This free CBSE Class 9 Maths sample paper 2026-27 covers the foundational topics of the pre-board year: number systems including irrational numbers and their representation, polynomials and the remainder and factor theorems, introduction to coordinate geometry, and properties of triangles with congruence criteria. Class 9 is the year CBSE shifts to formal examinations with defined marking schemes — developing exam-writing skills now is just as important as mastering content. The 20 MCQ questions in this paper mirror the section-A style questions seen in CBSE Class 9 annual papers, making this a practical warm-up for school exams. The answer key explains every solution in terms of the relevant theorem or rule — helping students learn to justify their answers, not just find them. Free and A4-printable.
✅ 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
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 paper mirrors that format exactly. 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 and triangles are also high-yield topics. This sample paper covers all four, giving students a balanced 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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