Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 760 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 2025 (b) 3025 (c) 2525 (d) 3035
2. 2.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 31° (c) 210° (d) 30°
3. 3.A bag has 9 red balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 10 (d) 13
4. 4.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
6. 6.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 16 (c) 32 (d) 10
7. 7.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/18 (c) 1/12 (d) 1/11
9. 9.In a class of 34 children, 15 like mangoes, 16 like bananas and 3 like both. How many like neither? (a) 7 (b) 3 (c) 9 (d) 6
10. 10.In a class of 38 children, 27 like maths, 16 like science and 10 like both. How many like neither? (a) 15 (b) 10 (c) 5 (d) 6
11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 21 (d) 20
12. 12.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 24 (d) 144
13. 13.In which quadrant does the point (8, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
14. 14.What is the median of 11, 3, 13, 28 and 7? (a) 13 (b) 7 (c) 12 (d) 11
15. 15.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 120° (d) 125°
16. 16.A bag has 8 white balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 9 (c) 18 (d) 2
17. 17.What is the mean of 16, 3, 4 and 21? (a) 13 (b) 12 (c) 11 (d) 10
18. 18.In a class of 33 children, 24 like cricket, 7 like football and 6 like neither. How many like both? (a) 27 (b) 6 (c) 4 (d) 5
19. 19.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 105° (c) 255° (d) 75°
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/12 (c) 1/9 (d) 1/11
21. 21.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 21 (c) 28 (d) 10
22. 22.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 70° (c) 215° (d) 35°
23. 23.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 256 sq cm (c) 64 sq cm (d) 384 sq cm
24. 24.How many factors does 115 have? (a) 3 (b) 2 (c) 4 (d) 5
25. 25.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 144 (c) 132 (d) 24
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
27. 27.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 3/4 (c) 1/4 (d) 1/8
28. 28.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/4 (c) 1/3 (d) 1/2
29. 29.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
30. 30.What is the mode of 15, 19, 11, 1, 19, 15 and 19? (a) 15 (b) 1 (c) 11 (d) 19
31. 31.What is the mode of 10, 10, 6, 14, 16, 10 and 14? (a) 16 (b) 14 (c) 10 (d) 6
32. 32.A cuboid is 6 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 168 cu cm (b) 144 cu cm (c) 16 cu cm (d) 24 cu cm
33. 33.What is the midpoint of the line joining (9, 10) and (11, 14)? (a) (20, 24) (b) (1, 2) (c) (12, 10) (d) (10, 12)
34. 34.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2 × 3 × 5⁴
35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 14 (b) 3 (c) 13 (d) 15
36. 36.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
37. 37.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 70° (d) 140°
38. 38.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 24 (c) 10 (d) 48
39. 39.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 231 (c) 462 (d) 210
40. 40.If a + b = 7 and ab = 6, what is a² + b²? (a) 61 (b) 37 (c) 49 (d) 43

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