Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 533 · 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.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 45° (b) 145° (c) 170° (d) 10°
2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
3. 3.What is the smallest prime factor of 69? (a) 1 (b) 23 (c) 2 (d) 3
4. 4.What is the prime factorisation of 18? (a) 2² × 3 (b) 2² × 3² (c) 2 × 3² (d) 2 × 3³
5. 5.What is the distance between the points (0, 6) and (4, 9)? (a) 5 (b) 6 (c) 7 (d) 25
6. 6.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 486 cu cm (d) 27 cu cm
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/11 (d) 1/12
8. 8.What is the 30th term of the AP 8, 12, 16, 20, …? (a) 128 (b) 124 (c) 116 (d) 120
9. 9.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 49 (c) 48 (d) 37
10. 10.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 36 (d) 72
11. 11.In a class of 34 children, 24 like tea, 14 like coffee and 6 like both. How many like at least one of the two? (a) 38 (b) 26 (c) 32 (d) 34
12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 16 (d) 18
13. 13.What are the roots of x² − 12x + 32 = 0? (a) 4 and 8 (b) 1 and 32 (c) 2 and 16 (d) 1 and 11
14. 14.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 597 (c) 470 (d) 598
15. 15.In a class of 30 children, 24 like cricket, 7 like football and 4 like both. How many like at least one of the two? (a) 27 (b) 30 (c) 31 (d) 23
16. 16.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
17. 17.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
18. 18.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
19. 19.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
20. 20.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 56 (c) 28 (d) 36
21. 21.What is the mean of 15, 6, 20 and 7? (a) 12 (b) 11 (c) 13 (d) 16
22. 22.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) 4 times (c) 2 times (d) 8 times
23. 23.What is the midpoint of the line joining (3, 12) and (11, 4)? (a) (14, 16) (b) (7, 8) (c) (4, 4) (d) (8, 7)
24. 24.The mean of 5 numbers is 15. When the number 9 is added to them, what is the new mean? (a) 12 (b) 13 (c) 15 (d) 14
25. 25.In a class of 47 children, 26 like cricket, 32 like football and 12 like both. How many like only cricket? (a) 26 (b) 20 (c) 15 (d) 14
26. 26.What are the roots of x² − 15x + 56 = 0? (a) 1 and 14 (b) 1 and 56 (c) 7 and 8 (d) 2 and 28
27. 27.In a class of 32 children, 24 like dance, 14 like music and 5 like neither. How many like both? (a) 6 (b) 27 (c) 5 (d) 11
28. 28.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/4
29. 29.What is the mean of 20, 8, 9 and 19? (a) 13 (b) 16 (c) 14 (d) 15
30. 30.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 21° (c) 20° (d) 200°
31. 31.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 54 (d) 153
32. 32.In a class of 36 children, 24 like dance, 16 like music and 7 like both. How many like neither? (a) 3 (b) 10 (c) 7 (d) 4
33. 33.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 130° (d) 40°
34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 18 (b) 20 (c) 8 (d) 19
36. 36.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 30 (c) 90 (d) 33
37. 37.What is the smallest prime factor of 33? (a) 3 (b) 2 (c) 11 (d) 1
38. 38.In a class of 39 children, 12 like dance, 23 like music and 6 like both. How many like at least one of the two? (a) 35 (b) 39 (c) 29 (d) 23
39. 39.A bag has 12 blue balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 20 (b) 13 (c) 14 (d) 2
40. 40.What is the median of 5, 25, 2, 20 and 27? (a) 2 (b) 5 (c) 20 (d) 25

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