Class 9 Maths Olympiad: 40 Questions with Answers (2026)

Class 9 Maths Olympiad: 40 Practice Questions and Worked Answers

Prepare for Class 9 Maths Olympiad with 40 original multiple-choice questions and explanations directly below each question. You can practise real numbers, algebra, coordinate geometry, equations, triangles, circles, surface area, statistics and probability without opening a separate PDF.

The questions on this page are original practice material rather than a reproduction of an official previous-year question paper. Use the School Connect Olympiad Class 9 Maths subject hub and the 2026 Class 9 Maths syllabus to decide which topics to revise for your examination.

How to get the most from this practice set

Answer one question before reading the solution.
Show the key calculation or geometric fact behind your choice.
Read the worked answer and identify where your reasoning differs.
Retry that skill with a fresh example, not by memorising the option letter.
Practise one section per session if you prefer shorter study periods.

Number systems

Question 1. Simplify √50 ÷ √2.
A. 2 | B. 5 | C. 10 | D. 25
Answer: B. 5. Combine the radicals: √(50/2) = √25 = 5.
Question 2. Which is an irrational number strictly between 2 and 3?
A. 5/2 | B. √5 | C. √9 | D. 9/4
Answer: B. √5. √5 is about 2.236 and irrational; 5/2 and 9/4 are rational, while √9 is 3 and not strictly between.
Question 3. Express 0.272727… as a fraction in simplest form.
A. 27/100 | B. 9/11 | C. 3/11 | D. 2/7
Answer: C. 3/11. Let x = 0.272727… . Then 100x − x = 27, so 99x = 27 and x = 27/99 = 3/11.
Question 4. Simplify 3/√3.
A. 3√3 | B. √3 | C. 1/3 | D. √9/3
Answer: B. √3. Multiply top and bottom by √3: 3√3/3 = √3.
Question 5. Evaluate (2³ × 2⁵) ÷ 2⁴.
A. 8 | B. 12 | C. 16 | D. 32
Answer: C. 16. Add powers when multiplying and subtract when dividing: 2^(3+5−4) = 2⁴ = 16.

Polynomials and identities

Question 6. Expand (x + 3)(x − 4).
A. x² + x − 12 | B. x² − x − 12 | C. x² − 7x + 12 | D. x² + 7x − 12
Answer: B. x² − x − 12. Multiply every term: x² − 4x + 3x − 12 = x² − x − 12.
Question 7. What is the value of p(2) if p(x) = x² − 5x + 6?
A. 0 | B. 2 | C. 4 | D. 6
Answer: A. 0. Substitute x = 2: 4 − 10 + 6 = 0.
Question 8. Factorise x² − 9x + 20.
A. (x − 2)(x − 10) | B. (x + 4)(x + 5) | C. (x − 4)(x − 5) | D. (x − 1)(x − 20)
Answer: C. (x − 4)(x − 5). Find two numbers multiplying to +20 and adding to −9: −4 and −5.
Question 9. If x = −1, what is x³ − 2x² + 1?
A. −4 | B. −3 | C. −2 | D. 2
Answer: C. −2. At x = −1: (−1)³ − 2(−1)² + 1 = −1 − 2 + 1 = −2.
Question 10. What is the degree of 4x³ − 2x⁴ + 7?
A. 2 | B. 3 | C. 4 | D. 7
Answer: C. 4. The highest power with a non-zero coefficient is 4, from −2x⁴.

Coordinate geometry

Question 11. A point lies three units left and four units above the origin. What are its coordinates?
A. (3,4) | B. (−3,4) | C. (3,−4) | D. (−4,3)
Answer: B. (−3,4). Left means a negative x-coordinate, and above means a positive y-coordinate: (−3,4).
Question 12. In which quadrant does (−4,−7) lie?
A. I | B. II | C. III | D. IV
Answer: C. III. Both x and y are negative, which identifies the third quadrant.
Question 13. What is the midpoint of the points (2,6) and (8,10)?
A. (6,8) | B. (5,6) | C. (5,8) | D. (10,16)
Answer: C. (5,8). Average the x-coordinates and y-coordinates: ((2+8)/2,(6+10)/2) = (5,8).
Question 14. How far is the point (6,8) from the origin?
A. 8 units | B. 10 units | C. 12 units | D. 14 units
Answer: B. 10 units. Distance = √(6²+8²) = √(36+64) = √100 = 10 units.
Question 15. Reflect the point (3,−5) in the y-axis. What is its image?
A. (−3,−5) | B. (−3,5) | C. (3,5) | D. (5,−3)
Answer: A. (−3,−5). Reflection across the y-axis changes the sign of x only. So (3,−5) becomes (−3,−5).

Linear equations in two variables

Question 16. Solve the equations x+y = 12 and x−y = 4.
A. x=4,y=8 | B. x=6,y=6 | C. x=8,y=4 | D. x=10,y=2
Answer: C. x=8,y=4. Add both equations: 2x = 16, so x = 8. Substitute in x+y = 12 to find y = 4.
Question 17. Which point satisfies 3x + 2y = 12?
A. (1,3) | B. (2,3) | C. (3,2) | D. (4,2)
Answer: B. (2,3). With (2,3), 3×2 + 2×3 = 6+6 = 12. The other points do not satisfy the equation.
Question 18. Which equation represents a vertical line five units to the right of the y-axis?
A. y=5 | B. x=−5 | C. x=5 | D. y=−5
Answer: C. x=5. Every point on that vertical line has x-coordinate 5, so its equation is x = 5.
Question 19. If x=3 and 2x + 3y = 21, find y.
A. 3 | B. 4 | C. 5 | D. 6
Answer: C. 5. Insert x = 3: 6 + 3y = 21, so 3y = 15 and y = 5.
Question 20. For y = 2x + 1, what is y when x = −2?
A. −5 | B. −4 | C. −3 | D. 3
Answer: C. −3. Substitute −2: y = 2×(−2)+1 = −4+1 = −3.

Lines, angles and triangles

Question 21. Two supplementary angles measure 126° and x°. Find x.
A. 44° | B. 54° | C. 64° | D. 74°
Answer: B. 54°. Supplementary angles sum to 180°. So x = 180° − 126° = 54°.
Question 22. Two straight lines intersect. If one angle is 67°, what is the vertically opposite angle?
A. 23° | B. 67° | C. 113° | D. 134°
Answer: B. 67°. Vertically opposite angles are equal, so the other angle is also 67°.
Question 23. Two interior angles of a triangle are 50° and 60°. Find the third.
A. 60° | B. 65° | C. 70° | D. 80°
Answer: C. 70°. The three interior angles total 180°. Third angle = 180° − 50° − 60° = 70°.
Question 24. A right triangle has perpendicular sides 5 cm and 12 cm. What is its hypotenuse?
A. 11 cm | B. 13 cm | C. 15 cm | D. 17 cm
Answer: B. 13 cm. By Pythagoras, hypotenuse² = 5² + 12² = 169, so the hypotenuse is 13 cm.
Question 25. Two triangles have two corresponding sides and their included angle equal. Which congruence rule applies?
A. AAA | B. SSA | C. SAS | D. RHS
Answer: C. SAS. SAS means side–angle–side: two sides and the angle between them determine congruence.

Quadrilaterals and circles

Question 26. A parallelogram has one interior angle of 112°. Find an adjacent angle.
A. 68° | B. 72° | C. 112° | D. 124°
Answer: A. 68°. Adjacent interior angles of a parallelogram add to 180°, so 180° − 112° = 68°.
Question 27. Three interior angles of a quadrilateral are 75°, 85° and 100°. What is its fourth angle?
A. 80° | B. 90° | C. 95° | D. 100°
Answer: D. 100°. The total is 360°. The known angles add to 260°, so the fourth is 100°.
Question 28. One angle of a cyclic quadrilateral is 108°. Find its opposite angle.
A. 62° | B. 72° | C. 82° | D. 108°
Answer: B. 72°. Opposite angles of a cyclic quadrilateral sum to 180°: 180° − 108° = 72°.
Question 29. The radius of a circle is 7 cm. What is its diameter?
A. 7 cm | B. 10.5 cm | C. 14 cm | D. 21 cm
Answer: C. 14 cm. The diameter is twice the radius: 2 × 7 = 14 cm.
Question 30. An angle in a semicircle subtended by the diameter measures:
A. 45° | B. 60° | C. 90° | D. 180°
Answer: C. 90°. An angle at a point on a circle subtended by a diameter is a right angle: 90°.

Area, Heron’s formula and volumes

Question 31. A triangle has sides 13 cm, 14 cm and 15 cm. What is its area?
A. 72 sq cm | B. 84 sq cm | C. 90 sq cm | D. 96 sq cm
Answer: B. 84 sq cm. Heron’s formula: s = (13+14+15)/2 = 21. Area = √(21×8×7×6) = √7056 = 84 sq cm.
Question 32. A triangle has base 18 cm and perpendicular height 7 cm. What is its area?
A. 42 sq cm | B. 56 sq cm | C. 63 sq cm | D. 126 sq cm
Answer: C. 63 sq cm. Area = (1/2) × base × perpendicular height = (1/2) × 18 × 7 = 63 sq cm.
Question 33. What is the curved surface area of a cylinder of radius 7 cm and height 10 cm? Use π = 22/7.
A. 220 sq cm | B. 308 sq cm | C. 440 sq cm | D. 770 sq cm
Answer: C. 440 sq cm. Curved surface area = 2πrh = 2 × 22/7 × 7 × 10 = 440 sq cm.
Question 34. A cone has radius 3 cm and height 7 cm. Find its volume using π = 22/7.
A. 22 cu cm | B. 44 cu cm | C. 66 cu cm | D. 198 cu cm
Answer: C. 66 cu cm. Volume = (1/3)πr²h = (1/3) × (22/7) × 9 × 7 = 66 cubic centimetres.
Question 35. Which expression is the volume of a sphere with radius 3 cm?
A. 9π cu cm | B. 12π cu cm | C. 27π cu cm | D. 36π cu cm
Answer: D. 36π cu cm. Volume = (4/3)πr³ = (4/3)π×27 = 36π cubic centimetres.

Statistics and probability

Question 36. Find the mean of 5, 9, 11 and 15.
A. 9 | B. 10 | C. 11 | D. 12
Answer: B. 10. Add 5+9+11+15 = 40, and divide by four values: 10.
Question 37. Find the median of 3, 5, 7, 9 and 15.
A. 5 | B. 6 | C. 7 | D. 9
Answer: C. 7. The five numbers are already ordered; the middle, third value is 7.
Question 38. Find the mode of 2, 3, 3, 4, 5, 5, 5.
A. 2 | B. 3 | C. 4 | D. 5
Answer: D. 5. The mode is the most frequent value. Five occurs three times.
Question 39. A bag contains two red and three blue identical marbles. What is the probability of drawing red?
A. 1/5 | B. 2/5 | C. 3/5 | D. 2/3
Answer: B. 2/5. Two of the five equally likely marbles are red, so probability = 2/5.
Question 40. A fair coin is tossed and a fair six-sided die is rolled. What is the probability of a head AND an even die number?
A. 1/8 | B. 1/4 | C. 1/3 | D. 1/2
Answer: B. 1/4. Probability(head) = 1/2 and probability(even number) = 3/6 = 1/2. Independent events give (1/2)×(1/2) = 1/4.

Review what you have learned

Questions	Skill	Revision activity
1–5	Real numbers, radicals and exponents	Estimate irrational values and check each simplification
6–10	Polynomials, factors and identities	Expand factors to verify each polynomial answer
11–15	Coordinate geometry	Plot the points on grid paper and mark the axes
16–20	Linear equations	Substitute the result back into every equation
21–25	Angles and triangles	Draw diagrams and label known lengths and angles
26–30	Quadrilaterals and circles	Sketch figures and explain the angle rules
31–35	Area, surface area and volume	Label units and select the formula before calculating
36–40	Statistics and probability	Organise a data list and count favourable outcomes

Four worked strategies for tricky questions

Check a factorisation by multiplying backwards

For x² − 9x + 20, the factors are (x − 4)(x − 5). Expand them to check: x² − 5x − 4x + 20 = x² − 9x + 20. This confirms both the signs and constant term.

Use a diagram before solving a geometry problem

For a right triangle with perpendicular sides 5 cm and 12 cm, draw a right angle and mark both sides. The hypotenuse is √(25 + 144) = 13 cm. A rough, labelled sketch helps you avoid choosing the wrong sides.

Check that your units match the question

A triangle with base 18 cm and height 7 cm has area 63 square centimetres. A perimeter answer, by contrast, is a length in centimetres. Units help detect otherwise plausible incorrect answers.

Explain why probability is between zero and one

With two red and three blue marbles, the chance of drawing red is 2/5. A probability cannot be negative or greater than 1. Use the total number of equally likely outcomes as the denominator.

Frequently asked questions

Are these Class 9 Maths Olympiad questions free?

Yes. All 40 practice questions, choices and worked explanations are directly available here without payment or registration.

Do I need a downloadable paper to find the answers?

No. Read and solve the questions above on this page. Every correct answer is followed by the calculation or reasoning.

Are these official previous-year examination questions?

No. They are original practice examples for Class 9 topics. For official examination resources, visit the SCO Class 9 Maths subject page.

What should I study first for a Class 9 Maths Olympiad?

Start with real numbers and algebra, then work through coordinate geometry, equations, triangles, circles, mensuration and statistics. Match your preparation to the syllabus of your chosen organiser.

Are SCO and SOF Maths Olympiads the same competition?

No. They are separate organisers. If you are entering SOF, consult its Class 9 mathematics syllabus for the applicable chapters and format.

Should I complete all the questions under a time limit?

Not at first. Learn the concept and check the method, then practise with time limits only when ready and when required by your particular competition.