Free CBSE Class 9 Maths Practice Paper | Olympiad Style Sample

Mathematics — Class 9 Practice Paper

Number Systems, Polynomials & Coordinate Geometry

📋 Board: CBSE 📚 Class: 9 ⏱ Time: 60 minutes 🏆 Max Marks: 80 ❓ Questions: 20

Instructions: All questions are compulsory. Each question carries 4 marks. There is no negative marking. Choose the most appropriate option.

Q1.

√5 is:

A) Rational

B) Irrational

C) Integer

D) Natural

Q2.

Arjun plots points A(2,3) and B(5,7). Length of AB?

A) 3

B) 4

C) 5

D) √7

Q3.

Factorise: 27x³ − 8y³

A) (3x−2y)(9x²+6xy+4y²)

B) (3x+2y)(9x²−6xy+4y²)

C) (3x−2y)(9x²−6xy+4y²)

D) (3x+2y)(9x²+6xy+4y²)

Q4.

If p(x) = x³ − 3x² + 3x − 1, then p(1) = ?

A) −1

B) 0

C) 1

D) 3

Q5.

The decimal expansion of 1/7 is:

A) Terminating

B) Non-terminating repeating

C) Non-terminating non-repeating

D) Cannot determine

Q6.

Remainder when x³ + 3x² − 5x + 2 is divided by (x − 2):

A) 0

B) 8

C) 10

D) 12

Q7.

Point (0, −5) lies on:

A) x-axis

B) y-axis

C) Origin

D) Quadrant III

Q8.

The graph of y = 3x + 2 intersects y-axis at:

A) (0, 2)

B) (0, 3)

C) (2, 0)

D) (−2, 0)

Q9.

Between which two consecutive integers does √50 lie?

A) 6 and 7

B) 7 and 8

C) 5 and 6

D) 8 and 9

Q10.

If x+y=7 and xy=12, then x²+y²=?

A) 13

B) 25

C) 37

D) 49

Q11.

Arjun's cricket pitch has area 3.66 × 22 m. In scientific notation, area ≈ ?

A) 8.05 × 10¹

B) 8.05 × 10²

C) 8.05 × 10⁰

D) 80.5 × 10¹

Q12.

Zeroes of polynomial p(x) = x² − 5x + 6:

A) 2, 3

B) −2, −3

C) 1, 6

D) −1, −6

Q13.

Rationalise: 1/(√5 + √3)

A) (√5−√3)/2

B) (√5+√3)/2

C) (√5−√3)/8

D) 1/(√15)

Q14.

In which quadrant does (−4, −9) lie?

A) I

B) II

C) III

D) IV

Q15.

Expand using identity: (2x + 3)(2x − 3)

A) 4x² + 9

B) 4x² − 9

C) 4x² + 12x − 9

D) 4x² − 12x − 9

Q16.

Euclid's Division Lemma: For integers a, b (b>0), a = bq + r where:

A) 0 ≤ r < b

B) 0 < r ≤ b

C) r = 0

D) r < 0

Q17.

The product of a rational and irrational number is:

A) Always rational

B) Always irrational

C) Sometimes rational

D) Always integer

Q18.

HCF of 132 and 156 using Euclid's algorithm:

A) 6

B) 12

C) 24

D) 36

Q19.

The number of zeroes in the polynomial shown in a graph that cuts x-axis at 3 points is:

A) 0

B) 1

C) 2

D) 3

Q20.

Which of these is NOT a real number?

A) √16

B) −√7

C) √(−4)

D) 0.333...

✅ Answer Key & Solutions

Q1 B √5 cannot be expressed as p/q; it is irrational

Q2 C AB = √[(5-2)²+(7-3)²] = √[9+16] = √25 = 5

Q3 A a³−b³=(a−b)(a²+ab+b²); 27x³−8y³=(3x−2y)(9x²+6xy+4y²)

Q4 B 1 − 3 + 3 − 1 = 0

Q5 B 1/7 = 0.142857142857... (repeating block of 6 digits)

Q6 D Remainder = p(2) = 8 + 12 − 10 + 2 = 12

Q7 B x=0 means the point lies on the y-axis

Q8 A At x=0: y = 3(0)+2 = 2. Point = (0, 2)

Q9 B √49 = 7, √64 = 8; so √50 lies between 7 and 8

Q10 B x²+y² = (x+y)² − 2xy = 49 − 24 = 25

Q11 A 3.66 × 22 ≈ 80.52 m² ≈ 8.052 × 10¹

Q12 A x² − 5x + 6 = (x−2)(x−3) = 0 → x = 2, 3

Q13 A Multiply by (√5−√3)/(√5−√3): = (√5−√3)/(5−3) = (√5−√3)/2

Q14 C Both negative → Quadrant III

Q15 B (a+b)(a−b) = a²−b² = 4x²−9

Q16 A r is remainder; 0 ≤ r < b

Q17 C 0 × √2 = 0 (rational); 2 × √3 = 2√3 (irrational). It depends — but non-zero rational × irrational = irrational

Q18 B 156=132×1+24; 132=24×5+12; 24=12×2+0. HCF=12

Q19 D Number of zeroes = number of points where graph cuts/touches x-axis = 3

Q20 C √(−4) is imaginary/complex, not real

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