Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 796 · 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 sum of the first 5 terms of the AP 3, 7, 11, …? (a) 19 (b) 110 (c) 65 (d) 55
2. 2.How many factors does 68 have? (a) 4 (b) 5 (c) 6 (d) 7
3. 3.What is the median of 25, 30, 16, 4, 8, 28 and 3? (a) 16 (b) 25 (c) 8 (d) 4
4. 4.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 21 (c) 6 (d) 54
5. 5.In a class of 20 children, 13 like tea, 7 like coffee and 4 like both. How many like only tea? (a) 13 (b) 9 (c) 4 (d) 3
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/12 (d) 1/9
7. 7.A bag has 5 green, 9 white and 4 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 5/18 (c) 13/18 (d) 7/9
8. 8.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) 24 (b) 13 (c) 25 (d) 12
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 2/11 (c) 1/18 (d) 1/12
10. 10.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 42 (c) 117 (d) 39
11. 11.The mean of 6 numbers is 15. When the number 43 is added to them, what is the new mean? (a) 29 (b) 20 (c) 15 (d) 19
12. 12.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4
13. 13.How many factors does 27 have? (a) 3 (b) 5 (c) 2 (d) 4
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/9 (c) 5/36 (d) 1/11
15. 15.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 36 sq cm (d) 54 sq cm
16. 16.What is the midpoint of the line joining (0, 6) and (12, 18)? (a) (6, 12) (b) (12, 24) (c) (12, 6) (d) (6, 6)
17. 17.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 16° (c) 195° (d) 165°
18. 18.A bag has 6 yellow, 2 red and 9 green balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 11/17 (c) 12/17 (d) 6/17
19. 19.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
20. 20.A drawer has lots of white, green, red and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 5 (c) 4 (d) 2
21. 21.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 10° (c) 160° (d) 20°
22. 22.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 217 (b) 196 (c) 46 (d) 392
23. 23.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 145° (b) 160° (c) 125° (d) 55°
24. 24.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 6 (d) 8
25. 25.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x + 7)(x + 9) (c) (x − 7)(x − 9) (d) (x + 1)(x + 63)
26. 26.What is the sum of the roots of x² − 13x + 36 = 0? (a) 12 (b) 36 (c) 13 (d) 14
27. 27.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
28. 28.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 81 (c) 30 (d) 27
29. 29.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
30. 30.A drawer has lots of blue, white, green and black 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) 8 (c) 5 (d) 2
31. 31.In a class of 36 children, 15 like tea, 23 like coffee and 12 like both. How many like only tea? (a) 3 (b) 13 (c) 11 (d) 15
32. 32.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 105° (c) 76° (d) 75°
33. 33.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 49 (b) 84 (c) 13 (d) 42
34. 34.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 240 (c) 20 (d) 25
35. 35.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
36. 36.In which quadrant does the point (−3, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
37. 37.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 156 (c) 72 (d) 78
38. 38.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 91 (d) 196
39. 39.In which quadrant does the point (7, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
40. 40.What is the sum of the roots of x² − 14x + 45 = 0? (a) 45 (b) 13 (c) 15 (d) 14

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