Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 724 · 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.How many prime numbers are there between 70 and 80? (a) 5 (b) 2 (c) 3 (d) 4
2. 2.What is the distance between the points (8, 5) and (14, 13)? (a) 10 (b) 14 (c) 100 (d) 11
3. 3.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 45° (d) 135°
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
5. 5.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 57 (c) 18 (d) 54
6. 6.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) 8 (b) 18 (c) 12 (d) 24
7. 7.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 60° (d) 75°
8. 8.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 3025 (b) 3035 (c) 2025 (d) 2525
9. 9.In which quadrant does the point (6, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
10. 10.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 100 (c) 55 (d) 45
11. 11.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 117 (c) 126 (d) 108
12. 12.If a + b = 16 and ab = 60, what is (a − b)²? (a) 16 (b) 136 (c) 256 (d) 4
13. 13.What is the median of 3, 9, 31, 1, 27, 13 and 19? (a) 13 (b) 19 (c) 1 (d) 9
14. 14.What is the distance between the points (7, 8) and (10, 12)? (a) 7 (b) 6 (c) 25 (d) 5
15. 15.A bag has 9 green, 6 white and 8 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 17/23 (b) 1/3 (c) 6/17 (d) 6/23
16. 16.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
17. 17.What is the median of 9, 16, 11, 32 and 38? (a) 11 (b) 32 (c) 17 (d) 16
18. 18.In which quadrant does the point (−6, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
19. 19.What is the midpoint of the line joining (4, 18) and (6, 10)? (a) (10, 28) (b) (1, 4) (c) (14, 5) (d) (5, 14)
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
21. 21.What is the distance between the points (0, 1) and (16, 13)? (a) 28 (b) 21 (c) 20 (d) 400
22. 22.How many factors does 16 have? (a) 5 (b) 4 (c) 6 (d) 3
23. 23.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 36 (d) 12
24. 24.What is the median of 1, 29, 16, 10, 9, 24 and 23? (a) 10 (b) 16 (c) 17 (d) 23
25. 25.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/8 (c) 1/8 (d) 3/4
26. 26.In which quadrant does the point (6, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
27. 27.In a class of 44 children, 24 like cricket, 28 like football and 9 like both. How many like neither? (a) 10 (b) 9 (c) 2 (d) 1
28. 28.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) 69 (b) 198 (c) 22 (d) 66
29. 29.A drawer has lots of 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) 3 (b) 5 (c) 4 (d) 2
30. 30.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) 51 (b) 153 (c) 54 (d) 17
31. 31.Which is the correct factorisation of x² + 10x + 21? (a) (x + 3)(x + 7) (b) (x − 3)(x − 7) (c) (x + 1)(x + 21) (d) (x + 1)(x + 9)
32. 32.In a class of 32 children, 12 like tea, 14 like coffee and 4 like both. How many like neither? (a) 6 (b) 14 (c) 10 (d) 4
33. 33.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 144 (b) 136 (c) 24 (d) 272
34. 34.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
35. 35.What is the median of 3, 37, 33, 34, 11, 14 and 35? (a) 14 (b) 33 (c) 32 (d) 34
36. 36.What is the median of 1, 38, 7, 37, 13, 16 and 15? (a) 16 (b) 15 (c) 37 (d) 13
37. 37.A bag has 10 blue balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 13 (c) 11 (d) 12
38. 38.What is the midpoint of the line joining (6, 6) and (10, 0)? (a) (8, 3) (b) (16, 6) (c) (3, 8) (d) (2, 3)
39. 39.What is the product of the roots of x² − 10x + 16 = 0? (a) 17 (b) 10 (c) 15 (d) 16
40. 40.In which quadrant does the point (−2, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

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