Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 166 · 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 mean of 17, 18, 3 and 10? (a) 16 (b) 11 (c) 13 (d) 12
2. 2.What is the midpoint of the line joining (6, 14) and (8, 4)? (a) (14, 18) (b) (7, 9) (c) (9, 7) (d) (1, 5)
3. 3.5 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) 40 (b) 12 (c) 70 (d) 35
4. 4.What is the 32nd term of the AP 6, 14, 22, 30, …? (a) 248 (b) 256 (c) 262 (d) 254
5. 5.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
6. 6.In a class of 35 children, 14 like maths, 27 like science and 11 like both. How many like at least one of the two? (a) 19 (b) 35 (c) 30 (d) 41
7. 7.What is the mode of 5, 9, 5, 12, 6, 6 and 6? (a) 12 (b) 9 (c) 6 (d) 5
8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 15 (b) 16 (c) 14 (d) 5
9. 9.What is the distance between the points (2, 9) and (9, 33)? (a) 26 (b) 25 (c) 625 (d) 31
10. 10.How many factors does 84 have? (a) 11 (b) 13 (c) 10 (d) 12
11. 11.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7²
12. 12.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 90° (c) 155° (d) 270°
13. 13.What is the mode of 16, 7, 7, 7, 5, 18 and 16? (a) 18 (b) 7 (c) 16 (d) 5
14. 14.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 28 (c) 64 (d) 36
15. 15.What is the mean of 2, 14, 10 and 6? (a) 10 (b) 8 (c) 7 (d) 9
16. 16.A bag has 4 green, 5 white and 8 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 4/17 (b) 14/17 (c) 1/3 (d) 13/17
17. 17.What is the product of the roots of x² − 8x + 12 = 0? (a) 13 (b) 12 (c) 11 (d) 8
18. 18.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 24 (c) 72 (d) 27
19. 19.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 24 (c) 37 (d) 25
20. 20.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
21. 21.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 16 (d) 12
22. 22.In a class of 43 children, 26 like dance, 24 like music and 11 like both. How many like at least one of the two? (a) 43 (b) 28 (c) 39 (d) 50
23. 23.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 132 (c) 144 (d) 78
24. 24.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 70° (c) 120° (d) 30°
25. 25.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 592 (c) 582 (d) 591
26. 26.How many factors does 12 have? (a) 7 (b) 5 (c) 6 (d) 4
27. 27.A bag has 12 red balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 13 (c) 14 (d) 19
28. 28.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 338 (c) 702 (d) 351
29. 29.In a class of 42 children, 21 like cricket, 25 like football and 7 like neither. How many like both? (a) 4 (b) 11 (c) 35 (d) 7
30. 30.In a class of 47 children, 18 like mangoes, 22 like bananas and 2 like both. How many like neither? (a) 7 (b) 11 (c) 2 (d) 9
31. 31.Using (a + b)² = a² + 2ab + b², what is 24²? (a) 256 (b) 416 (c) 576 (d) 586
32. 32.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 109 (c) 108 (d) 216
33. 33.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 100 (d) 19
35. 35.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 15 (c) 10 (d) 25
36. 36.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 24 (d) 16
37. 37.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
38. 38.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 119 (b) 110 (c) 128 (d) 120
39. 39.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 55° (b) 150° (c) 155° (d) 125°
40. 40.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7

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