Class 8 Maths Olympiad: 40 Questions with Answers (2026)

Class 8 Maths Olympiad: 40 Practice Questions with Worked Answers

Practise 40 free Class 8 Maths Olympiad questions with the answers and explanations displayed directly after each problem. This study guide covers rational numbers, linear equations, quadrilaterals, data handling, squares and cubes, percentage problems, algebra, and mensuration.

Each question is an original practice example, designed to strengthen understanding of the class topics. For current chapters and learning material, see the School Connect Olympiad Class 8 Maths resources and Class 8 Maths 2026 syllabus.

How to practise these questions

Read one problem and work it out before looking at the answer.
Write a short calculation or reason for choosing your option.
Read the worked explanation and check where your steps agree or differ.
Try a fresh example if you found that concept difficult.
Work through a topic section at a time rather than rushing through all 40 questions.

Rational numbers

Question 1. Calculate −3/4 + 5/6.
A. 1/12 | B. −1/12 | C. 2/5 | D. 19/12
Answer: A. 1/12. Use denominator 12: −9/12 + 10/12 = 1/12.
Question 2. What is (−7/9) × (18/14)?
A. 1 | B. −1 | C. −7/14 | D. −2
Answer: B. −1. Cancel 18 ÷ 9 = 2, then (−7 × 2)/14 = −14/14 = −1.
Question 3. Calculate 5/8 ÷ (−15/16).
A. −1/3 | B. 2/3 | C. −2/3 | D. −3/2
Answer: C. −2/3. Multiply by the reciprocal: (5/8) × (−16/15) = −80/120 = −2/3.
Question 4. Which rational number is greatest?
A. −2/3 | B. −3/5 | C. −5/8 | D. −7/10
Answer: B. −3/5. The values are approximately −0.667, −0.600, −0.625 and −0.700. The greatest is −3/5, which is closest to zero.
Question 5. Which fraction lies strictly between 1/3 and 1/2?
A. 1/4 | B. 2/3 | C. 5/12 | D. 3/4
Answer: C. 5/12. Convert the endpoints to twelfths: 1/3 = 4/12 and 1/2 = 6/12. The fraction 5/12 lies between them.

Linear equations

Question 6. Solve 5x − 7 = 3x + 15.
A. 8 | B. 10 | C. 11 | D. 12
Answer: C. 11. Subtract 3x: 2x − 7 = 15. Add 7: 2x = 22, so x = 11.
Question 7. Solve 3(2y − 1) = 4y + 9.
A. 5 | B. 6 | C. 7 | D. 8
Answer: B. 6. Expand: 6y − 3 = 4y + 9. Then 2y = 12 and y = 6.
Question 8. If (x − 4)/3 + 2 = 7, what is x?
A. 13 | B. 15 | C. 17 | D. 19
Answer: D. 19. Subtract 2: (x − 4)/3 = 5. Multiply by 3: x − 4 = 15, giving x = 19.
Question 9. Solve 7x/4 = 21.
A. 10 | B. 11 | C. 12 | D. 14
Answer: C. 12. Multiply both sides by 4/7: x = 21 × 4/7 = 12.
Question 10. Half a number plus eight equals 23. What is the number?
A. 22 | B. 26 | C. 30 | D. 46
Answer: C. 30. Let the number be n. Then n/2 + 8 = 23, so n/2 = 15 and n = 30.

Quadrilaterals and polygons

Question 11. What is the sum of the interior angles of a pentagon?
A. 360° | B. 450° | C. 540° | D. 720°
Answer: C. 540°. For an n-sided polygon the sum is (n − 2) × 180°. With n = 5, this gives 3 × 180° = 540°.
Question 12. One interior angle of a parallelogram is 68°. What is an adjacent interior angle?
A. 68° | B. 112° | C. 122° | D. 136°
Answer: B. 112°. Adjacent angles of a parallelogram add to 180°, so 180° − 68° = 112°.
Question 13. Three interior angles of a quadrilateral are 80°, 95° and 100°. Find the fourth.
A. 75° | B. 80° | C. 85° | D. 95°
Answer: C. 85°. Quadrilateral angles total 360°. The three known angles total 275°, leaving 85°.
Question 14. What is each exterior angle of a regular octagon?
A. 40° | B. 45° | C. 50° | D. 60°
Answer: B. 45°. Exterior angles of any polygon sum to 360°. For a regular octagon, 360° ÷ 8 = 45°.
Question 15. How many diagonals does a hexagon have?
A. 6 | B. 8 | C. 9 | D. 12
Answer: C. 9. Use n(n − 3)/2. For six sides: 6 × 3 ÷ 2 = 9 diagonals.

Data handling

Question 16. Find the median of 4, 7, 7, 12 and 15.
A. 4 | B. 7 | C. 9 | D. 12
Answer: B. 7. The numbers are already in order. The third of five values is the median: 7.
Question 17. What is the mean of 8, 12, 16 and 20?
A. 12 | B. 13 | C. 14 | D. 16
Answer: C. 14. Their sum is 56, and 56 ÷ 4 = 14.
Question 18. Which is the mode of 3, 5, 3, 7, 3 and 5?
A. 3 | B. 5 | C. 6 | D. 7
Answer: A. 3. The number 3 occurs three times, more than any other value.
Question 19. What is the range of 18, 25, 12 and 29?
A. 13 | B. 15 | C. 17 | D. 19
Answer: C. 17. Range = maximum − minimum = 29 − 12 = 17.
Question 20. A bag contains 4 red and 6 blue marbles. What is the probability of picking a red marble at random?
A. 1/5 | B. 2/5 | C. 3/5 | D. 2/3
Answer: B. 2/5. There are 10 marbles, and four are red. Probability = 4/10 = 2/5.

Squares and square roots

Question 21. What is the square root of 2025?
A. 35 | B. 40 | C. 45 | D. 55
Answer: C. 45. 45 × 45 = 2025, so the principal square root of 2025 is 45.
Question 22. What is the smallest positive whole number by which 72 must be multiplied to make a perfect square?
A. 2 | B. 3 | C. 6 | D. 8
Answer: A. 2. 72 = 2³ × 3². One more factor of 2 makes each prime exponent even: 72 × 2 = 144 = 12².
Question 23. What is 19²?
A. 341 | B. 361 | C. 381 | D. 391
Answer: B. 361. Use (20 − 1)² = 400 − 40 + 1 = 361.
Question 24. Find the principal square root of 0.0081.
A. 0.009 | B. 0.09 | C. 0.9 | D. 0.81
Answer: B. 0.09. 0.09 × 0.09 = 0.0081, so its positive square root is 0.09.
Question 25. What is the smallest perfect square greater than 300?
A. 306 | B. 320 | C. 324 | D. 361
Answer: C. 324. 17² = 289, which is below 300; 18² = 324 is the next perfect square.

Cubes and cube roots

Question 26. What is 7³?
A. 21 | B. 49 | C. 243 | D. 343
Answer: D. 343. A cube is a number multiplied by itself three times: 7 × 7 × 7 = 343.
Question 27. What is the cube root of 1728?
A. 9 | B. 10 | C. 12 | D. 14
Answer: C. 12. 12 × 12 × 12 = 1728, so its cube root is 12.
Question 28. Find the value of 3³ + 2³.
A. 17 | B. 27 | C. 35 | D. 36
Answer: C. 35. 3³ is 27 and 2³ is 8; add them to get 35.
Question 29. What is the volume of a cube with side length 6 cm?
A. 36 cubic cm | B. 72 cubic cm | C. 216 cubic cm | D. 256 cubic cm
Answer: C. 216 cubic cm. Volume of a cube = side × side × side = 6³ = 216 cubic centimetres.
Question 30. What is the smallest positive whole number that must multiply 54 to make a perfect cube?
A. 2 | B. 3 | C. 4 | D. 9
Answer: C. 4. 54 = 2 × 3³. Multiply by 2² = 4 to make 2³ × 3³ = 216 = 6³.

Comparing quantities

Question 31. A product costs 1,250 units. What is its price after a 20% discount?
A. 950 units | B. 1,000 units | C. 1,050 units | D. 1,200 units
Answer: B. 1,000 units. 20% of 1,250 = 250. Subtract the discount: 1,250 − 250 = 1,000 units.
Question 32. Increase 800 by 15%. What is the new value?
A. 840 | B. 880 | C. 900 | D. 920
Answer: D. 920. 15% of 800 = 120; add it to the original 800 to get 920.
Question 33. Find simple interest on 3,000 units at 6% per year for two years.
A. 180 units | B. 300 units | C. 360 units | D. 600 units
Answer: C. 360 units. Simple interest = 3000 × 6 × 2 ÷ 100 = 360 units.
Question 34. An item bought for 300 units sells for 345 units. What is the profit percentage?
A. 10% | B. 12% | C. 15% | D. 18%
Answer: C. 15%. Profit = 345 − 300 = 45. Profit percentage = 45 ÷ 300 × 100 = 15%.
Question 35. What compound interest is earned on 1,000 units at 10% per year over two years, compounded annually?
A. 100 units | B. 200 units | C. 210 units | D. 220 units
Answer: C. 210 units. After year one, the amount is 1,100; after year two, it is 1,210. Interest earned = 1,210 − 1,000 = 210 units.

Algebra and mensuration

Question 36. If x = 3, what is (x + 5)²?
A. 16 | B. 25 | C. 49 | D. 64
Answer: D. 64. Substitute x = 3 first: (3 + 5)² = 8² = 64.
Question 37. Which is the factorised form of x² − 81?
A. (x − 9)(x + 9) | B. (x − 9)² | C. (x + 81)(x − 1) | D. (x − 3)(x + 27)
Answer: A. (x − 9)(x + 9). Use the difference of squares identity: a² − b² = (a − b)(a + b), with b = 9.
Question 38. Simplify (2a + 3b) − (a − b).
A. a + 2b | B. a + 4b | C. 3a + 2b | D. a − 4b
Answer: B. a + 4b. Remove brackets carefully: 2a + 3b − a + b = a + 4b.
Question 39. Find the area of a trapezium whose parallel sides measure 8 cm and 12 cm and whose height is 5 cm.
A. 40 square cm | B. 45 square cm | C. 50 square cm | D. 60 square cm
Answer: C. 50 square cm. Area = 1/2 × (8 + 12) × 5 = 50 square centimetres.
Question 40. What is the total surface area of a cube with side length 4 cm?
A. 64 square cm | B. 80 square cm | C. 96 square cm | D. 128 square cm
Answer: C. 96 square cm. A cube has six square faces, each of area 4 × 4 = 16. Total surface area = 6 × 16 = 96 square centimetres.

What to revise after practising

Questions	Topic	A useful next step
1–5	Rational numbers	Draw a number line and compare fractions using common denominators
6–10	Linear equations in one variable	Substitute answers into both sides to check equality
11–15	Polygons and quadrilaterals	Sketch shapes, label angles and explain each rule
16–20	Data handling and probability	Read the data carefully before calculating averages or chances
21–25	Squares and square roots	Practise factorisation and estimate between consecutive squares
26–30	Cubes and cube roots	Find prime factors and group them in sets of three
31–35	Discount, profit and interest	Identify the original value, rate and period before calculating
36–40	Algebra and mensuration	Write the formula, substitute values and check units

Four short worked lessons

Why negative rational numbers can be compared correctly

To compare −3/5 and −5/8, change them to decimals: −0.600 and −0.625. Because −0.600 is closer to zero, −3/5 is greater. A number line helps explain this.

How to verify an equation

For 5x − 7 = 3x + 15, solving gives x = 11. Verify it by substitution: the left side is 55 − 7 = 48; the right side is 33 + 15 = 48. Both are equal.

How to avoid confusing area and perimeter

A rectangle of length 12 cm and width 7 cm has an area of 84 square centimetres, while its perimeter is 38 centimetres. Area counts the surface; perimeter measures the boundary.

Why compound interest differs from simple interest

With 1,000 units at 10% per year for two years, simple interest is 200 units. Compound interest calculated annually is 210 units, because the second year’s interest includes interest on the first year’s growth.

Frequently asked questions

Are all 40 Class 8 Maths Olympiad practice questions free?

Yes. Each question and its explanation can be read here without paying or registering.

Can I practise without downloading a PDF?

Yes. All 40 worked solutions appear directly beneath the questions. You can use your browser’s Print option for paper-based practice.

Are these questions copied from an official previous-year examination?

No. They are original study exercises covering Class 8 mathematical concepts. Visit the SCO Class 8 Maths subject page to find the organiser’s separate official resources.

What topics should I prioritise for Class 8 Maths Olympiad?

Start with rational numbers and simple equations. Then practise quadrilaterals, data handling, square and cube roots, percentages, algebra, identities and mensuration. Use your chosen organiser’s current syllabus to decide which to study first.

How should I practise when I get a question wrong?

Check the formula or rule, compare your steps with the solution, then solve a different problem using the same concept. Do not only memorise the answer letter.