Class 9 Maths Extra Questions 2026–27

Class 9 Maths Extra Questions provide additional practice in coordinates, algebra, numbers, circles, mensuration, probability and sequences. The questions follow the CBSE 2026–27 Ganita Manjari Part I chapter structure and focus on reasoning, calculation and application.

Ganita Manjari introduces deeper mathematical reasoning, visualisation and problem-solving in Class 9. Students need to explain methods, identify patterns and apply concepts instead of memorising formulas alone.

These Class 9 Maths Extra Questions cover all eight chapters through MCQs, short calculations, reasoning problems and case-based questions. Solve each question independently before checking the given answer.

Key Takeaways

• 8 chapters: Ganita Manjari Part I contains eight chapters in the current Class 9 Maths book.
• Core skills: Questions test reasoning, visualisation, calculation, modelling and mathematical communication.
• Question formats: The practice set includes MCQs, short answers, long calculations and case-based questions.
• Answer method: Numerical answers show the formula, substitution and final result.

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Ganita Manjari Class 9 Maths Extra Questions Chapter List

Ganita Manjari Part I begins with coordinates and algebra before moving to geometry, mensuration, probability and sequences.

Class 9 Maths MCQ Ganita Manjari

These MCQs test definitions, formulas and quick concept identification across the eight chapters.

Q1. In which quadrant does the point (−4, 3) lie?

(a) First quadrant
(b) Second quadrant
(c) Third quadrant
(d) Fourth quadrant

Answer: (b) Second quadrant

The x-coordinate is negative and the y-coordinate is positive.

Q2. Which expression is a linear polynomial in x?

(a) 3x² + 2
(b) 5x − 7
(c) 1/x + 4
(d) x³ − 1

Answer: (b) 5x − 7

The highest power of x is 1.

Q3. Which number is irrational?

(a) 0.125
(b) −6
(c) √11
(d) 7/9

Answer: (c) √11

√11 cannot be written as p/q, where q ≠ 0.

Q4. The factorised form of x² − 25 is:

(a) (x − 5)²
(b) (x + 5)²
(c) (x − 5)(x + 5)
(d) x(x − 25)

Answer: (c) (x − 5)(x + 5)

Use a² − b² = (a − b)(a + b).

Q5. A line joining the centre of a circle to a point on the circle is called:

(a) Chord
(b) Radius
(c) Diameter
(d) Arc

Answer: (b) Radius

Q6. The probability of an impossible event is:

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

Answer: (a) 0

Q7. The common difference of 5, 9, 13, 17, … is:

(a) 3
(b) 4
(c) 5
(d) 8

Answer: (b) 4

Each term is obtained by adding 4.

Coordinates, Polynomials and Number Questions

These NCERT Class 9 Maths Extra Questions cover the first three Ganita Manjari chapters.

Q8. Plotting a point requires which two values?

Answer: Plotting a point requires its x-coordinate and y-coordinate.

In (x, y), x shows horizontal movement and y shows vertical movement from the origin.

Q9. Find the distance between A(2, 3) and B(8, 3).

Answer:

Both points have the same y-coordinate, so the segment is horizontal.

Distance = |8 − 2|
= 6 units

Q10. Find the midpoint of P(−2, 4) and Q(6, 8).

Answer:

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

= ((−2 + 6)/2, (4 + 8)/2)

= (4/2, 12/2)

= (2, 6)

Q11. Find the value of p(x) = 4x − 5 when x = 3.

Answer:

p(3) = 4(3) − 5
= 12 − 5
= 7

Q12. The temperature in Fahrenheit is given by F = 9C/5 + 32. Find F when C = 20.

Answer:

F = 9C/5 + 32

F = 9(20)/5 + 32

F = 36 + 32

F = 68°F

Q13. Explain why 0.375 is a rational number.

Answer:

0.375 is a terminating decimal.

0.375 = 375/1000

= 3/8

It can be written as p/q, where p and q are integers and q ≠ 0. Therefore, it is rational.

Q14. Is the sum of a rational number and an irrational number always irrational?

Answer: Yes.

Suppose r is rational and x is irrational. If r + x were rational, then:

x = (r + x) − r

The difference of two rational numbers would be rational. This contradicts the fact that x is irrational.

Therefore, r + x is irrational.

Algebraic Identities and Circle Questions

These questions test expansion, factorisation and the relationships between different parts of a circle.

Q15. Expand (2x + 3)².

Answer:

Use (a + b)² = a² + 2ab + b².

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

Q16. Factorise 9y² − 16.

Answer:

9y² − 16 = (3y)² − 4²

Use a² − b² = (a − b)(a + b).

9y² − 16 = (3y − 4)(3y + 4)

Q17. Evaluate 103² using an algebraic identity.

Answer:

103² = (100 + 3)²

= 100² + 2(100)(3) + 3²

= 10,000 + 600 + 9

= 10,609

Q18. A circle has radius 6 cm. Find its diameter.

Answer:

Diameter = 2 × radius

= 2 × 6

= 12 cm

Q19. A chord passes through the centre of a circle. What is the chord called?

Answer: It is called a diameter.

The diameter is the longest chord of a circle.

Q20. Why are all radii of the same circle equal?

Answer: Every radius joins the fixed centre to a point on the same circle.

All points on a circle are at the same distance from its centre. Therefore, all its radii are equal.

Mensuration, Probability and Sequence Questions

These Class 9 Maths Extra Questions with Answers cover Chapters 6, 7 and 8.

Q21. Find the perimeter and area of a rectangle measuring 12 cm by 7 cm.

Answer:

Perimeter = 2(l + b)

= 2(12 + 7)

= 38 cm

Area = l × b

= 12 × 7

= 84 cm²

Q22. Find the area of a triangle with base 15 cm and height 8 cm.

Answer:

Area = 1/2 × base × height

= 1/2 × 15 × 8

= 60 cm²

Q23. Find the circumference of a circle with radius 7 cm. Use π = 22/7.

Answer:

Circumference = 2πr

= 2 × 22/7 × 7

= 44 cm

Q24. A coin is tossed 80 times and shows heads 46 times. Find the experimental probability of getting heads.

Answer:

Experimental probability = Number of heads/Total tosses

= 46/80

= 23/40

Q25. A bag contains five red, three blue and two green balls. Find the probability of drawing a blue ball.

Answer:

Total balls = 5 + 3 + 2

= 10

Number of blue balls = 3

P(blue) = 3/10

Q26. Find the 15th term of the arithmetic progression 4, 7, 10, 13, …

Answer:

First term, a = 4

Common difference, d = 3

nth term = a + (n − 1)d

15th term = 4 + (15 − 1)(3)

= 4 + 42

= 46

Q27. Identify the pattern and write the next two terms: 3, 6, 12, 24, …

Answer: Each term is multiplied by 2.

Next term = 24 × 2 = 48

Term after that = 48 × 2 = 96

The next two terms are 48 and 96.

Class 9 Maths Competency-Based Questions

These questions require students to select concepts, organise information and explain their reasoning.

Q28. A taxi charges ₹50 as a fixed amount and ₹12 per kilometre. Write an expression for a journey of x kilometres. Find the charge for 15 km.

Answer:

Fixed charge = ₹50

Distance charge = ₹12 per kilometre

Total charge = 12x + 50

For x = 15:

Total charge = 12(15) + 50

= 180 + 50

= ₹230

Q29. A square and a rectangle have the same perimeter. The square has side 8 cm. The rectangle has length 10 cm. Find its breadth.

Answer:

Perimeter of square = 4 × side

= 4 × 8

= 32 cm

Perimeter of rectangle = 2(l + b)

32 = 2(10 + b)

16 = 10 + b

b = 6 cm

Q30. A student claims that √4 is irrational because it contains a square-root sign. Is the claim correct?

Answer: No.

√4 = 2

The number 2 can be written as 2/1. Therefore, it is rational.

A square-root sign does not always represent an irrational number.

Class 9 Maths Case-Based Questions

Q31. Case Study: Locating Places on a Map

A school is represented by S(2, 3), a library by L(8, 3) and a park by P(8, 9).

(a) Find the distance between the school and library.

SL = |8 − 2| = 6 units

(b) Find the distance between the library and park.

LP = |9 − 3| = 6 units

(c) What type of angle is formed at L?

SL is horizontal and LP is vertical.

Therefore, ∠SLP = 90°.

It is a right angle.

Q32. Case Study: Circular Running Track

A circular running track has radius 14 m. A student completes two full rounds.

(a) Find the distance covered in one round.

Circumference = 2πr

= 2 × 22/7 × 14

= 88 m

(b) Find the distance covered in two rounds.

Distance = 2 × 88

= 176 m

(c) Which concept is used?

The question uses the circumference of a circle.

Q33. Case Study: Growing Savings

Riya saves ₹100 in the first month, ₹150 in the second month and ₹200 in the third month. She continues the same pattern.

(a) Identify the sequence.

100, 150, 200, …

It is an arithmetic progression.

(b) Find the common difference.

d = 150 − 100

= ₹50

(c) Find her saving in the tenth month.

a₁₀ = a + (n − 1)d

= 100 + 9(50)

= ₹550

Class 9 Maths Formulas for Extra Questions

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