Class 7 Mathematics

Advanced / Olympiad-Oriented Sample Paper

Time: 2.5 Hours
Maximum Marks: 80
Level: High / Olympiad Practice

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Section A (1 × 10 = 10 Marks)

Answer briefly.

1. Find the value of $8^{2/3}$82/3.
2. Simplify: $(-5)^3 + 4^3$(−5)3+43.
3. Find the smallest number by which 288 must be multiplied to make it a perfect cube.
4. If the ratio of two numbers is 3:5 and their sum is 64, find the numbers.
5. Solve: $4x – 7 = 13$4x−7=13.
6. Evaluate: $\frac{2}{3} + \frac{3}{4} – \frac{5}{6}$32​+43​−65​.
7. A sum of ₹1500 is invested at 6% p.a. simple interest for 3 years. Find the interest.
8. A triangle has sides 7 cm, 24 cm, and 25 cm. Find its area.
9. A number leaves a remainder of 4 when divided by 6. What is the remainder when its square is divided by 6?
10. Evaluate: $(x + y)^2 – (x – y)^2$(x+y)2−(x−y)2.

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Section B (3 × 8 = 24 Marks)

Answer any 8 questions.

11. Factorise: $x^2 – 11x + 28$x2−11x+28.
12. Solve: $\frac{3x – 5}{4} = \frac{x + 2}{2}$43x−5​=2x+2​.
13. Find HCF and LCM of 180 and 270.
14. The sum of interior angles of a polygon is 1440°. Find the number of sides.
15. If 10 men can do a work in 18 days, how long will 15 men take?
16. Expand and simplify: $(x – 3y)^2$(x−3y)2.
17. A shopkeeper marks an article 20% above cost price and gives a discount of 10%. Find his gain or loss percent.
18. Find the probability of getting an odd number when a die is rolled once.
19. The parallel sides of a trapezium are 12 cm and 20 cm, height = 8 cm. Find its area.
20. Solve: $7(x – 3) – 4(x + 5) = 6$7(x−3)−4(x+5)=6.

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Section C (6 × 6 = 36 Marks)

Answer any 6 questions.

21. Two numbers differ by 9 and their product is 180. Find the numbers.
22. A car travels 180 km in 4 hours. Find its speed in km/h.
23. Find the cube root of 2744 using prime factorisation.
24. Solve: $x^2 – 9x + 20 = 0$x2−9x+20=0.
25. A rectangle has perimeter 60 cm. If length is 6 cm more than breadth, find its dimensions.
26. A bag contains 4 red, 3 blue, and 2 green balls. One ball is drawn at random. Find the probability of getting a blue or green ball.
27. Construct a rhombus with diagonals 10 cm and 8 cm. Name its properties.

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Section D (10 × 1 = 10 Marks)

Answer the following.

28. A cylinder has radius 5 cm and height 14 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 7 Mathematics – Answer Key

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Section A

Q. No.	Answer
1	4
2	-61
3	3
4	24 and 40
5	x = 5
6	4/3
7	₹270
8	84 cm²
9	4
10	4xy

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Section B

Q. No.	Answer
11	(x − 4)(x − 7)
12	x = 7
13	HCF = 90, LCM = 540
14	n = 10 sides
15	12 days
16	x² − 6xy + 9y²
17	Gain = 8%
18	1/2
19	128 cm²
20	x = 7

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Section C

Q. No.	Answer
21	15 and 24
22	45 km/h
23	14
24	x = 4, 5
25	Length = 18 cm, Breadth = 12 cm
26	5/9
27	Rhombus; diagonals perpendicular and bisect each other

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Section D

Q. No.	Answer
28	1100 cm³

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