Punjab School Education Board (PSEB)
Class VIII – Mathematics
Model Test Paper / Sample Question Paper
Session 2025–26
Student Name: ___________________________
Roll Number: ___________________________
School Name: ___________________________
Time Allowed: 3 Hours
Maximum Marks: 80
Instructions
All questions are compulsory.
Use of calculator is not permitted.
Draw neat and labelled diagrams wherever required.
Write answers clearly and legibly.
Use blue or black ink only.
Prepared for Exam Practice and Revision
Based on PSEB Exam Pattern 2025–26
Class – VIII
Subject – Mathematics
Time: 3 Hours M.M: 80
Part – A (Multiple Choice Questions)
(20 × 1 = 20)
1. The multiplicative identity of rational number ‘a’ is
(a) 1
(b) 0
(c) 1/a
(d) −a
2. The additive identity of 2/3 is
(a) 0
(b) −2/3
(c) −2/3
(d) 3/2
3. Value of x in 3x + 4 = x − 6 is
(a) −1
(b) 2/3
(c) −13/3
(d) −5
4. Which of the following is not a quadrilateral?
(a) Square
(b) Rectangle
(c) Triangle
(d) Parallelogram
5. If adjacent angles of a rhombus are equal then which polygon it will become
(a) Rectangle
(b) Square
(c) Trapezium
(d) Parallelogram
6. Tally marks are used to find which of the following
(a) Frequency
(b) Lower limits
(c) Upper limits
(d) None of these
7. The square of a proper fraction is
(a) Less than the fraction
(b) Greater than the fraction
(c) Equal to the fraction
(d) None of these
8. What will be number of digits in square root of 676?
(a) 1
(b) 2
(c) 3
(d) 4
9. Find 7³ − 6³
(a) 127
(b) 397
(c) 1141
(d) 200
10. In case of simple and compound interest for a period more than one year
(a) S.I = C.I
(b) C.I > S.I
(c) S.I = C.I
(d) None of these
11. Out of given expressions which are like terms?
(a) 7x and 7y
(b) 3x and 3x²
(c) x² and 3x²
(d) x³ + 3
12. To multiply (2x − 3)(2x + 5), identify the identity that should be used
(a) (a + b)(a − b) = a² − b²
(b) (a + b)² = a² + 2ab + b²
(c) (x + a)(x + b) = x² + (a + b)x + ab
(d) (a − b)² = a² − 2ab + b²
13. Lateral surface area of cube is
(a) 6l²
(b) 5l²
(c) 4l²
(d) 2l²
14. Area of triangle with base (b) and height (h) is
(a) bh
(b) ½ bh
(c) 2bh
(d) None of these
15. Value of (5³)⁴ is
(a) 5⁷
(b) 5¹²
(c) 5⁻¹
(d) 5⁸
16. Usual form of 3.2805 × 10⁻⁴ is
(a) 302805
(b) 32805
(c) 0.32805
(d) 0.00032805
17. If the cost of 5 pencils is ₹15. Find the cost of 12 such pencils
(a) ₹15
(b) ₹18
(c) ₹36
(d) ₹24
18. (a + b)² − (a − b)² =
(a) −4ab
(b) 2a + 2b
(c) 2a − 2b
(d) 4ab
19. Common factor of 10xy and 12y is
(a) 10x
(b) 2xy
(c) 2y
(d) 2x
20. The point (1, 0) lies on
(a) x-axis
(b) y-axis
(c) origin
(d) none
Part – B
(7 × 2 = 14)
2. Solve:
9/10 × (−15/27) × 18/−5
3. In a class, there are 15 girls and 12 boys, one student is selected as a monitor. Find the probability that monitor is:
(i) a boy
(ii) a girl
4. Find the smallest number by which the following number must be divided to obtain a perfect cube:
2187
5. Find the amount which Ram will get on Rs. 4096, if he gave it for 18 months at 12½% per annum, half-yearly.
6. Multiply the binomials:
(a + 3b) and (x + 5)
7. Find the area of the quadrilateral given below in figure.
8. Find the value of:
(8² × 2⁴) + 2⁴
Part – C
(7 × 4 = 28)
9. Solve:
(3a / 4) − (a − 1) / 2 = (a − 1) / 3
10. In figure PQRS is a parallelogram. Find the values of x, y and z.
OR
In the given figure, ABCD is a rectangle. If ∠BAC = 36°, find ∠ACB.
11. Write a Pythagorean triplet whose one number is 8.
OR
Find the least number which when subtracted from 1308, it becomes a square number. Also find the square root of the number.
12. Add:
2xy + y + z and 3y (x² − xy + xz)
Then subtract from 5x (xy + y² − 4yz).
13. A machine in a factory fills 680 bottles in 5 hours. How many bottles will it fill in 3 hours?
14. Factorise the following:
9p² + 24pm − 16m²
OR
Show the following as a sum of two consecutive numbers:
21²
Part – D
(3 × 6 = 18)
15. Draw the graph of the following:
| Side of square (in cm) | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Area (in cm²) | 9 | 16 | 25 | 36 | 49 |
Is it a linear graph?
16. Draw Histogram of the following:
| Marks | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 |
|---|---|---|---|---|---|---|
| No. of Students | 6 | 9 | 12 | 8 | 10 | 5 |
OR
In a hostel number of students using different languages are as follows:
| Language | No. of Students |
|---|---|
| Hindi | 10 |
| Punjabi | 30 |
| English | 12 |
| Marathi | 9 |
| Tamil | 7 |
| Bengali | 4 |
| Total | 72 |
17. Population of town is 1,50,000. The annual birth rate is 5% and mortality rate is 3%. Find the population after 2 years.
OR
Find the compound interest on Rs. 14000 for 2 years at 10% per annum, compounded annually.
18. A road roller takes 950 complete revolutions to move once over to level a road. Find the area of road levelled if the diameter of road roller is 84 cm and length is 1 m.
OR
A cylinder is formed with a rectangular sheet of size 11 cm × 4 cm, having height 4 cm without overlapping. Find the volume of the cylinder.
