CBSE Class 8 Mathematics Sample Paper | ZERO PERIOD

PRAMOD SHARMA October 17, 2026 0 Comments

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Sample Paper - CBSE Class VIII Mathematics

Time: 3 Hours  |  MM: 80

Section - A

Each question carries 1 mark
In the questions 1 to 18, choose the correct options.

1. Which of the following is not a linear equation with one variable?
(a) 3x + 4/9 = -8     (b) z + 1 = 3z + 8
(c) 2x - 3x(x - 1) = 0     (d) 2y - 3(y + 8) = 0

2. ABCD is a quadrilateral. If all sides are equal, then what type of quadrilateral is ABCD?
(a) A Square     (b) A rectangle
(c) A parallelogram     (d) A rhombus / none of these

3. The product of 6r and 7r2 is
(a) 42r4     (b) 42r3
(c) 48r3     (d) 48r4

4. The side of a square is a. What will be its area if its side is doubled?
(a) a2 sq. cm     (b) 4a4 sq. cm
(c) 4a2 sq. cm     (d) none of these

5. Exponential form of (-125 / 343) is
(a) (-5 / 17)3     (b) (-5 / 7)3
(c) 25 / 7     (d) (-5 / 7)4

6. The factors of ab - a - b + 1 are
(a) (a - 1)(b - 1)     (b) (a - 1)(1 - b)
(c) (1 - a)(1 - b)     (d) (1 - a)(b - 1)

7. Which of the following vary inversely with each other?
(a) Speed and distance covered, keeping the time constant
(b) Distance covered and taxi fare
(c) Distance travelled and time taken, keeping the speed same
(d) Speed and time taken, keeping distance same

8. Which of the following co-ordinates lie on the x-axis
(a) (3, 0)     (b) (0, 3)
(c) (2, 1)     (d) (1, 2)

9. The solution of the equation 5x - 11 = x + 9 is
(a) 2     (b) 0     (c) 5     (d) -5

10. The sum of the interior angles of a regular pentagon is
(a) 180°     (b) 360°     (c) 540°     (d) none of these

11. If the length, breadth and height of a cuboid are pq, 2r and 3qr then its volume is
(a) 5pqr2     (b) 6pqr2
(c) 6p2q2r2     (d) 6pq2r2

12. If the length of two diagonals of a rhombus are 8 m and 14 m, then its area is
(a) 56 m2     (b) 122 m2
(c) 28 m2     (d) 80 m2

13. Standard form of 0.0000000085 is
(a) 8.5 × 109     (b) 8.5 × 10-9
(c) 85 × 1010     (d) 0.85 × 108

14. If a and b vary directly, then the constant of variation is given by
(a) ab     (b) a / b     (c) a2b2     (d) None of these

15. One of the factors of x2 - 9 is
(a) x2 - 3     (b) 3 - x     (c) x(x - 3)     (d) x - 3

16. If the capacity of a cubical pot is 1000 litre, then the length of its edge is
(a) 1 m.     (b) 1 cm     (c) 10 m     (d) 1000 cm

17. Multiplicative inverse of (2 / 3)2 is
(a) (-2 / 3)2     (b) (3 / 2)2     (c) (-2 / -3)2     (d) (3 / 2)-2

18. A graph that displays data that changes continuously over period of time is called a
(a) Bar graph     (b) Pie Graph     (c) Histogram     (d) Line Graph

In the questions 19 to 20, a statement of assertion followed by a statement of reason is given. Choose the correct answer out of the following choices:
(a) Both Assertion and Reason are true, and Reason is correct explanation of the Assertion.
(b) Both Assertion and Reason are true, but Reason is not the correct explanation of the Assertion.
(c) Assertion is true, but Reason is false.
(d) Assertion is false, but Reason is true.

19. Assertion: (x + 5)(x + 2) = x2 + 7x + 10
Reason: (x + a)(x + b) = x2 + (a + b)x + ab

20. Assertion: Factors of ax2 + bx are x(a + b)
Reason: Factorisation is defined as expressing a number or an algebraic expression as a product of its irreducible factors.

Section - B

Each question carries 2 marks

  1. Solve the equation: 5x + 9 = 5 + 3x
  2. Find the area of a trapezium whose parallel sides are 38 cm and 12 cm, the perpendicular distance between them is 4 cm.
    OR
    Find the perimeter of an equilateral triangle of side 4.5 cm.
  3. Find the value of x, y and z in the given parallelogram.
  4. Find the factors of 15xy - 6x + 5y - 2.
  5. Factorise: p2 + 6p + 8
    OR
    Using the identity find the factors of m4 - 12m2 + 36

Section - C

Each question carries 3 marks

  1. Simplify the expression (a - b)(a2 + b2 + ab) and find the value, if a = -2, b = -1
    OR
    Simplify using identity (4c - 5d)2
  2. Simplify, using laws of exponents: (3-5 × 25 × 52) / (9-3 × 53)
  3. 30 persons can reap a field in 17 days. How many more persons should be employed to reap the same field in 10 days?
  4. Find the value of x: (5 / 6)4 × (5 / 6)7 = (5 / 6)2x+1
    OR
    Evaluate the following expression
    [a × 4(2a) × x2] / 3
    for a = 2
  5. A photograph of bacteria enlarged 60,000 times attains a length of 6 cm. What is the actual length of the bacteria? If the photograph is enlarged 40,000 times only, what would be the enlarged length?
  6. Solve and check the solution: 3(t - 3) = 5(2t + 1)

Section - D

Each question carries 5 marks

  1. Solve using identities: (a) 101 × 99     (b) (104)2
    OR
    (a) Simplify: (7m - 8n)2 + (7m + 8n)2
    (b) The perimeter of the triangle is x4 + 5x2 - 2x + 7 and the sum of its two sides is x3 + 4x2 + 2x - 1, find its third side.
  2. (a) How many cubes of side 3 cm can be cut from a solid cuboid whose length, breadth and height are 21 cm, 9 cm and 5 cm respectively?
    (b) A right circular cylinder has base radius 7 m and height 35 m. Find the curved surface area of the cylinder.
    OR
    (a) Find the cost of plastering four walls and ceiling of room of dimension 6m by 4m by 10 m at the rate of 120 per m2.
    (b) Find the height of a cylinder whose volume is 8316 cm³ and diameter of the base is 42 cm.
  3. (a) Divide (2x2 + 4x + 8) ÷ (x + 2)
    (b) Find the factors of p2 + 9p + 20
  4. The given table gives the quantity of petrol and its cost. Draw a line graph to represent the data.
    Quantity of petrol (in Litres) 581218
    Cost of petrol (in ₹) 150240360540
    Answer the following questions from the graph:
    (a) The quantity of petrol which can be purchased for ₹300.
    (b) Find the cost of 15 litres of petrol.

Section - E

Each question carries 4 marks

  1. A quadrilateral is a two dimensional closed polygon with four sides, four vertices and four angles...
    (a) How many diagonals are there in an octagon? [1]
    (b) If each interior angle of a regular polygon is 156° then, find the number of sides of the polygon. [1]
    (c) Find the number of diagonals in a pentagon. [2]
    OR
    (c) Two adjacent angles of a parallelogram are in the ratio 4:5. Find the measure of all the angles of the parallelogram. [2]
  2. Mensuration is the branch of mathematics that studies the measurement of geometric figures...
    (a) Find the breadth of a rectangle whose length is 120 cm and perimeter is 400 cm [1]
    (b) Calculate the area of a parallelogram whose base is 10 cm and height is 5 cm. [1]
    (c) Find the area of a trapezium whose parallel sides are 5cm and 7cm and distance between their parallel sides is 7 cm. [2]
    OR
    (c) Find the edge of a cube whose surface area is 2400 cm². [2]
  3. Direct proportion means when one quantity increases, the other also increases...
    (a) Find x2 if x and y vary directly (x: 36, x2 | y: 6, 4) [1]
    (b) Find b2 if a and b vary inversely (a: 14, 6 | b: 3, b2) [1]
    (c) Cost of 5 identical gift hampers is 1250. What will be the cost of 8 gift hampers? [2]
    OR
    (c) 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? [2]

08/MAT/Prepared by Pramod Sharma | Page 1 of 4

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