Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 829 · 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.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 120° (c) 30° (d) 60°
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 1/11 (c) 5/11 (d) 5/36
3. 3.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 15 (d) 30
4. 4.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 30° (d) 120°
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
6. 6.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 70° (c) 20° (d) 110°
7. 7.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 66 (d) 144
8. 8.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
9. 9.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
10. 10.In a class of 30 children, 16 like tea, 13 like coffee and 6 like neither. How many like both? (a) 6 (b) 24 (c) 4 (d) 5
11. 11.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
12. 12.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 71° (c) 70° (d) 110°
13. 13.6 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 48 (b) 30 (c) 24 (d) 10
14. 14.In a class of 36 children, 19 like mangoes, 19 like bananas and 11 like both. How many like at least one of the two? (a) 16 (b) 38 (c) 27 (d) 36
15. 15.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 92 (c) 91 (d) 182
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
17. 17.A drawer has lots of black and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 2 (d) 3
18. 18.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 64 (d) 15
19. 19.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 145° (d) 120°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 85° (c) 170° (d) 95°
21. 21.In a class of 20 children, 13 like cricket, 6 like football and 3 like both. How many like at least one of the two? (a) 16 (b) 20 (c) 19 (d) 13
22. 22.What is the smallest prime factor of 91? (a) 7 (b) 1 (c) 2 (d) 13
23. 23.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 45 (d) 20
24. 24.What is the mode of 13, 14, 15, 10, 10, 13 and 13? (a) 15 (b) 10 (c) 13 (d) 14
25. 25.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3528 (c) 3570 (d) 3486
26. 26.Using (a + b)² = a² + 2ab + b², what is 93²? (a) 8109 (b) 8649 (c) 8659 (d) 7569
27. 27.A bag has 12 white balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 13 (b) 14 (c) 2 (d) 21
28. 28.In a class of 32 children, 14 like cricket, 19 like football and 2 like both. How many like neither? (a) 2 (b) 3 (c) 1 (d) 0
29. 29.What is the 13th term of the AP 8, 10, 12, 14, …? (a) 34 (b) 26 (c) 24 (d) 32
30. 30.What is the median of 35, 15, 13, 7, 2, 32 and 37? (a) 13 (b) 32 (c) 15 (d) 7
31. 31.What is the midpoint of the line joining (1, 7) and (5, 1)? (a) (2, 3) (b) (4, 3) (c) (6, 8) (d) (3, 4)
32. 32.What is the 18th term of the AP 20, 22, 24, 26, …? (a) 56 (b) 34 (c) 36 (d) 54
33. 33.The mean of 5 numbers is 29. When the number 35 is added to them, what is the new mean? (a) 32 (b) 31 (c) 29 (d) 30
34. 34.What is the distance between the points (5, 0) and (10, 12)? (a) 169 (b) 17 (c) 14 (d) 13
35. 35.Which term of the AP 20, 26, 32, 38, … is 116? (a) 18th (b) 19th (c) 17th (d) 16th
36. 36.In a class of 12 children, 6 like maths, 6 like science and 3 like both. How many like at least one of the two? (a) 12 (b) 6 (c) 9 (d) 10
37. 37.What is the mean of 14, 6, 9, 13 and 13? (a) 12 (b) 11 (c) 10 (d) 13
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/12 (c) 1/11 (d) 1/36
39. 39.What is the mean of 5, 18, 20 and 9? (a) 13 (b) 15 (c) 12 (d) 14
40. 40.What is the smallest prime factor of 35? (a) 7 (b) 1 (c) 5 (d) 2

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