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VARDAAN LEARNING INSTITUTE

MOCK TEST SERIES - 04 (2025-26)
CLASS: VIII SUBJECT: MATHEMATICS
TIME: 3 HOURS MAX. MARKS: 80
General Instructions:
  1. This question paper contains 38 questions. All questions are compulsory.
  2. The paper is divided into Five Sections: A, B, C, D and E.
  3. Section A: 20 MCQs (1 mark each).
  4. Section B: 5 Questions (2 marks each).
  5. Section C: 6 Questions (3 marks each).
  6. Section D: 4 Questions (5 marks each).
  7. Section E: 3 Case-Based Questions (4 marks each).
  8. Calculators are not allowed.
SECTION A (20 MARKS)
1.
Which of the following is the standard form of 0.00001275?
(a) 1.275 × 10-5 (b) 1.275 × 10-4 (c) 12.75 × 10-5 (d) 127.5 × 10-6
1
2.
If a number is increased by 20% and then decreased by 20%, the net change is:
(a) No change (b) 4% increase (c) 4% decrease (d) 1% decrease
1
3.
The compound interest on ₹ 1000 at 10% p.a. for 2 years is:
(a) ₹ 200 (b) ₹ 210 (c) ₹ 1100 (d) ₹ 1210
1
4.
The value of (xa / xb)a+b × (xb / xc)b+c × (xc / xa)c+a is:
(a) 0 (b) xabc (c) 1 (d) x
1
5.
A polygon has 9 diagonals. The number of sides of the polygon is:
(a) 6 (b) 5 (c) 7 (d) 8
1
6.
Two adjacent angles of a rhombus are (3x - 10)° and (2x + 15)°. The value of x is:
(a) 35 (b) 30 (c) 25 (d) 40
1
7.
The probability of getting a sum of 9 when two dice are thrown simultaneously is:
(a) 1/6 (b) 1/9 (c) 1/12 (d) 4/9
1
8.
If x + 1/x = 4, then x2 + 1/x2 is equal to:
(a) 16 (b) 14 (c) 12 (d) 18
1
9.
The degree of the polynomial 5x2y - 3xy3 + 8 is:
(a) 2 (b) 3 (c) 4 (d) 5
1
10.
Which of the following points lies on the x-axis?
(a) (0, 5) (b) (2, 2) (c) (-3, 0) (d) (0, -3)
1
11.
The volume of a cube is 729 cm3. Its total surface area is:
(a) 486 cm2 (b) 324 cm2 (c) 216 cm2 (d) 243 cm2
1
12.
If 12 men can complete a work in 20 days, how many men are required to complete the same work in 15 days?
(a) 15 (b) 18 (c) 16 (d) 24
1
13.
The factorisation of 4x2 - 12x + 9 is:
(a) (2x + 3)2 (b) (2x - 3)2 (c) (2x - 3)(2x + 3) (d) (4x - 3)(x - 3)
1
14.
The smallest number by which 392 must be multiplied to make it a perfect cube is:
(a) 2 (b) 3 (c) 5 (d) 7
1
15.
Solve for y: 1.6 = y / 1.5
(a) 2.4 (b) 2.44 (c) 2.5 (d) 2.25
1
16.
The sum of two numbers is 95. If one exceeds the other by 15, the numbers are:
(a) 40, 55 (b) 35, 60 (c) 45, 50 (d) 30, 65
1
17.
The diagonals of a rhombus are 16 cm and 30 cm. Its perimeter is:
(a) 34 cm (b) 68 cm (c) 64 cm (d) 46 cm
1
18.
Which of the following is not a case of direct variation?
(a) Distance and Time (at constant speed) (b) Work done and Number of workers (c) Cost and Quantity of articles (d) Area of circle and square of its radius
1
19.
The area of a trapezium is 34 cm2 and the length of one of the parallel sides is 10 cm and its height is 4 cm. The length of the other parallel side is:
(a) 5 cm (b) 7 cm (c) 8 cm (d) 6 cm
1
20.
The coordinate of the origin is:
(a) (1, 1) (b) (0, 1) (c) (1, 0) (d) (0, 0)
1
SECTION B (10 MARKS)
21.
Find the smallest square number which is divisible by each of the numbers 8, 15 and 20.
2
22.
If 52x+1 ÷ 25 = 125, find the value of x.
2
23.
Find the value of m so that (-3)m+1 × (-3)5 = (-3)7.
2
24.
The ratio of two adjacent angles of a parallelogram is 2:3. Find the measure of each of its angles.
2
25.
A machine in a soft drink factory fills 840 bottles in 6 hours. How many bottles will it fill in 5 hours?
2
SECTION C (18 MARKS)
26.
Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, find the cube root of the larger number.
3
27.
Fabina borrows ₹ 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
3
28.
Divide z(5z2 - 80) by 5z(z + 4).
OR
Factorise: p2 + 6p - 16
3
29.
The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m2 is ₹ 4.
3
30.
Solve: (3t - 2)/4 - (2t + 3)/3 = 2/3 - t
3
31.
The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.
3
SECTION D (20 MARKS)
32.
Using identities, evaluate:
(i) 102 × 103
(ii) 992
(iii) 297 × 303
OR
Simplify: (a + b + c)(a + b - c)
5
33.
A rectangular piece of paper 11 cm × 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder. Also find the ratio of the volume of this cylinder to the volume of a cylinder formed by rolling the paper along its length (height = 11 cm).
5
34.
A train is moving at a uniform speed of 75 km/hour.
(i) How far will it travel in 20 minutes?
(ii) Find the time required to cover a distance of 250 km.
5
35.
Plot the following points on a graph sheet. Verify if they lie on a line.
(a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)
(b) P(1, 1), Q(2, 2), R(3, 3), S(4, 4)
(c) K(2, 3), L(5, 3), M(5, 5), N(2, 5)
5
SECTION E: CASE BASED QUESTIONS (12 MARKS)
36.
Case Study 1: Geometry in Architecture
A playground is in the shape of a quadrilateral ABCD. The diagonal AC is 48 m long. The perpendiculars dropped from the opposite vertices B and D to the diagonal AC are 15 m and 25 m respectively.
Based on the above information, answer the following:
(i) Find the area of triangle ABC. (1)
(ii) Find the area of triangle ADC. (1)
(iii) Find the total area of the playground. (2)
4
37.
Case Study 2: Sales Tax and Discount
During a festival sale, a shop offered a discount of 10% on the marked prices of all the items. A customer bought a pair of jeans marked at ₹ 1450 and two shirts marked at ₹ 850 each.
Based on the above information, answer the following:
(i) Find the total marked price of all the items. (1)
(ii) Calculate the total discount offered. (1)
(iii) Calculate the net amount payable by the customer after discount. (2)
4
38.
Case Study 3: Data Handling
The weekly wages (in ₹) of 30 workers in a factory are: 830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840.
Using tally marks, make a frequency table with intervals as 800-810, 810-820 and so on.
(i) Which group has the maximum number of workers? (1)
(ii) How many workers earn ₹ 850 and more? (1)
(iii) How many workers earn less than ₹ 830? (2)
4
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