Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 854 · 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. 1.6 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) 9 (b) 18 (c) 24 (d) 36
2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 4 (b) 7 (c) 5 (d) 6
3. 3.What is the distance between the points (9, 10) and (17, 4)? (a) 11 (b) 100 (c) 10 (d) 14
4. 4.What is the midpoint of the line joining (6, 10) and (16, 4)? (a) (5, 3) (b) (22, 14) (c) (7, 11) (d) (11, 7)
5. 5.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
6. 6.In a class of 35 children, 18 like maths, 25 like science and 12 like both. How many like neither? (a) 16 (b) 4 (c) 5 (d) 12
7. 7.How many factors does 20 have? (a) 5 (b) 4 (c) 7 (d) 6
8. 8.Which is the correct factorisation of x² + 14x + 48? (a) (x − 6)(x − 8) (b) (x + 1)(x + 48) (c) (x + 6)(x + 8) (d) (x + 1)(x + 13)
9. 9.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 36 (d) 12
10. 10.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
11. 11.What is the mode of 6, 6, 6, 11, 12, 12 and 5? (a) 12 (b) 11 (c) 5 (d) 6
12. 12.What is the distance between the points (9, 17) and (21, 1)? (a) 400 (b) 28 (c) 21 (d) 20
13. 13.A cuboid is 9 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 168 cu cm (b) 18 cu cm (c) 108 cu cm (d) 17 cu cm
14. 14.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 48 (c) 15 (d) 135
15. 15.What is the median of 35, 9, 34, 13, 30, 8 and 15? (a) 13 (b) 15 (c) 16 (d) 30
16. 16.A bag has 11 black balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 13 (b) 12 (c) 23 (d) 2
17. 17.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 160° (b) 120° (c) 60° (d) 140°
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 6/11 (c) 1/11 (d) 1/6
19. 19.What is the median of 11, 5, 26, 8, 40, 14 and 28? (a) 11 (b) 14 (c) 26 (d) 8
20. 20.What is the mode of 13, 12, 8, 12, 17, 12 and 13? (a) 8 (b) 17 (c) 13 (d) 12
21. 21.How many factors does 30 have? (a) 6 (b) 7 (c) 9 (d) 8
22. 22.What is the midpoint of the line joining (7, 5) and (13, 17)? (a) (11, 10) (b) (20, 22) (c) (10, 11) (d) (3, 6)
23. 23.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 110° (b) 160° (c) 70° (d) 130°
24. 24.What is the mean of 4, 12, 15, 6 and 8? (a) 11 (b) 10 (c) 9 (d) 8
25. 25.If a + b = 9 and ab = 14, what is a² + b²? (a) 81 (b) 109 (c) 67 (d) 53
26. 26.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 11 (c) 36 (d) 99
27. 27.A bag has 8 red balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 10 (d) 17
28. 28.What is the distance between the points (3, 2) and (19, 14)? (a) 400 (b) 21 (c) 28 (d) 20
29. 29.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 55 (d) 66
30. 30.What is the distance between the points (2, 27) and (9, 3)? (a) 25 (b) 31 (c) 26 (d) 625
31. 31.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 36 (c) 9 (d) 18
32. 32.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 28 (d) 64
33. 33.A bag has 10 green balls and 5 black 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) 15 (c) 11 (d) 6
34. 34.If a + b = 16 and ab = 60, what is (a − b)²? (a) 4 (b) 256 (c) 16 (d) 136
35. 35.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
36. 36.4 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) 48 (b) 24 (c) 10 (d) 28
37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 7 (b) 17 (c) 18 (d) 19
38. 38.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 36 (c) 25 (d) 37
39. 39.How many factors does 64 have? (a) 8 (b) 5 (c) 7 (d) 6
40. 40.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 12 (d) 9

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