Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 157 · 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 20th term of the AP 3, 7, 11, 15, …? (a) 83 (b) 79 (c) 76 (d) 80
2. 2.How many factors does 111 have? (a) 2 (b) 5 (c) 3 (d) 4
3. 3.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 10 (d) 20
4. 4.A bag has 8 blue, 2 green and 8 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 4/5 (b) 1/3 (c) 5/9 (d) 4/9
5. 5.What is the median of 32, 11, 3, 9 and 30? (a) 11 (b) 30 (c) 17 (d) 3
6. 6.What is the median of 25, 31, 2, 12, 21, 40 and 38? (a) 12 (b) 21 (c) 31 (d) 25
7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 33 (d) 289
8. 8.How many factors does 76 have? (a) 4 (b) 5 (c) 6 (d) 7
9. 9.Using (a − b)² = a² − 2ab + b², what is 59²? (a) 3491 (b) 3481 (c) 3599 (d) 3721
10. 10.What is the sum of all the whole numbers from 1 to 60? (a) 1830 (b) 1770 (c) 3660 (d) 1800
11. 11.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 342 (c) 351 (d) 352
12. 12.In a class of 22 children, 11 like cricket, 8 like football and 3 like both. How many like at least one of the two? (a) 22 (b) 13 (c) 19 (d) 16
13. 13.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 120° (b) 155° (c) 85° (d) 25°
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/11 (c) 1/12 (d) 3/11
15. 15.The mean of 8 numbers is 31. When the number 4 is added to them, what is the new mean? (a) 29 (b) 28 (c) 27 (d) 31
16. 16.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 4418 (c) 4465 (d) 8930
17. 17.The mean of 8 numbers is 26. When the number 8 is added to them, what is the new mean? (a) 17 (b) 26 (c) 25 (d) 24
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/11 (c) 4/11 (d) 1/9
19. 19.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 702 (c) 351 (d) 338
20. 20.What is the median of 3, 35, 17, 1 and 6? (a) 3 (b) 7 (c) 17 (d) 6
21. 21.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
22. 22.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 43 (d) 506
23. 23.Using (a − b)² = a² − 2ab + b², what is 39²? (a) 1531 (b) 1521 (c) 1681 (d) 1599
24. 24.A bag has 8 white, 2 red and 8 yellow balls. One ball is taken out without looking. What is the probability that it is not white? (a) 11/18 (b) 1/3 (c) 5/9 (d) 4/9
25. 25.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 11 (b) 67 (c) 66 (d) 132
26. 26.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 35 (c) 56 (d) 11
27. 27.How many factors does 106 have? (a) 5 (b) 3 (c) 4 (d) 2
28. 28.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
29. 29.What is the mean of 18, 20, 16, 8 and 3? (a) 14 (b) 15 (c) 12 (d) 13
30. 30.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 140° (b) 65° (c) 115° (d) 105°
31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 17 (b) 18 (c) 7 (d) 16
32. 32.What is the median of 9, 40, 2, 37, 34, 25 and 23? (a) 23 (b) 25 (c) 34 (d) 37
33. 33.Which is the correct factorisation of x² + 14x + 48? (a) (x + 6)(x + 8) (b) (x + 1)(x + 13) (c) (x + 1)(x + 48) (d) (x − 6)(x − 8)
34. 34.What is the mean of 2, 17, 19, 18, 19 and 21? (a) 18 (b) 17 (c) 15 (d) 16
35. 35.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
36. 36.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
37. 37.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 91 (d) 105
38. 38.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) 25 (c) 24 (d) 37
39. 39.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 65° (c) 115° (d) 50°
40. 40.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) 48 (b) 49 (c) 37 (d) 36

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