Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 647 · 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.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 5550 (c) 2775 (d) 2701
2. 2.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 78 (b) 39 (c) 42 (d) 9
3. 3.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
4. 4.In a class of 39 children, 14 like mangoes, 24 like bananas and 7 like both. How many like only mangoes? (a) 7 (b) 15 (c) 17 (d) 14
5. 5.What is the product of the roots of x² − 9x + 14 = 0? (a) 14 (b) 9 (c) 15 (d) 13
6. 6.A bag has 10 yellow balls and 12 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) 13 (c) 11 (d) 22
7. 7.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 10 (d) 15
8. 8.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 100° (d) 50°
9. 9.A drawer has lots of black, green, 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) 4 (b) 8 (c) 2 (d) 5
10. 10.If a + b = 8 and ab = 7, what is (a − b)²? (a) 50 (b) 6 (c) 36 (d) 64
11. 11.The mean of 4 numbers is 12. When the number 32 is added to them, what is the new mean? (a) 12 (b) 22 (c) 17 (d) 16
12. 12.In a class of 45 children, 18 like maths, 24 like science and 7 like both. How many like only maths? (a) 18 (b) 21 (c) 11 (d) 17
13. 13.What is the mean of 19, 9, 17, 17, 9 and 7? (a) 15 (b) 13 (c) 14 (d) 12
14. 14.How many prime numbers are there between 10 and 30? (a) 5 (b) 7 (c) 6 (d) 8
15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
16. 16.In a class of 31 children, 13 like maths, 16 like science and 8 like both. How many like only maths? (a) 13 (b) 5 (c) 8 (d) 15
17. 17.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
18. 18.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 30° (b) 120° (c) 150° (d) 90°
19. 19.What is the missing term in the AP 20, 26, ?, 38, 44? (a) 33 (b) 31 (c) 32 (d) 38
20. 20.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 3/8 (d) 7/8
21. 21.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 125° (b) 155° (c) 55° (d) 150°
22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 19 (b) 8 (c) 18 (d) 20
23. 23.A bag has 7 blue, 4 yellow and 5 white balls. One ball is taken out without looking. What is the probability that it is blue? (a) 7/9 (b) 1/3 (c) 9/16 (d) 7/16
24. 24.What is the mode of 8, 7, 6, 6, 7, 16 and 6? (a) 8 (b) 7 (c) 16 (d) 6
25. 25.A drawer has lots of green, white 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) 6 (b) 2 (c) 3 (d) 4
26. 26.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 315° (c) 45° (d) 135°
27. 27.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 91 (c) 156 (d) 78
28. 28.What is the 27th term of the AP 2, 4, 6, 8, …? (a) 55 (b) 54 (c) 56 (d) 52
29. 29.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 210 (b) 420 (c) 230 (d) 39
30. 30.A drawer has lots of white, blue, 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) 2 (b) 4 (c) 8 (d) 5
31. 31.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 30 (d) 15
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
33. 33.Which is the correct factorisation of x² + 12x + 32? (a) (x − 4)(x − 8) (b) (x + 1)(x + 32) (c) (x + 1)(x + 11) (d) (x + 4)(x + 8)
34. 34.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 57 (c) 162 (d) 54
35. 35.A drawer has lots of red, green and yellow 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) 6 (c) 4 (d) 2
36. 36.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 29 (d) 22
37. 37.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 64 (c) 16 (d) 56
38. 38.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) 13 (b) 12 (c) 24 (d) 25
39. 39.In a class of 41 children, 24 like mangoes, 25 like bananas and 9 like both. How many like at least one of the two? (a) 40 (b) 49 (c) 41 (d) 31
40. 40.6 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) 8 (b) 24 (c) 18 (d) 12

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