Class 7 Maths Olympiad: 40 Questions with Answers (2026)

Class 7 Maths Olympiad: 40 Practice Questions with Answers

Improve your mathematics with 40 free Class 7 Maths Olympiad questions and clearly explained answers. You can work through integers, fractions, rational numbers, equations, angles, triangles, percentages, algebra, exponents and data handling without downloading anything. Each correct answer appears directly below its question.

These are original practice questions intended to build understanding, with clear worked answers after each question. The topics follow the School Connect Olympiad Class 7 Maths learning chapters and its 2026 Maths syllabus. Different organisers have different competition rules.

How to use this practice guide

Read a question carefully, then choose one of the four options.
Write your method or draw a diagram before looking at the solution.
Compare your work with the explanation and check each step.
For a wrong answer, learn that concept and solve another example.
Choose manageable sections rather than rushing through all questions.

Integers

Question 1. Calculate −18 + 27 − 6.
A. −3 | B. 3 | C. 9 | D. −9
Answer: B. 3. First −18 + 27 = 9. Then 9 − 6 = 3.
Question 2. What is (−7) × (−6) − 15?
A. −57 | B. −27 | C. 27 | D. 57
Answer: C. 27. The product of two negative numbers is positive: 42 − 15 = 27.
Question 3. Calculate −48 ÷ 6 + (−5).
A. −3 | B. −13 | C. 13 | D. 3
Answer: B. −13. −48 ÷ 6 = −8, then −8 + (−5) = −13.
Question 4. The temperature is −4°C, rises by 11°C and then drops by 6°C. What is the final temperature?
A. −1°C | B. 0°C | C. 1°C | D. 3°C
Answer: C. 1°C. Start at −4, add 11 to reach 7, then subtract 6: 1°C.
Question 5. Which number is greatest?
A. −19 | B. −12 | C. −7 | D. −15
Answer: C. −7. For negative integers, the number closest to zero is greatest: −7.

Fractions and decimals

Question 6. Calculate 3/4 + 5/8.
A. 8/12 | B. 11/8 | C. 1/8 | D. 9/8
Answer: B. 11/8. 3/4 = 6/8. Add 5/8 to obtain 11/8 or 1 3/8.
Question 7. Calculate 7/9 − 2/3.
A. 1/9 | B. 5/6 | C. 5/9 | D. 2/9
Answer: A. 1/9. Convert 2/3 to 6/9 and subtract: 7/9 − 6/9 = 1/9.
Question 8. What is 2.4 × 1.5?
A. 2.6 | B. 3.4 | C. 3.6 | D. 36
Answer: C. 3.6. 24 × 15 = 360; divide by 100 for two decimal places to obtain 3.6.
Question 9. Calculate 9.6 ÷ 0.3.
A. 3.2 | B. 32 | C. 0.32 | D. 320
Answer: B. 32. Multiply both dividend and divisor by 10: 96 ÷ 3 = 32.
Question 10. What is 5/6 of 72?
A. 48 | B. 54 | C. 60 | D. 66
Answer: C. 60. One-sixth of 72 is 12; five-sixths is 5 × 12 = 60.

Rational numbers

Question 11. Calculate −3/5 + 1/2.
A. −1/10 | B. 1/10 | C. −11/10 | D. −1/2
Answer: A. −1/10. Convert to tenths: −6/10 + 5/10 = −1/10.
Question 12. What is (−2/3) × (9/4)?
A. −2/3 | B. −3/2 | C. 3/2 | D. −1/6
Answer: B. −3/2. Multiply numerators and denominators: −18/12 = −3/2.
Question 13. Calculate (−4/7) ÷ (2/3).
A. −8/21 | B. −6/7 | C. 6/7 | D. −2/7
Answer: B. −6/7. Multiply by the reciprocal: (−4/7) × (3/2) = −12/14 = −6/7.
Question 14. Which of these rational numbers is greatest?
A. −5/6 | B. −3/4 | C. −2/3 | D. −7/8
Answer: C. −2/3. −2/3 is about −0.667, which is greater than −0.75, −0.833 and −0.875.
Question 15. What number lies exactly halfway between 1/4 and 3/4?
A. 1/3 | B. 1/2 | C. 2/3 | D. 1/4
Answer: B. 1/2. Find the average: (1/4 + 3/4) ÷ 2 = 1 ÷ 2 = 1/2.

Simple equations

Question 16. Solve 3x + 7 = 34.
A. 7 | B. 8 | C. 9 | D. 10
Answer: C. 9. Subtract 7 from both sides: 3x = 27. Divide by 3: x = 9.
Question 17. If 5(y − 2) = 35, find y.
A. 5 | B. 7 | C. 9 | D. 12
Answer: C. 9. Divide by 5 to get y − 2 = 7; add 2 so y = 9.
Question 18. Solve x/4 + 6 = 11.
A. 16 | B. 20 | C. 24 | D. 44
Answer: B. 20. Subtract 6 to get x/4 = 5, then multiply by 4: x = 20.
Question 19. Solve 2(x + 3) = 3x − 5.
A. 1 | B. 5 | C. 11 | D. 17
Answer: C. 11. Expand: 2x + 6 = 3x − 5. Move terms to get x = 11.
Question 20. Three times a number minus 8 equals 28. What is the number?
A. 10 | B. 11 | C. 12 | D. 14
Answer: C. 12. Write 3n − 8 = 28; add 8 to get 3n = 36; divide by 3 for n = 12.

Lines, angles and triangles

Question 21. An angle measures 118°. What is its supplementary angle?
A. 52° | B. 62° | C. 72° | D. 82°
Answer: B. 62°. Supplementary angles add to 180°. Calculate 180 − 118 = 62°.
Question 22. Two parallel lines are crossed by a transversal. One acute alternate interior angle is 65°. What is the other alternate interior angle?
A. 25° | B. 65° | C. 115° | D. 130°
Answer: B. 65°. Alternate interior angles are equal when the lines are parallel.
Question 23. Two angles of a triangle are 48° and 67°. Find the third angle.
A. 55° | B. 65° | C. 75° | D. 85°
Answer: B. 65°. Angles in a triangle total 180°. The third angle is 180 − 48 − 67 = 65°.
Question 24. An exterior angle of a triangle has two opposite interior angles of 35° and 65°. What is the exterior angle?
A. 30° | B. 65° | C. 100° | D. 115°
Answer: C. 100°. The exterior angle equals the sum of the two opposite interior angles: 35 + 65 = 100°.
Question 25. A triangle has sides measuring 4 cm, 7 cm and x cm. Which value of x can form a triangle?
A. 2 cm | B. 3 cm | C. 6 cm | D. 12 cm
Answer: C. 6 cm. The third side must be greater than 7 − 4 = 3 cm and less than 7 + 4 = 11 cm. Only 6 cm qualifies.

Comparing quantities

Question 26. What is 15% of 240?
A. 24 | B. 30 | C. 36 | D. 48
Answer: C. 36. 10% of 240 is 24 and 5% is 12. Add them: 36.
Question 27. A bag with a marked price of 800 units is offered at a 25% discount. What is the sale price?
A. 200 units | B. 575 units | C. 600 units | D. 625 units
Answer: C. 600 units. A quarter of 800 is 200. Subtract the discount: 800 − 200 = 600 units.
Question 28. An item costs 500 units and sells for 575 units. What is the profit percentage?
A. 10% | B. 12% | C. 15% | D. 20%
Answer: C. 15%. Profit is 75; profit percentage is 75 ÷ 500 × 100 = 15%.
Question 29. Find the simple interest on 2,000 units at 6% per year for 2 years.
A. 120 units | B. 200 units | C. 240 units | D. 260 units
Answer: C. 240 units. Simple interest = 2000 × 6 × 2 ÷ 100 = 240 units.
Question 30. The ratio of boys to girls in a club is 3:5. There are 40 members. How many are boys?
A. 12 | B. 15 | C. 20 | D. 25
Answer: B. 15. There are 3 + 5 = 8 equal parts. Each part is 40 ÷ 8 = 5, so 3 parts are 15 boys.

Geometry, area and symmetry

Question 31. A parallelogram has a base of 12 cm and a perpendicular height of 7 cm. What is its area?
A. 38 square cm | B. 72 square cm | C. 84 square cm | D. 96 square cm
Answer: C. 84 square cm. Area of a parallelogram equals base × perpendicular height = 12 × 7 = 84 square centimetres.
Question 32. Find the circumference of a circle of radius 7 cm, using π = 22/7.
A. 22 cm | B. 44 cm | C. 49 cm | D. 154 cm
Answer: B. 44 cm. Circumference = 2πr = 2 × 22/7 × 7 = 44 cm.
Question 33. A trapezium has parallel sides of 6 cm and 10 cm, with height 5 cm. Find its area.
A. 30 square cm | B. 35 square cm | C. 40 square cm | D. 80 square cm
Answer: C. 40 square cm. Area = half × (sum of parallel sides) × height = 1/2 × 16 × 5 = 40 square centimetres.
Question 34. Two triangles have two corresponding sides equal and the angle between those sides equal. Which congruence rule applies?
A. AAA | B. SSA | C. SAS | D. RHS
Answer: C. SAS. SAS stands for side–angle–side, using the included angle between the equal sides.
Question 35. How many lines of symmetry does a regular hexagon have?
A. 3 | B. 4 | C. 5 | D. 6
Answer: D. 6. A regular hexagon has three lines through opposite vertices and three through opposite side midpoints.

Algebra, powers and data

Question 36. Simplify 3(2a − 4) + 2a.
A. 8a − 12 | B. 6a − 10 | C. 8a + 12 | D. 4a − 12
Answer: A. 8a − 12. Distribute 3 to get 6a − 12, then combine 6a + 2a to give 8a − 12.
Question 37. What is 2³ × 2⁴?
A. 16 | B. 32 | C. 64 | D. 128
Answer: D. 128. Multiplying powers of the same base adds exponents: 2^(3+4) = 2^7 = 128.
Question 38. Calculate 5⁰ + 3².
A. 9 | B. 10 | C. 14 | D. 26
Answer: B. 10. Any nonzero number to power zero equals 1, and 3 squared is 9, so 1 + 9 = 10.
Question 39. Find the mean of 4, 8, 12, 16 and 20.
A. 10 | B. 11 | C. 12 | D. 14
Answer: C. 12. Their sum is 60. Divide by five values to get a mean of 12.
Question 40. A bar chart gives sales of 12, 18, 15 and 21 books over four days. What is the difference between the highest and lowest daily sales?
A. 6 | B. 7 | C. 9 | D. 12
Answer: C. 9. The largest count is 21 and the smallest is 12. Difference = 21 − 12 = 9.

Which topics should you practise next?

Question numbers	Topics covered	Useful next activity
1–5	Integers	Draw a number line and check the signs in each calculation
6–10	Fractions and decimals	Use common denominators and estimate decimal calculations
11–15	Rational numbers	Plot positive and negative fractions on a number line
16–20	Simple equations	Substitute your solved value to verify both sides match
21–25	Lines, angles and triangles	Sketch and label each angle before calculating
26–30	Percentages, ratio, discount and interest	Identify the original amount and units before applying a rate
31–35	Perimeter, area, congruence and symmetry	Draw shapes and distinguish lengths from square units
36–40	Algebra, exponents and data	Show each simplification step and read chart scales carefully

Four strategies to solve harder Olympiad questions

1. Check the sign before solving

For integer problems such as (−7) × (−6) − 15, a negative multiplied by a negative becomes positive: 42 − 15 = 27. Predict the sign before carrying out the arithmetic.

2. Substitute to check an equation

When you get x = 11 from 2(x + 3) = 3x − 5, test it: left side 2 × 14 = 28; right side 33 − 5 = 28. Both sides agree.

3. Sketch the geometry before using a formula

For a triangle with two known angles of 48° and 67°, draw a rough triangle and mark the angles. The remaining angle is 180° − 48° − 67° = 65°. You do not need a perfectly scaled drawing to reason about the angle sum.

4. Ask what percentage is based on

If the cost is 500 units and the sale price is 575, the profit is 75. Profit percentage is based on the original cost price: 75/500 × 100 = 15%. This prevents a common denominator mistake.

Frequently asked questions

Can I practise these Class 7 Maths questions for free?

Yes. All 40 questions and explanations are provided directly on the page without a payment or sign-in.

Do I need a PDF to see the answer key?

No. The correct answer and working follow each question. You can print the page from your browser if you prefer paper practice.

Are these actual past-year Olympiad questions?

No. These are original practice questions based on age-appropriate Maths topics. For official examination papers, use your chosen organiser’s website.

What topics are covered in Class 7 Maths Olympiad?

This guide covers integers, fractions, decimals, rational numbers, equations, lines and angles, triangles, quantities, area, symmetry, algebra, exponents and data. See the SCO Class 7 subject guide for more lessons.

Are SCO and SOF Maths Olympiads identical?

No. School Connect Olympiad and Science Olympiad Foundation run different programmes. Refer to the SOF Class 7 Maths Olympiad syllabus if that is your chosen examination.