Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 40 · 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 straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 30° (c) 31° (d) 150°
2. 2.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 756 (c) 378 (d) 53
3. 3.In a class of 34 children, 16 like maths, 20 like science and 9 like both. How many like neither? (a) 8 (b) 7 (c) 16 (d) 9
4. 4.What is the smallest prime factor of 169? (a) 3 (b) 1 (c) 2 (d) 13
5. 5.What is the midpoint of the line joining (0, 18) and (10, 8)? (a) (5, 5) (b) (13, 5) (c) (10, 26) (d) (5, 13)
6. 6.A bag has 9 red balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 4 (c) 10 (d) 12
7. 7.In a class of 20 children, 11 like cricket, 10 like football and 6 like both. How many like at least one of the two? (a) 15 (b) 21 (c) 9 (d) 20
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 day of the week? (a) 15 (b) 7 (c) 8 (d) 14
9. 9.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/4 (c) 1/4 (d) 3/8
10. 10.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 25 (d) 20
11. 11.The mean of 4 numbers is 16. When the number 21 is added to them, what is the new mean? (a) 19 (b) 16 (c) 17 (d) 18
12. 12.What is the midpoint of the line joining (4, 18) and (6, 10)? (a) (1, 4) (b) (5, 14) (c) (10, 28) (d) (14, 5)
13. 13.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 110° (b) 130° (c) 70° (d) 160°
14. 14.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 40° (d) 130°
15. 15.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 64 (c) 40 (d) 32
16. 16.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 436 (c) 406 (d) 435
17. 17.A bag has 6 red balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 8 (d) 7
18. 18.In a class of 38 children, 15 like maths, 15 like science and 2 like both. How many like neither? (a) 8 (b) 2 (c) 10 (d) 12
19. 19.What is the smallest prime factor of 115? (a) 23 (b) 1 (c) 2 (d) 5
20. 20.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 50° (b) 150° (c) 160° (d) 130°
21. 21.What is the distance between the points (0, 25) and (12, 9)? (a) 28 (b) 400 (c) 21 (d) 20
22. 22.How many prime numbers are there between 90 and 110? (a) 7 (b) 6 (c) 5 (d) 4
23. 23.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 1/3 (d) 2/3
24. 24.Which is the correct factorisation of x² + 11x + 18? (a) (x + 1)(x + 18) (b) (x − 2)(x − 9) (c) (x + 2)(x + 9) (d) (x + 1)(x + 10)
25. 25.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 231 (c) 226 (d) 232
26. 26.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 36 (c) 72 (d) 81
27. 27.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 50° (c) 320° (d) 140°
28. 28.A bag has 3 black balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 5 (c) 6 (d) 4
29. 29.What is the midpoint of the line joining (6, 14) and (8, 2)? (a) (14, 16) (b) (8, 7) (c) (7, 8) (d) (1, 6)
30. 30.A bag has 7 white balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 8 (b) 9 (c) 15 (d) 2
31. 31.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 230° (b) 100° (c) 50° (d) 130°
32. 32.What is the median of 5, 38, 33, 23, 25, 8 and 10? (a) 23 (b) 25 (c) 24 (d) 10
33. 33.What are the roots of x² − 14x + 48 = 0? (a) 1 and 48 (b) 1 and 13 (c) 2 and 24 (d) 6 and 8
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
35. 35.A bag has 5 red balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 10 (c) 2 (d) 7
36. 36.What is the mean of 19, 4, 20 and 17? (a) 15 (b) 16 (c) 12 (d) 20
37. 37.In which quadrant does the point (5, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
38. 38.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) 27 (b) 81 (c) 9 (d) 30
39. 39.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 145° (b) 135° (c) 80° (d) 35°
40. 40.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 49 (c) 14 (d) 21

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