Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 598 · 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 distance between the points (8, 5) and (23, 13)? (a) 23 (b) 289 (c) 17 (d) 18
2. 2.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 145° (d) 130°
3. 3.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 81 (c) 36 (d) 45
4. 4.In a class of 38 children, 21 like dance, 21 like music and 10 like both. How many like only dance? (a) 10 (b) 17 (c) 21 (d) 11
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 5/11 (c) 1/11 (d) 1/6
6. 6.What is the smallest prime factor of 33? (a) 11 (b) 1 (c) 2 (d) 3
7. 7.Using (a + b)² = a² + 2ab + b², what is 81²? (a) 6401 (b) 6241 (c) 6561 (d) 6571
8. 8.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 156 (c) 166 (d) 165
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
10. 10.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
11. 11.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 160° (d) 155°
12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 17 (d) 18
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 5/36 (c) 1/11 (d) 1/9
14. 14.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 36 (c) 45 (d) 54
15. 15.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 162 (b) 324 (c) 171 (d) 26
16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 16 (d) 5
17. 17.A drawer has lots of yellow, blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 6 (c) 2 (d) 3
18. 18.A bag has 4 white, 4 green and 4 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 3/4 (b) 1/12 (c) 1/3 (d) 2/3
19. 19.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 110° (c) 250° (d) 70°
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/36 (c) 1/11 (d) 1/12
21. 21.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
22. 22.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
23. 23.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x + 1)(x + 72)
24. 24.A bag has 4 white, 3 yellow and 4 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 8/11 (b) 9/11 (c) 1/3 (d) 3/11
25. 25.What is the 14th term of the AP 17, 22, 27, 32, …? (a) 65 (b) 70 (c) 82 (d) 87
26. 26.In a class of 42 children, 18 like mangoes, 28 like bananas and 8 like both. How many like neither? (a) 5 (b) 4 (c) 12 (d) 8
27. 27.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
28. 28.In a class of 31 children, 19 like tea, 11 like coffee and 5 like both. How many like at least one of the two? (a) 20 (b) 31 (c) 30 (d) 25
29. 29.How many prime numbers are there between 70 and 90? (a) 7 (b) 4 (c) 6 (d) 5
30. 30.What is the median of 16, 23, 36, 7, 27, 5 and 14? (a) 23 (b) 7 (c) 16 (d) 14
31. 31.What is the mode of 7, 20, 7, 20, 5, 17 and 7? (a) 7 (b) 20 (c) 17 (d) 5
32. 32.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 85° (d) 135°
33. 33.What is the smallest prime factor of 57? (a) 3 (b) 2 (c) 1 (d) 19
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
35. 35.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 6 (b) 18 (c) 9 (d) 12
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
37. 37.A bag has 5 black balls and 12 red 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) 6 (c) 17 (d) 2
38. 38.In a class of 40 children, 20 like cricket, 22 like football and 3 like both. How many like at least one of the two? (a) 36 (b) 40 (c) 39 (d) 42
39. 39.What is the median of 23, 40, 19, 3, 35, 37 and 25? (a) 25 (b) 3 (c) 26 (d) 35
40. 40.A drawer has lots of yellow and red 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) 4 (c) 5 (d) 3

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