Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 262 · 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 dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 1/11 (c) 1/18 (d) 2/11
2. 2.What is the smallest prime factor of 85? (a) 17 (b) 2 (c) 1 (d) 5
3. 3.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
4. 4.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 42 (c) 10 (d) 28
5. 5.A cuboid is 8 cm long, 7 cm wide and 10 cm high. What is its volume? (a) 56 cu cm (b) 412 cu cm (c) 25 cu cm (d) 560 cu cm
6. 6.In a class of 28 children, 16 like mangoes, 16 like bananas and 12 like both. How many like only mangoes? (a) 4 (b) 16 (c) 12 (d) 5
7. 7.What is the smallest prime factor of 203? (a) 1 (b) 2 (c) 29 (d) 7
8. 8.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
9. 9.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 36 (d) 72
10. 10.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 125° (b) 140° (c) 95° (d) 55°
11. 11.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 10 (d) 25
12. 12.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) 15 (b) 20 (c) 30 (d) 8
13. 13.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
14. 14.A drawer has lots of blue and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 3 (c) 5 (d) 4
15. 15.What is the prime factorisation of 36? (a) 2 × 3² (b) 2³ × 3² (c) 2² × 3² (d) 2² × 3³
16. 16.How many factors does 44 have? (a) 5 (b) 6 (c) 7 (d) 4
17. 17.A bag has 5 green balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 6 (c) 17 (d) 2
18. 18.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/11 (c) 1/9 (d) 3/11
20. 20.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
21. 21.A drawer has lots of white, black, yellow, red and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 10 (d) 6
22. 22.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
23. 23.A drawer has lots of white and blue 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) 3 (d) 2
24. 24.Which is the correct factorisation of x² + 13x + 40? (a) (x − 5)(x − 8) (b) (x + 1)(x + 12) (c) (x + 5)(x + 8) (d) (x + 1)(x + 40)
25. 25.In a class of 30 children, 18 like mangoes, 12 like bananas and 6 like both. How many like neither? (a) 12 (b) 6 (c) 0 (d) 7
26. 26.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/2 (d) 1/3
27. 27.8 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) 32 (b) 24 (c) 48 (d) 11
28. 28.How many factors does 38 have? (a) 3 (b) 4 (c) 2 (d) 5
29. 29.A bag has 9 red 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) 12 (b) 10 (c) 4 (d) 2
30. 30.What is the distance between the points (8, 9) and (11, 13)? (a) 6 (b) 7 (c) 25 (d) 5
31. 31.What is the mean of 2, 2, 16 and 20? (a) 9 (b) 11 (c) 10 (d) 8
32. 32.How many factors does 24 have? (a) 6 (b) 7 (c) 9 (d) 8
33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 78? (a) 18 (b) 17 (c) 7 (d) 19
34. 34.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 145° (c) 70° (d) 105°
35. 35.A bag has 3 white 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) 7 (b) 4 (c) 5 (d) 2
36. 36.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 64 (d) 16
37. 37.In a class of 21 children, 12 like tea, 9 like coffee and 3 like both. How many like only tea? (a) 12 (b) 6 (c) 3 (d) 9
38. 38.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 841 (b) 901 (c) 961 (d) 971
39. 39.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 75 (b) 65 (c) 130 (d) 21
40. 40.In a class of 37 children, 12 like cricket, 24 like football and 8 like both. How many like only cricket? (a) 16 (b) 13 (c) 12 (d) 4

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