Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 773 · 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 midpoint of the line joining (4, 6) and (6, 0)? (a) (10, 6) (b) (5, 3) (c) (1, 3) (d) (3, 5)
2. 2.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 55 (d) 90
3. 3.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
4. 4.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) 15 (b) 135 (c) 45 (d) 48
5. 5.A bag has 4 blue balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 6 (c) 11 (d) 5
6. 6.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 120 (d) 25
7. 7.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 15 (d) 36
8. 8.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 75° (b) 120° (c) 135° (d) 105°
9. 9.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4560 (c) 4608 (d) 4656
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 7/36 (c) 6/11 (d) 1/11
12. 12.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
13. 13.The mean of 4 numbers is 25. When the number 10 is added to them, what is the new mean? (a) 23 (b) 21 (c) 25 (d) 22
14. 14.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 3/8 (c) 7/8 (d) 1/4
15. 15.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
16. 16.A bag has 11 white 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) 15 (b) 12 (c) 2 (d) 5
17. 17.In a class of 37 children, 18 like maths, 16 like science and 3 like both. How many like neither? (a) 9 (b) 6 (c) 3 (d) 7
18. 18.6 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) 36 (b) 18 (c) 24 (d) 9
19. 19.What is the mean of 2, 11, 19, 15 and 13? (a) 12 (b) 13 (c) 15 (d) 10
20. 20.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
21. 21.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 24 (c) 12 (d) 8
22. 22.What is the smallest prime factor of 33? (a) 11 (b) 1 (c) 2 (d) 3
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/11 (c) 5/36 (d) 1/6
24. 24.In a class of 27 children, 20 like dance, 14 like music and 10 like both. How many like neither? (a) 13 (b) 4 (c) 10 (d) 3
25. 25.If a + b = 13 and ab = 42, what is (a − b)²? (a) 1 (b) 169 (c) 85 (d) 127
26. 26.In a class of 45 children, 23 like maths, 23 like science and 4 like neither. How many like both? (a) 5 (b) 1 (c) 4 (d) 41
27. 27.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 66 (c) 78 (d) 156
28. 28.A bag has 7 green balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 8 (c) 6 (d) 2
29. 29.A bag has 9 green, 7 blue and 7 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 9/14 (b) 14/23 (c) 1/3 (d) 9/23
30. 30.What is the median of 17, 5, 15, 37, 6, 32 and 10? (a) 17 (b) 37 (c) 10 (d) 15
31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
32. 32.What is the 32nd term of the AP 15, 21, 27, 33, …? (a) 192 (b) 207 (c) 186 (d) 201
33. 33.What is the smallest prime factor of 39? (a) 2 (b) 13 (c) 3 (d) 1
34. 34.What is the mode of 1, 2, 1, 7, 1, 18 and 18? (a) 18 (b) 7 (c) 2 (d) 1
35. 35.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 60° (b) 150° (c) 300° (d) 120°
36. 36.In a class of 44 children, 28 like cricket, 24 like football and 2 like neither. How many like both? (a) 42 (b) 8 (c) 2 (d) 10
37. 37.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 10) (b) (x − 5)(x − 6) (c) (x + 1)(x + 30) (d) (x + 5)(x + 6)
38. 38.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 18 (c) 72 (d) 36
39. 39.Which is the correct factorisation of x² + 14x + 45? (a) (x + 1)(x + 13) (b) (x − 5)(x − 9) (c) (x + 5)(x + 9) (d) (x + 1)(x + 45)
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) 12 (b) 24 (c) 8 (d) 18

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