Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 642 · 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 distance between the points (8, 13) and (16, 7)? (a) 10 (b) 11 (c) 100 (d) 14
2. 2.A drawer has lots of black, blue and white 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) 3 (c) 4 (d) 2
3. 3.How many prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 5 (d) 3
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 1/11 (c) 7/36 (d) 6/11
5. 5.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 66 (c) 69 (d) 198
6. 6.A bag has 5 yellow balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 11 (d) 15
7. 7.How many factors does 90 have? (a) 10 (b) 13 (c) 12 (d) 11
8. 8.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 65° (b) 155° (c) 140° (d) 115°
9. 9.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 36 (d) 15
10. 10.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
11. 11.What is the median of 6, 20, 24, 27 and 30? (a) 27 (b) 24 (c) 25 (d) 20
12. 12.In a class of 45 children, 23 like cricket, 19 like football and 3 like both. How many like at least one of the two? (a) 45 (b) 42 (c) 39 (d) 36
13. 13.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
14. 14.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 86° (d) 85°
15. 15.What is the smallest prime factor of 119? (a) 17 (b) 1 (c) 2 (d) 7
16. 16.What is the distance between the points (6, 7) and (14, 13)? (a) 100 (b) 11 (c) 14 (d) 10
17. 17.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 45° (c) 135° (d) 91°
18. 18.A bag has 7 green balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 9 (d) 8
19. 19.In which quadrant does the point (4, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
20. 20.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
21. 21.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 300° (b) 60° (c) 150° (d) 120°
22. 22.Using (a − b)² = a² − 2ab + b², what is 96²? (a) 9226 (b) 10816 (c) 9216 (d) 9984
23. 23.In a class of 33 children, 18 like maths, 9 like science and 3 like both. How many like at least one of the two? (a) 27 (b) 21 (c) 33 (d) 24
24. 24.In a class of 31 children, 13 like maths, 17 like science and 9 like both. How many like only maths? (a) 4 (b) 14 (c) 13 (d) 8
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 3/11 (c) 1/12 (d) 1/11
26. 26.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 225 (b) 450 (c) 243 (d) 41
27. 27.What is the mode of 6, 11, 4, 6, 6, 11 and 10? (a) 10 (b) 6 (c) 11 (d) 4
28. 28.If a + b = 11 and ab = 24, what is (a − b)²? (a) 73 (b) 121 (c) 5 (d) 25
29. 29.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
30. 30.What is the mean of 6, 12, 7 and 23? (a) 16 (b) 13 (c) 11 (d) 12
31. 31.What is the midpoint of the line joining (3, 8) and (13, 14)? (a) (5, 3) (b) (11, 8) (c) (16, 22) (d) (8, 11)
32. 32.A bag has 4 green balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 5 (c) 6 (d) 2
33. 33.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 3/4 (c) 1/3 (d) 1/2
34. 34.A bag has 12 yellow balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 13 (c) 2 (d) 5
35. 35.There are 4 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 28 (b) 24 (c) 48 (d) 10
36. 36.What is the mean of 2, 15, 15, 2 and 6? (a) 9 (b) 8 (c) 7 (d) 10
37. 37.Which is the correct factorisation of x² + 13x + 40? (a) (x − 5)(x − 8) (b) (x + 5)(x + 8) (c) (x + 1)(x + 40) (d) (x + 1)(x + 12)
38. 38.What is the midpoint of the line joining (8, 8) and (10, 10)? (a) (10, 9) (b) (9, 9) (c) (18, 18) (d) (1, 1)
39. 39.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) 24 (c) 12 (d) 25
40. 40.What is the 11th term of the AP 14, 17, 20, 23, …? (a) 33 (b) 30 (c) 47 (d) 44

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