Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 449 · 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 coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 3/4 (c) 1/4 (d) 1/3
2. 2.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 14 (c) 49 (d) 98
3. 3.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 18 (c) 12 (d) 24
4. 4.What is the 39th term of the AP 1, 10, 19, 28, …? (a) 352 (b) 342 (c) 351 (d) 343
5. 5.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 40° (c) 50° (d) 130°
6. 6.How many prime numbers are there between 60 and 70? (a) 2 (b) 3 (c) 4 (d) 1
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 2/11 (c) 1/11 (d) 1/18
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 3/11 (c) 1/11 (d) 1/12
9. 9.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 320 (b) 160 (c) 176 (d) 34
10. 10.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 100 (d) 45
11. 11.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2³ × 3 × 7
12. 12.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 9) (b) (x + 1)(x + 24) (c) (x + 4)(x + 6) (d) (x − 4)(x − 6)
13. 13.A bag has 3 white, 4 green and 2 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 4/9 (b) 1/2 (c) 2/3 (d) 1/3
14. 14.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) 48 (c) 49 (d) 37
15. 15.A drawer has lots of white 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) 2 (b) 3 (c) 4 (d) 5
16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
17. 17.What is the 24th term of the AP 13, 16, 19, 22, …? (a) 85 (b) 82 (c) 72 (d) 69
18. 18.A bag has 2 green, 9 white and 4 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 2/13 (b) 2/15 (c) 1/3 (d) 13/15
19. 19.What is the distance between the points (1, 14) and (25, 7)? (a) 26 (b) 625 (c) 31 (d) 25
20. 20.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 33 (c) 36 (d) 11
21. 21.What is the median of 8, 7, 34, 16, 3, 4 and 6? (a) 6 (b) 7 (c) 16 (d) 8
22. 22.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) 180 (b) 63 (c) 60 (d) 20
23. 23.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 816 (c) 444 (d) 408
24. 24.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 256 cu cm (c) 24 cu cm (d) 384 cu cm
25. 25.In a class of 39 children, 12 like maths, 21 like science and 10 like neither. How many like both? (a) 4 (b) 5 (c) 10 (d) 29
26. 26.In a class of 45 children, 19 like maths, 30 like science and 10 like both. How many like only maths? (a) 9 (b) 15 (c) 20 (d) 19
27. 27.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
28. 28.What is the mean of 2, 12, 7, 7, 11 and 3? (a) 8 (b) 7 (c) 9 (d) 6
29. 29.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
30. 30.How many prime numbers are there between 20 and 50? (a) 9 (b) 6 (c) 8 (d) 7
31. 31.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 10° (c) 80° (d) 100°
32. 32.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 56 (c) 11 (d) 32
33. 33.What is the smallest prime factor of 341? (a) 31 (b) 2 (c) 11 (d) 1
34. 34.How many factors does 84 have? (a) 12 (b) 10 (c) 13 (d) 11
35. 35.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 80° (d) 100°
36. 36.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
37. 37.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 120° (c) 30° (d) 60°
38. 38.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 6 (c) 12 (d) 9
39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 16 (b) 5 (c) 17 (d) 15
40. 40.Which is the correct factorisation of x² + 6x + 8? (a) (x − 2)(x − 4) (b) (x + 2)(x + 4) (c) (x + 1)(x + 8) (d) (x + 1)(x + 5)

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