Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 154 · 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 mean of 2, 16, 10, 7, 13 and 12? (a) 12 (b) 11 (c) 9 (d) 10
2. 2.In a class of 53 children, 29 like dance, 31 like music and 12 like both. How many like at least one of the two? (a) 53 (b) 60 (c) 48 (d) 36
3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/36 (c) 5/11 (d) 1/6
4. 4.In a class of 22 children, 8 like maths, 16 like science and 2 like neither. How many like both? (a) 5 (b) 20 (c) 2 (d) 4
5. 5.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 55° (d) 90°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 20° (b) 200° (c) 100° (d) 80°
7. 7.Which term of the AP 12, 16, 20, 24, … is 52? (a) 13th (b) 11th (c) 10th (d) 12th
8. 8.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 3/4 (c) 1/2 (d) 1/3
9. 9.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 15 (d) 10
10. 10.In a class of 47 children, 18 like tea, 25 like coffee and 6 like both. How many like only tea? (a) 12 (b) 22 (c) 19 (d) 18
11. 11.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 135° (b) 20° (c) 160° (d) 65°
12. 12.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
13. 13.What is the 15th term of the AP 4, 9, 14, 19, …? (a) 79 (b) 74 (c) 70 (d) 75
14. 14.A drawer has lots of red, blue, black 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) 4 (b) 5 (c) 8 (d) 2
15. 15.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
16. 16.What is the mean of 12, 13, 18, 6 and 6? (a) 12 (b) 13 (c) 11 (d) 10
17. 17.A bag has 8 white, 8 red and 2 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 17/18 (b) 1/3 (c) 1/9 (d) 8/9
18. 18.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 50° (b) 140° (c) 130° (d) 90°
19. 19.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1830 (c) 1800 (d) 1770
20. 20.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x − 7)(x − 8) (c) (x + 1)(x + 14) (d) (x + 7)(x + 8)
21. 21.What is the product of the roots of x² − 5x + 6 = 0? (a) 5 (b) 8 (c) 7 (d) 6
22. 22.Using (a − b)² = a² − 2ab + b², what is 57²? (a) 3259 (b) 3969 (c) 3249 (d) 3591
23. 23.A bag has 5 yellow balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 7 (b) 13 (c) 2 (d) 6
24. 24.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
25. 25.In a class of 31 children, 15 like dance, 17 like music and 6 like both. How many like at least one of the two? (a) 20 (b) 31 (c) 32 (d) 26
26. 26.What is the sum of all the whole numbers from 1 to 37? (a) 666 (b) 703 (c) 704 (d) 1406
27. 27.What is the mode of 12, 13, 5, 5, 5, 13 and 4? (a) 12 (b) 5 (c) 4 (d) 13
28. 28.What is the smallest prime factor of 217? (a) 31 (b) 7 (c) 2 (d) 1
29. 29.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 49 (b) 14 (c) 56 (d) 98
30. 30.There are 5 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 20 (c) 15 (d) 8
31. 31.In a class of 21 children, 12 like mangoes, 9 like bananas and 3 like both. How many like neither? (a) 3 (b) 4 (c) 0 (d) 6
32. 32.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 127 cu cm (b) 190 cu cm (c) 18 cu cm (d) 126 cu cm
33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 6 (d) 16
34. 34.A bag has 7 white, 7 blue and 3 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 14/17 (b) 3/14 (c) 1/3 (d) 3/17
35. 35.A drawer has lots of green, blue, black, white 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) 6 (b) 5 (c) 10 (d) 2
36. 36.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 60° (c) 61° (d) 120°
37. 37.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 1/11 (c) 1/9 (d) 3/11
39. 39.A bag has 5 white balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 7 (b) 10 (c) 2 (d) 6
40. 40.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 20° (c) 160° (d) 40°

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