Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 295 · 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.The mean of 6 numbers is 37. When the number 58 is added to them, what is the new mean? (a) 37 (b) 41 (c) 39 (d) 40
2. 2.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2499 (b) 2601 (c) 2401 (d) 2411
3. 3.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) 29 (b) 22 (c) 28 (d) 21
4. 4.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 80° (d) 70°
5. 5.A bag has 11 yellow balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 23 (b) 12 (c) 2 (d) 13
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/11 (c) 7/36 (d) 1/6
7. 7.A drawer has lots of red 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) 5 (c) 4 (d) 2
8. 8.A drawer has lots of yellow, 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) 5 (b) 2 (c) 6 (d) 10
9. 9.What is the mean of 4, 16, 8, 12, 19 and 13? (a) 11 (b) 12 (c) 14 (d) 13
10. 10.What is the distance between the points (3, 20) and (8, 8)? (a) 13 (b) 169 (c) 14 (d) 17
11. 11.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/8 (c) 1/7 (d) 7/8
12. 12.A drawer has lots of black, white, blue 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) 5 (b) 8 (c) 4 (d) 2
13. 13.What is the midpoint of the line joining (0, 11) and (4, 7)? (a) (2, 2) (b) (9, 2) (c) (4, 18) (d) (2, 9)
14. 14.How many prime numbers are there between 90 and 110? (a) 6 (b) 4 (c) 7 (d) 5
15. 15.A bag has 11 red balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 19 (c) 13 (d) 12
16. 16.Using (a + b)² = a² + 2ab + b², what is 54²? (a) 2916 (b) 2926 (c) 2516 (d) 2116
17. 17.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 108 (b) 216 (c) 20 (d) 117
18. 18.If a + b = 18 and ab = 77, what is (a − b)²? (a) 4 (b) 324 (c) 170 (d) 16
19. 19.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
20. 20.5 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 70 (b) 35 (c) 12 (d) 40
21. 21.What is the mode of 20, 9, 13, 15, 9, 9 and 20? (a) 13 (b) 20 (c) 9 (d) 15
22. 22.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 73 (c) 17 (d) 72
23. 23.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 275° (d) 5°
24. 24.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
25. 25.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 66 (c) 78 (d) 132
26. 26.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
27. 27.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 216 (c) 75 (d) 24
28. 28.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 2/3 (c) 1/4 (d) 1/2
29. 29.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
30. 30.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 10 (b) 16 (c) 8 (d) 9
31. 31.7 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 49 (c) 98 (d) 14
32. 32.In a class of 13 children, 7 like cricket, 8 like football and 2 like neither. How many like both? (a) 11 (b) 4 (c) 2 (d) 5
33. 33.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 15 (c) 7 (d) 10
34. 34.What is the sum of the roots of x² − 13x + 36 = 0? (a) 12 (b) 13 (c) 36 (d) 14
35. 35.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
36. 36.What is the distance between the points (9, 5) and (13, 2)? (a) 7 (b) 6 (c) 5 (d) 25
37. 37.What is the mean of 10, 13, 10, 5, 16 and 18? (a) 12 (b) 11 (c) 14 (d) 13
38. 38.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 160° (b) 165° (c) 35° (d) 15°
39. 39.In a class of 19 children, 15 like dance, 8 like music and 5 like both. How many like at least one of the two? (a) 18 (b) 13 (c) 23 (d) 19
40. 40.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 87 (b) 96 (c) 88 (d) 78

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