CBSE Class 9 Maths Practice Paper 2026-27

20 questions · MCQ · Answer key · A4

A 20-question CBSE Class 9 Maths practice paper for 2026-27 on number systems, polynomials & coordinate geometry. Free to view and print on A4, no login needed; the answer key with worked solutions is below the questions.

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.

  1. Q1.

    √5 is:

    1. (A) Irrational
    2. (B) Rational
    3. (C) Integer
    4. (D) Natural
  2. Q2.

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

    1. (A) 3
    2. (B) 4
    3. (C) √7
    4. (D) 5
  3. Q3.

    Factorise: 27x³ − 8y³

    1. (A) (3x−2y)(9x²+6xy+4y²)
    2. (B) (3x+2y)(9x²−6xy+4y²)
    3. (C) (3x−2y)(9x²−6xy+4y²)
    4. (D) (3x+2y)(9x²+6xy+4y²)
  4. Q4.

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

    1. (A) −1
    2. (B) 0
    3. (C) 1
    4. (D) 3
  5. Q5.

    The decimal expansion of 1/7 is:

    1. (A) Non-terminating repeating
    2. (B) Terminating
    3. (C) Non-terminating non-repeating
    4. (D) Cannot determine
  6. Q6.

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

    1. (A) 0
    2. (B) 8
    3. (C) 10
    4. (D) 12
  7. Q7.

    Point (0, −5) lies on:

    1. (A) x-axis
    2. (B) y-axis
    3. (C) Origin
    4. (D) Quadrant III
  8. Q8.

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

    1. (A) (0, 3)
    2. (B) (2, 0)
    3. (C) (0, 2)
    4. (D) (−2, 0)
  9. Q9.

    Between which two consecutive integers does √50 lie?

    1. (A) 6 and 7
    2. (B) 5 and 6
    3. (C) 8 and 9
    4. (D) 7 and 8
  10. Q10.

    If x+y=7 and xy=12, then x²+y²=?

    1. (A) 25
    2. (B) 13
    3. (C) 37
    4. (D) 49
  11. Q11.

    A cricket practice strip is 3.66 m wide and 22 m long. Its area, in scientific notation correct to 3 significant figures, is:

    1. (A) 8.05 × 10²
    2. (B) 8.05 × 10¹
    3. (C) 8.05 × 10⁰
    4. (D) 80.5 × 10¹
  12. Q12.

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

    1. (A) −2, −3
    2. (B) 1, 6
    3. (C) 2, 3
    4. (D) −1, −6
  13. Q13.

    Rationalise: 1/(√5 + √3)

    1. (A) (√5+√3)/2
    2. (B) (√5−√3)/8
    3. (C) 1/(√15)
    4. (D) (√5−√3)/2
  14. Q14.

    In which quadrant does (−4, −9) lie?

    1. (A) III
    2. (B) I
    3. (C) II
    4. (D) IV
  15. Q15.

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

    1. (A) 4x² + 9
    2. (B) 4x² + 12x − 9
    3. (C) 4x² − 9
    4. (D) 4x² − 12x − 9
  16. Q16.

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

    1. (A) 0 < r ≤ b
    2. (B) r = 0
    3. (C) r < 0
    4. (D) 0 ≤ r < b
  17. Q17.

    The product of a non-zero rational number and an irrational number is:

    1. (A) Always rational
    2. (B) Always irrational
    3. (C) Sometimes rational
    4. (D) Always integer
  18. Q18.

    HCF of 132 and 156 using Euclid's algorithm:

    1. (A) 6
    2. (B) 24
    3. (C) 12
    4. (D) 36
  19. Q19.

    The graph of a polynomial cuts the x-axis at 3 distinct points. The number of zeroes of the polynomial is:

    1. (A) 0
    2. (B) 3
    3. (C) 1
    4. (D) 2
  20. Q20.

    Which of these is NOT a real number?

    1. (A) √16
    2. (B) −√7
    3. (C) √(−4)
    4. (D) 0.333...

Answer key and solutions

  1. Q1A√5 cannot be expressed as p/q; it is irrational
  2. Q2DAB = √[(5-2)²+(7-3)²] = √[9+16] = √25 = 5
  3. Q3Aa³−b³=(a−b)(a²+ab+b²); 27x³−8y³=(3x−2y)(9x²+6xy+4y²)
  4. Q4B1 − 3 + 3 − 1 = 0
  5. Q5A1/7 = 0.142857142857... (repeating block of 6 digits)
  6. Q6DRemainder = p(2) = 8 + 12 − 10 + 2 = 12
  7. Q7Bx=0 means the point lies on the y-axis
  8. Q8CAt x=0: y = 3(0)+2 = 2. Point = (0, 2)
  9. Q9D√49 = 7, √64 = 8; so √50 lies between 7 and 8
  10. Q10Ax²+y² = (x+y)² − 2xy = 49 − 24 = 25
  11. Q11B3.66 × 22 ≈ 80.52 m² ≈ 8.052 × 10¹
  12. Q12Cx² − 5x + 6 = (x−2)(x−3) = 0 → x = 2, 3
  13. Q13DMultiply by (√5−√3)/(√5−√3): = (√5−√3)/(5−3) = (√5−√3)/2
  14. Q14ABoth negative → Quadrant III
  15. Q15C(a+b)(a−b) = a²−b² = 4x²−9
  16. Q16Dr is remainder; 0 ≤ r < b
  17. Q17BA non-zero rational times an irrational is always irrational, e.g. 2 × √3 = 2√3. (The word non-zero matters: 0 × √2 = 0 is rational.)
  18. Q18C156=132×1+24; 132=24×5+12; 24=12×2+0. HCF=12
  19. Q19BNumber of zeroes = number of points where graph cuts/touches x-axis = 3
  20. Q20C√(−4) is imaginary/complex, not real

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Frequently asked questions

How does the CBSE Class 9 marking scheme work for MCQ sections?

In CBSE Class 9 annual exams, Section A typically contains 20 MCQ questions worth 1 mark each — no negative marking. This practice set gives you 20 MCQs in that style, scored here at 4 marks each (80 in all). Understanding the marking scheme helps students make strategic decisions: attempt all questions, eliminate options systematically, and never leave MCQs blank since there is no penalty for wrong answers.

Which Class 9 topics carry the most weight in the CBSE annual exam?

Number systems and polynomials together form a significant portion of the Class 9 paper, as they underpin most of the remaining units. Coordinate geometry is also a high-yield topic. This practice paper covers all three, giving students a quick diagnostic before they go deeper into exam preparation.

Should a Class 9 student start preparing for Class 10 boards now?

Yes — about 60% of the Class 10 CBSE syllabus builds directly on Class 9 topics. Students who master Class 9 thoroughly find Class 10 significantly more manageable. Use this paper as a Class 9 checkpoint; Vybd can then generate targeted papers to close any gaps before Class 10 begins.

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