
Common difference, d = 7 − 3 = 4

nth term of an AP = a + (n − 1)d

10th term = 3 + (10 − 1)4
= 3 + 36
= 39

So, the 10th term is 39.

Class 9 Maths Case Based Questions

These Class 9 Maths case based questions connect textbook concepts with situations. Students should read the data first and then solve each part step by step.

Q31. Case-Based Question: Seating Plan on a Coordinate Grid

A school uses a coordinate grid to arrange seats for a quiz competition. The teacher marks the first team at A(2, 3), the second team at B(6, 3), and the third team at C(6, 7).

(a) What is the distance between A and B?
A(2, 3) and B(6, 3) lie on the same horizontal line.

Distance = 6 − 2 = 4 units

(b) What is the distance between B and C?
B(6, 3) and C(6, 7) lie on the same vertical line.

Distance = 7 − 3 = 4 units

(c) What type of angle is formed at B?
AB is horizontal and BC is vertical, so the angle at B is a right angle.

(d) What does this case show about coordinates?
Coordinates help locate positions and study geometric relationships using numbers.

Q32. Case-Based Question: Garden Design

A square garden has side 14 m. A circular fountain of radius 3.5 m is built at the centre.

(a) Find the area of the square garden.
Area = side² = 14² = 196 m²

(b) Find the area of the circular fountain.
Area = πr²
= 22/7 × 3.5 × 3.5
= 38.5 m²

(c) Find the remaining garden area.
Remaining area = 196 − 38.5 = 157.5 m²

(d) Which Class 9 Maths topic is used here?
This question uses mensuration, especially area of square and circle.

Useful Links for Class 9 Maths