Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 517 · 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 smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 13 (c) 12 (d) 25
2. 2.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 45 (c) 90 (d) 55
3. 3.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 1/11 (c) 1/6 (d) 5/36
5. 5.A drawer has lots of black, red 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) 6 (b) 4 (c) 3 (d) 2
6. 6.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/4 (c) 7/8 (d) 1/8
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
8. 8.What is the smallest prime factor of 133? (a) 1 (b) 7 (c) 19 (d) 2
9. 9.A bag has 3 red balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 4 (c) 9 (d) 7
10. 10.If a + b = 18 and ab = 77, what is a² + b²? (a) 324 (b) 478 (c) 170 (d) 247
11. 11.In a class of 37 children, 18 like cricket, 25 like football and 7 like both. How many like neither? (a) 2 (b) 1 (c) 8 (d) 7
12. 12.If a + b = 17 and ab = 70, what is (a − b)²? (a) 3 (b) 289 (c) 149 (d) 9
13. 13.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 576 sq cm
14. 14.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
15. 15.Which is the correct factorisation of x² + 7x + 12? (a) (x + 1)(x + 12) (b) (x + 1)(x + 6) (c) (x + 3)(x + 4) (d) (x − 3)(x − 4)
16. 16.In a class of 20 children, 10 like cricket, 10 like football and 3 like both. How many like at least one of the two? (a) 18 (b) 20 (c) 14 (d) 17
17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 9 (d) 19
18. 18.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 12 (d) 16
19. 19.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 48 (c) 15 (d) 45
20. 20.What is the distance between the points (1, 7) and (9, 13)? (a) 14 (b) 100 (c) 10 (d) 11
21. 21.In a class of 44 children, 23 like tea, 30 like coffee and 12 like both. How many like at least one of the two? (a) 44 (b) 29 (c) 53 (d) 41
22. 22.In a class of 40 children, 15 like mangoes, 23 like bananas and 7 like both. How many like only mangoes? (a) 15 (b) 16 (c) 8 (d) 17
23. 23.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 14 (d) 42
24. 24.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 110° (d) 70°
25. 25.In a class of 37 children, 28 like cricket, 18 like football and 3 like neither. How many like both? (a) 3 (b) 34 (c) 12 (d) 9
26. 26.What is the prime factorisation of 14? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7 (d) 2 × 7²
27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
28. 28.In a class of 39 children, 22 like cricket, 16 like football and 4 like both. How many like neither? (a) 4 (b) 1 (c) 5 (d) 9
29. 29.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6084 (b) 6734 (c) 6404 (d) 6724
30. 30.A drawer has lots of black and white 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) 3 (c) 5 (d) 2
31. 31.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 30 (c) 33 (d) 90
32. 32.7 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) 10 (b) 42 (c) 28 (d) 21
33. 33.What is the distance between the points (1, 19) and (13, 3)? (a) 28 (b) 20 (c) 21 (d) 400
34. 34.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/5 (b) 5/6 (c) 1/6 (d) 1/3
35. 35.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 210 (c) 105 (d) 225
36. 36.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 7 (c) 14 (d) 8
37. 37.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
38. 38.What is the distance between the points (3, 9) and (15, 18)? (a) 21 (b) 16 (c) 15 (d) 225
39. 39.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 90 (d) 17
40. 40.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 198 (c) 69 (d) 66

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