Class 8 Mathematics

Higher Difficulty Sample Paper

Time: 2.5 Hours
Maximum Marks: 80
Level: Advanced / Olympiad-Oriented

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Section A (1 × 10 = 10 Marks)

Answer briefly.

1. Find the value of:
   $125^{\frac{2}{3}}$12532​
2. Simplify:
   $(-3)^4 – (-3)^3$(−3)4−(−3)3
3. Find the smallest number by which 675 must be multiplied to make it a perfect cube.
4. If the ratio of two numbers is 5 : 7 and their sum is 144, find the numbers.
5. Solve:
   $3x – 7 = 2x + 9$3x−7=2x+9
6. Find the value of:
   $\frac{3}{4} + \frac{5}{6} – \frac{7}{12}$43​+65​−127​
7. Find the compound interest on ₹2000 at 5% p.a. for 2 years (compounded annually).
8. The diagonals of a rhombus are 16 cm and 12 cm. Find its area.
9. A number when divided by 7 leaves remainder 5. What will be the remainder when its square is divided by 7?
10. Evaluate:
    $(a + b)^2 – (a – b)^2$(a+b)2−(a−b)2

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Section B (3 × 8 = 24 Marks)

Answer any 8 questions.

11. Factorise:
    $x^2 – 9x + 20$x2−9x+20
12. Solve:
    $\frac{2x – 3}{5} = \frac{x + 4}{3}$52x−3​=3x+4​
13. Find the HCF and LCM of 360 and 504.
14. The sum of angles of a polygon is 1620°. Find the number of sides.
15. If 12 men can complete a work in 15 days, how many days will 20 men take? (Same efficiency)
16. Expand and simplify:
    $(2x – 3y)^2$(2x−3y)2
17. A shopkeeper marks an item 40% above cost price and allows 10% discount. Find his gain or loss percent.
18. The probability of getting a red ball from a bag containing 5 red and 3 blue balls (one draw).
19. Find the area of a trapezium with parallel sides 10 cm and 18 cm and height 7 cm.
20. Solve:
    $5(x – 2) – 3(x + 4) = 7$5(x−2)−3(x+4)=7

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Section C (6 × 6 = 36 Marks)

Answer any 6 questions.

21. The difference of two numbers is 8 and their product is 240. Find the numbers.
22. A train 150 m long passes a pole in 10 seconds. Find its speed in km/h.
23. Find the cube root of 10648 by prime factorisation.
24. Solve:
    $x^2 – 7x + 10 = 0$x2−7x+10=0
25. The perimeter of a rectangle is 100 cm. If length is 10 cm more than breadth, find its dimensions.
26. A die is thrown twice. Find probability of getting sum 8.
27. Construct a quadrilateral where diagonals bisect each other at right angles. Name it and justify.

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Section D (10 × 1 = 10 Marks)

Answer the following.

28. A cylinder has radius 7 cm and height 10 cm. Find its volume.
    (Use π = 22/7)

Disclaimer: This is an independently created practice paper for educational use only and is not affiliated with any official Olympiad organization.

Answer

Class 8 Mathematics – Answer Key

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Section A

Q. No.	Answer
1	25
2	108
3	5
4	60 and 84
5	x = 16
6	1
7	₹205
8	96 cm²
9	4
10	4ab

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Section B

Q. No.	Answer
11	(x − 5)(x − 4)
12	x = 27
13	HCF = 72, LCM = 2520
14	11 sides
15	9 days
16	4x² − 12xy + 9y²
17	Gain = 26%
18	5/8
19	98 cm²
20	x = 1

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Section C

Q. No.	Answer
21	20 and 12
22	54 km/h
23	22
24	x = 5, 2
25	Length = 30 cm, Breadth = 20 cm
26	5/36
27	Rhombus (Diagonals perpendicular and bisect each other)

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Section D

Q. No.	Answer
28	1540 cm³