Grade 8 PECTAA Mathematics Model Paper 2026-27

1. Which of the following is an example of a rational number? (1.00 marks)

1. √5
2. π
3. 3/4
4. e

Correct answer: C — 3/4

2. Identify the irrational number among the options. (1.00 marks)

1. 0.25
2. √7
3. √16
4. -3

Correct answer: B — √7

3. What is the absolute value of 6? (1.00 marks)

1. -6
2. 6
3. 0
4. 1

Correct answer: B — 6

4. Find the multiplicative inverse of 2. (1.00 marks)

1. -2
2. 2
3. 1/2
4. -1/2

Correct answer: C — 1/2

5. Round 15.6389 to two decimal places. (1.00 marks)

1. 15.63
2. 15.64
3. 15.65
4. 15.66

Correct answer: B — 15.64

6. Approximate -43.549 to one decimal place. (1.00 marks)

1. -43.6
2. -43.5
3. -43.54
4. -43.55

Correct answer: B — -43.5

7. The set of integers is represented by: (1.00 marks)

1. N
2. W
3. Z
4. Q

Correct answer: C — Z

8. List the first four positive even numbers. (1.00 marks)

1. {1, 3, 5, 7}
2. {2, 4, 6, 8}
3. {0, 2, 4, 6}
4. {3, 5, 7, 9}

Correct answer: B — {2, 4, 6, 8}

9. If B = {p,q}, then the power set P(B) is: (1.00 marks)

1. {∅, {p}, {q}, {p,q}}
2. {{p}, {q}}
3. {∅, {p,q}}
4. {{p}, {q}, {p,q}}

Correct answer: A — {∅, {p}, {q}, {p,q}}

10. De-Morgan's law states that (A ∩ B)' equals: (1.00 marks)

1. A ∩ B
2. A' ∩ B'
3. A ∪ B
4. A' ∪ B'

Correct answer: D — A' ∪ B'

11. If set X = {a, b, c} and set Y = {b, c, d}, then X ∩ Y is: (1.00 marks)

1. {a, b, c, d}
2. {b, c}
3. {a, d}
4. {}

Correct answer: B — {b, c}

12. The number of elements in the power set of A = {x, y} is: (1.00 marks)

1. 2
2. 4
3. 3
4. 1

Correct answer: B — 4

13. In the proportion 5 : x :: x : 20, the value of x is: (1.00 marks)

1. 5
2. 10
3. 15
4. 20

Correct answer: B — 10

14. If the price of 8 books is Rs 400, then the price of 12 such books will be: (1.00 marks)

1. Rs 500
2. Rs 600
3. Rs 700
4. Rs 800

Correct answer: B — Rs 600

15. In the proportion a : b :: c : d, the third term is: (1.00 marks)

1. a
2. b
3. c
4. d

Correct answer: C — c

16. A shirt costs Rs 250 and is sold for Rs 200. The discount percent is: (1.00 marks)

1. 10%
2. 20%
3. 30%
4. 40%

Correct answer: B — 20%

17. If a man buys a bike for Rs 70,000 and sells it for Rs 80,000, his profit is: (1.00 marks)

1. Rs 5,000
2. Rs 10,000
3. Rs 15,000
4. Rs 20,000

Correct answer: B — Rs 10,000

18. The formula for the nth term of an arithmetic sequence is: (1.00 marks)

1. an = a1 - (n-1)d
2. an = a1 + (n-1)d
3. an = a1 × d
4. an = a1 / d

Correct answer: B — an = a1 + (n-1)d

19. If an = 3n + 2, then the value of a4 is: (1.00 marks)

1. 10
2. 14
3. 12
4. 16

Correct answer: B — 14

20. The next term in the arithmetic sequence 2, 5, 8, 11, _ is: (1.00 marks)

1. 12
2. 14
3. 15
4. 13

Correct answer: B — 14

21. The sum of interior angles of a triangle is: (1.00 marks)

1. 180°
2. 360°
3. 90°
4. 270°

Correct answer: A — 180°

22. If 3x + 5 = 20, then the value of x is: (1.00 marks)

1. 3
2. 5
3. 7
4. 9

Correct answer: B — 5

23. The quadratic equation with roots 2 and 3 is: (1.00 marks)

1. x^2 - 5x + 6 = 0
2. x^2 + 5x + 6 = 0
3. x^2 - 5x - 6 = 0
4. x^2 + 5x - 6 = 0

Correct answer: A — x^2 - 5x + 6 = 0

24. The median of 3, 5, 7, 9, 11 is: (1.00 marks)

1. 5
2. 7
3. 9
4. 11

Correct answer: B — 7

25. Factorization of a^2 - b^2 is: (1.00 marks)

1. (a + b)(a - b)
2. (a - b)(a - b)
3. (a + b)(a + b)
4. (a^2 + b^2)

Correct answer: A — (a + b)(a - b)

26. The area of a circle with radius r is: (1.00 marks)

1. πr^2
2. 2πr
3. πr
4. 4πr^2

Correct answer: A — πr^2

27. If log_2(8) = x, then x is: (1.00 marks)

1. 2
2. 3
3. 4
4. 5

Correct answer: B — 3

28. The value of sin(90°) is: (sin (1.00 marks)

1. 0
2. 1
3. -1
4. 1/2

Correct answer: B — 1

29. The distance formula between two points (x1, y1) and (x2, y2) is: (1.00 marks)

1. √((x2 - x1)^2 + (y2 - y1)^2)
2. √((x2 + x1)^2 + (y2 + y1)^2)
3. (x2 - x1) + (y2 - y1)
4. (x2 + x1) - (y2 + y1)

Correct answer: A — √((x2 - x1)^2 + (y2 - y1)^2)

30. The sum of first 10 natural numbers is: (1.00 marks)

1. 45
2. 55
3. 50
4. 60

Correct answer: B — 55

31. The slant height of a square pyramid with base side 9 cm and triangular face height 11 cm is: (1.00 marks)

1. 9 cm
2. 10 cm
3. 11 cm
4. 12 cm

Correct answer: C — 11 cm

32. If the radius of a sphere is 4 cm, the volume of the sphere will be: (1.00 marks)

1. (64/3)π cm^3
2. 32π cm^3
3. 48π cm^3
4. (256/3)π cm^3

Correct answer: D — (256/3)π cm^3

33. In a right-angled triangle with legs 7 cm and 24 cm, the hypotenuse is: (1.00 marks)

1. 23 cm
2. 25 cm
3. 26 cm
4. 30 cm

Correct answer: B — 25 cm

34. Identify the pair of congruent figures (SSS congruence): (1.00 marks)

1. Two scalene triangles
2. Two equilateral triangles with side 6 cm
3. Two rectangles
4. Two circles

Correct answer: B — Two equilateral triangles with side 6 cm

35. If ΔABC ≅ ΔDEF, the pair of congruent sides is: (1.00 marks)

1. AB ≅ DF
2. BC ≅ DF
3. AC ≅ DE
4. AB ≅ DE

Correct answer: D — AB ≅ DE

36. A cone has radius 3 cm and height 4 cm; the slant height is: (1.00 marks)

1. 3 cm
2. 4 cm
3. 5 cm
4. 6 cm

Correct answer: C — 5 cm

37. The volume formula of a sphere is: (1.00 marks)

1. (4/3)πr^3
2. 4πr^2
3. (1/3)πr^2h
4. πr^2h

Correct answer: A — (4/3)πr^3

38. The three angles of an equilateral triangle are: (1.00 marks)

1. 45°, 45°, 90°
2. 60°, 60°, 60°
3. 30°, 60°, 90°
4. 40°, 50°, 90°

Correct answer: B — 60°, 60°, 60°

39. The median of the data 3, 7, 9, 9, 12 is: (1.00 marks)

1. 7
2. 9
3. 8
4. 12

Correct answer: B — 9

40. The mode of the data 4, 6, 6, 8, 10 is: (1.00 marks)

1. 4
2. 6
3. 8
4. 10

Correct answer: B — 6