Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 993 · 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. 1.7 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 14 (b) 98 (c) 56 (d) 49
2. 2.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 171 (c) 19 (d) 57
3. 3.What is the midpoint of the line joining (2, 10) and (12, 2)? (a) (6, 7) (b) (14, 12) (c) (7, 6) (d) (5, 4)
4. 4.What is the mode of 13, 3, 13, 9, 3, 11 and 13? (a) 11 (b) 9 (c) 13 (d) 3
5. 5.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
6. 6.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 105° (b) 70° (c) 110° (d) 145°
7. 7.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 60 (c) 20 (d) 180
8. 8.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/4 (c) 5/6 (d) 1/3
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 1/11 (c) 2/11 (d) 1/12
10. 10.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 422 (b) 525 (c) 526 (d) 516
11. 11.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 15 (d) 22
12. 12.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 190 (d) 180
13. 13.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 35° (c) 110° (d) 70°
14. 14.A bag has 9 red, 5 white and 3 yellow balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 12/17 (c) 13/17 (d) 5/17
15. 15.If a + b = 17 and ab = 60, what is a² + b²? (a) 289 (b) 169 (c) 229 (d) 409
16. 16.A bag has 4 yellow, 4 green and 7 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 11/15 (b) 4/15 (c) 4/11 (d) 1/3
17. 17.In a class of 39 children, 16 like maths, 22 like science and 2 like both. How many like neither? (a) 5 (b) 1 (c) 2 (d) 3
18. 18.How many factors does 64 have? (a) 6 (b) 5 (c) 7 (d) 8
19. 19.How many prime numbers are there between 40 and 70? (a) 8 (b) 6 (c) 9 (d) 7
20. 20.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 130° (d) 85°
21. 21.A bag has 6 black balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 7 (d) 10
22. 22.What is the sum of the roots of x² − 14x + 45 = 0? (a) 15 (b) 45 (c) 13 (d) 14
23. 23.In a class of 50 children, 26 like cricket, 21 like football and 10 like neither. How many like both? (a) 40 (b) 10 (c) 7 (d) 8
24. 24.What is the median of 29, 36, 40, 6 and 7? (a) 40 (b) 7 (c) 29 (d) 36
25. 25.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
26. 26.A drawer has lots of white, green, blue, red 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) 2 (b) 5 (c) 10 (d) 6
27. 27.What is the distance between the points (0, 9) and (12, 0)? (a) 15 (b) 16 (c) 225 (d) 21
28. 28.In which quadrant does the point (−7, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
29. 29.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/2 (c) 1/4 (d) 1/3
30. 30.Which is the correct factorisation of x² + 11x + 24? (a) (x + 1)(x + 24) (b) (x + 1)(x + 10) (c) (x + 3)(x + 8) (d) (x − 3)(x − 8)
31. 31.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
32. 32.What is the distance between the points (1, 8) and (4, 4)? (a) 25 (b) 6 (c) 7 (d) 5
33. 33.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 7 (c) 21 (d) 63
34. 34.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°
35. 35.In a class of 26 children, 20 like dance, 11 like music and 1 like neither. How many like both? (a) 25 (b) 1 (c) 5 (d) 6
36. 36.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 81 (c) 45 (d) 36
37. 37.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 36 (d) 81
38. 38.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
39. 39.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 624 (c) 633 (d) 634
40. 40.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 435 (c) 870 (d) 57

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