C
CraftExam

CBSE Class 9 Mathematics Sample Paper

Marks:
40
Time:
1½ Hours
Questions:
19
Chapters:
8
Session:
2026-27
Class_9_Mathematics_Sample_Paper_CraftExam.pdfA4 · Set A

Academic Session 2026-27

SAMPLE PAPER

MATHEMATICS

Class IX

Time Allowed1½ HoursMaximum Marks40SetA

Assessment: CBSE-Aligned School Assessment

Marks Distribution

SectionQuestion TypeMarks
AMCQs (10×1)10
BShort Answer (6×3)18
CLong Answer (2×5)10
DCase Study (2×1)2

General Instructions

  1. 1.This question paper has 4 sections.
  2. 2.Marks are shown beside each question.
  3. 3.Read each section instruction carefully.
  4. 4.Attempt only one alternative where internal choice is given.

SECTION A — Objective Type Questions (1×10=10)

Q1 to Q10 are Multiple Choice Questions. Choose the correct option.

Q1. A toy car wheel has radius 3.5 cm. If it makes 10 complete rotations, how far does the wheel move forward? Use π = 22/7.
(1)
  1. (a)22 cm
  2. (b)220 cm
  3. (c)110 cm
  4. (d)385 cm2
Q2. A student says, "A circle has many lines of symmetry, but not infinitely many, because we can draw only a few neatly in a notebook." What is the best correction?
(1)
  1. (a)There are infinitely many lines of symmetry because infinitely many diameters can pass through the centre.
  2. (b)There are exactly four lines of symmetry because the circle can be divided into four equal quarters.
  3. (c)There are exactly two lines of symmetry because one horizontal and one vertical diameter are enough.
  4. (d)There are many lines of symmetry only when the circle is large enough to draw them clearly.
Q3. A medicine in the body reduces to half of its amount every hour. If the initial amount is 80 mg, which model should be used to find the amount after 6 hours?
(1)
  1. (a)AP, because the amount decreases as time passes.
  2. (b)AP with d = -40, because the first decrease is 40 mg.
  3. (c)GP with a = 80 and r = 1/2, using the repeated halving pattern.
  4. (d)GP with a = 40 and r = 1/2, because the first hour amount becomes 40 mg.
Q4. While finding the distance between M(-5, 3) and N(1, -5), Arjun writes the x-difference as 1 - 5. What correction should be made?
(1)
  1. (a)It should be 1 - (-5), so the x-difference is 6.
  2. (b)It should be -5 - 1, so the x-difference must stay negative.
  3. (c)It should be 1 + 5 only if the y-coordinates are also positive.
  4. (d)It should be found by adding all four coordinates first.
Q5. Two coins are tossed together. Which list can be used as the complete sample space?
(1)
  1. (a){H, T}
  2. (b){HH, TT}
  3. (c){HH, HT, TH, TT}
  4. (d){HT, TH}
Q6. In a class discussion, one student says 4/9 is rational but 9/4 is not, because 9/4 is greater than 1. How should the class respond?
(1)
  1. (a)The student is right because rational fractions must be less than 1.
  2. (b)The student is right because the numerator cannot be greater than the denominator.
  3. (c)The student is wrong because 9/4 is also in p/q form with a non-zero denominator.
  4. (d)The student is wrong only because 9/4 can be rounded to 2.
Q7. A graph contains the points (-2, 4), (0, 4), and (5, 4). Which equation fits this line?
(1)
  1. (a)x = 4
  2. (b)y = 4
  3. (c)x + y = 4
  4. (d)y = x + 4
Q8. Meena sees the statement m2-9 = (m-3)(m + 3). Her friend says it is true only when m = 3 or m = -3. How should Meena correct this?
(1)
  1. (a)It is true for all allowed values of m because the right side expands to m2-9.
  2. (b)It is true only for m = 3 and m = -3 because those numbers make one factor zero.
  3. (c)It is true only for positive values of m because squares are positive.
  4. (d)It is false because a product form and an expanded form cannot be equal.
Q9. A game counter was drawn from a bag 75 times with replacement. The results were: green 24, blue 21, red 18, yellow 12. What is the experimental probability of drawing either green or blue from these trials?
(1)
  1. (a)45/75
  2. (b)2/4
  3. (c)24/75
  4. (d)30/75
Q10. A line is drawn parallel to the x-axis and passes through the point (2, 7). What is the equation of this line?
(1)
  1. (a)y = 7
  2. (b)x = 2
  3. (c)y = 2
  4. (d)x = 7

SECTION B — Short Answer Questions (3×6=18)

Q11 to Q16 are Short Answer Questions.

Q11. A triangular plot has sides 12 m, 16 m and 20 m. Find its area using Heron's formula and verify whether the answer is reasonable for a right triangle.
(3)
Q12. A school ground is marked using two perpendicular paths meeting at a flag post. A dustbin is 8 m east and 3 m north of the flag post. Write its coordinates if east is taken as the first direction and north as the second. Also state the reference point.
(3)
Q13. Using algebra tiles, expand (2x + 3)2 and state the area of each region.
(3)
Q14. Find the sum of the first 15 terms of the AP 6, 10, 14, ... .
(3)
Q15. Find three rational numbers between -1 and 0 and justify your answer.
(3)
Q16. A circle is rotated about its centre through 18 degrees, then again through 42 degrees. After the two rotations, does the circle coincide with its original position? Justify.
(3)

SECTION C — Long Answer Questions (5×2=10)

Q17 to Q18 are Long Answer Questions.

Q17. Without fully expanding first, prove by factorisation that n2 + 12n + 36 is divisible by 9 whenever n is a multiple of 3.
(5)
Q18. Prove using the distance formula that the points P(-2, 3), Q(2, 6), R(5, 2) and S(1, -1) form a square.
(5)

OR

Q18. A school notice board has a triangular design painted on it. The lower edge of the triangle is 2.4 m long, and the perpendicular distance from the opposite vertex to this edge is 1.5 m. Paint costs Rs 60 per square metre. Find the area of the triangular design and the total cost of painting it.
(5)

SECTION D — Case-Based Questions (1×2=2)

Q19 is a case-based question. Read the case carefully and answer the sub-questions.

Q19

During a Mathematics activity in a Jaipur school, three groups measured the sides of square tiles marked as x cm, y cm and 2 cm. The teacher asked them to imagine placing the three lengths together to form one longer side and then finding the area of the big square. One group wrote only x2 + y2 + 4 + 2xy, while another group included all pairwise products. The class discussed which expression correctly represents (x + y + 2)2.
(i) Which two double-product terms are missing from the expression x2 + y2 + 4 + 2xy for (x + y + 2)2?
(1)
(ii) Write the correct expansion of (x + y + 2)2.
(1)

End of Question Paper