Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 175 · 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.A bag has 9 green balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 9 (c) 17 (d) 10
2. 2.If a + b = 10 and ab = 24, what is (a − b)²? (a) 100 (b) 2 (c) 52 (d) 4
3. 3.What is the median of 18, 24, 30, 20, 28, 12 and 40? (a) 20 (b) 28 (c) 24 (d) 25
4. 4.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 130° (d) 50°
5. 5.If a + b = 6 and ab = 5, what is a² + b²? (a) 36 (b) 31 (c) 46 (d) 26
6. 6.In a class of 36 children, 9 like maths, 21 like science and 10 like neither. How many like both? (a) 26 (b) 10 (c) 5 (d) 4
7. 7.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 36 sq cm (c) 217 sq cm (d) 144 sq cm
8. 8.What is the median of 22, 30, 12, 25, 33, 13 and 17? (a) 17 (b) 22 (c) 23 (d) 25
9. 9.A bag has 3 white, 8 green and 7 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 5/6 (b) 1/3 (c) 1/6 (d) 8/9
10. 10.A bag has 12 white balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 23 (c) 12 (d) 13
11. 11.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 25 (b) 330 (c) 176 (d) 165
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/9 (c) 1/11 (d) 1/12
13. 13.How many prime numbers are there between 70 and 80? (a) 2 (b) 3 (c) 5 (d) 4
14. 14.What is the missing term in the AP 13, ?, 31, 40, 49? (a) 23 (b) 21 (c) 31 (d) 22
15. 15.How many factors does 116 have? (a) 7 (b) 6 (c) 4 (d) 5
16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 5 (b) 15 (c) 17 (d) 16
17. 17.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 49 (d) 42
18. 18.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 15 (c) 30 (d) 20
19. 19.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 40° (b) 85° (c) 140° (d) 135°
20. 20.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
21. 21.A bag has 8 black balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 16 (b) 2 (c) 10 (d) 9
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
23. 23.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 55 (d) 45
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 1/11 (c) 1/6 (d) 5/36
25. 25.If a + b = 17 and ab = 60, what is (a − b)²? (a) 169 (b) 289 (c) 7 (d) 49
26. 26.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
27. 27.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
28. 28.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
29. 29.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 84 (b) 49 (c) 13 (d) 42
30. 30.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 60° (d) 120°
31. 31.In a class of 36 children, 15 like maths, 28 like science and 9 like both. How many like neither? (a) 3 (b) 11 (c) 9 (d) 2
32. 32.A drawer has lots of red 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) 3 (b) 2 (c) 4 (d) 5
33. 33.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
34. 34.In a class of 21 children, 13 like dance, 10 like music and 4 like both. How many like neither? (a) 4 (b) 2 (c) 3 (d) 6
35. 35.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
36. 36.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/2 (c) 1/4 (d) 1/3
37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
38. 38.A bag has 9 yellow balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 12 (c) 2 (d) 10
39. 39.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 160° (c) 80° (d) 20°
40. 40.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 135° (b) 35° (c) 80° (d) 145°

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