Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 381 · 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 captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 42 (c) 21 (d) 14
2. 2.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
3. 3.A bag has 10 black balls and 6 red 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) 16 (c) 2 (d) 7
4. 4.What is the mean of 13, 14, 5, 16 and 7? (a) 12 (b) 10 (c) 13 (d) 11
5. 5.A bag has 9 green, 4 blue and 3 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/4 (b) 1/3 (c) 3/4 (d) 13/16
6. 6.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 80° (c) 81° (d) 260°
7. 7.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
8. 8.What is the mode of 14, 2, 14, 16, 14, 16 and 4? (a) 14 (b) 4 (c) 16 (d) 2
9. 9.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2² × 3 (c) 2³ × 3 (d) 2⁴ × 3
10. 10.How many prime numbers are there between 30 and 50? (a) 7 (b) 6 (c) 5 (d) 4
11. 11.What is the missing term in the AP 15, 20, ?, 30, 35? (a) 25 (b) 26 (c) 24 (d) 30
12. 12.How many factors does 36 have? (a) 8 (b) 10 (c) 7 (d) 9
13. 13.A drawer has lots of blue, green, yellow and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 8 (d) 4
14. 14.How many prime numbers are there between 50 and 80? (a) 8 (b) 9 (c) 6 (d) 7
15. 15.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 84 (b) 48 (c) 13 (d) 42
16. 16.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 16 (d) 12
17. 17.A drawer has lots of green, blue, black, yellow 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) 10 (b) 6 (c) 5 (d) 2
18. 18.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 24 (c) 25 (d) 13
19. 19.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3² × 7 (c) 3 × 7² (d) 3 × 7
20. 20.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 576 (b) 266 (c) 384 (d) 256
21. 21.What is the midpoint of the line joining (4, 1) and (8, 13)? (a) (7, 6) (b) (2, 6) (c) (12, 14) (d) (6, 7)
22. 22.A bag has 6 yellow balls and 8 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) 14 (c) 9 (d) 2
23. 23.What is the sum of the roots of x² − 16x + 63 = 0? (a) 17 (b) 63 (c) 15 (d) 16
24. 24.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
25. 25.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 110° (c) 40° (d) 220°
26. 26.3 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) 5 (b) 6 (c) 9 (d) 12
27. 27.Using (a + b)² = a² + 2ab + b², what is 93²? (a) 7569 (b) 8659 (c) 8649 (d) 8109
28. 28.8 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) 14 (b) 96 (c) 56 (d) 48
29. 29.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
30. 30.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) 37 (b) 24 (c) 25 (d) 36
31. 31.Which is the correct factorisation of x² + 11x + 18? (a) (x + 2)(x + 9) (b) (x + 1)(x + 10) (c) (x − 2)(x − 9) (d) (x + 1)(x + 18)
32. 32.In a class of 25 children, 14 like cricket, 14 like football and 1 like neither. How many like both? (a) 3 (b) 1 (c) 4 (d) 24
33. 33.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 125° (b) 95° (c) 140° (d) 85°
34. 34.What is the smallest prime factor of 403? (a) 1 (b) 13 (c) 2 (d) 31
35. 35.A bag has 6 blue 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) 9 (b) 2 (c) 7 (d) 4
36. 36.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 19
38. 38.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 16 (d) 12
39. 39.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 506 (c) 231 (d) 253
40. 40.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 245° (c) 65° (d) 66°

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