Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 77 · 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.In a class of 20 children, 15 like mangoes, 8 like bananas and 2 like neither. How many like both? (a) 18 (b) 2 (c) 3 (d) 5
2. 2.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 8 cu cm (d) 6 cu cm
3. 3.What is the median of 6, 33, 36, 4 and 13? (a) 6 (b) 33 (c) 36 (d) 13
4. 4.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 55 (d) 121
5. 5.What is the midpoint of the line joining (0, 0) and (2, 8)? (a) (1, 4) (b) (4, 1) (c) (2, 4) (d) (2, 8)
6. 6.In a class of 36 children, 21 like dance, 23 like music and 12 like both. How many like at least one of the two? (a) 32 (b) 20 (c) 36 (d) 44
7. 7.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 660 (b) 352 (c) 50 (d) 330
8. 8.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x − 8)(x − 9) (c) (x + 1)(x + 72) (d) (x + 8)(x + 9)
9. 9.4 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 9 (c) 20 (d) 40
10. 10.How many prime numbers are there between 50 and 80? (a) 9 (b) 7 (c) 8 (d) 6
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 1/11 (c) 5/11 (d) 5/36
12. 12.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 155° (b) 55° (c) 150° (d) 125°
13. 13.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 54 (c) 17 (d) 153
14. 14.A drawer has lots of black, blue, green 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) 8 (c) 5 (d) 4
15. 15.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 30 (d) 21
16. 16.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/4 (c) 1/4 (d) 3/8
17. 17.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 55° (d) 70°
18. 18.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 130 (b) 21 (c) 75 (d) 65
19. 19.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 60° (b) 160° (c) 140° (d) 40°
20. 20.What is the midpoint of the line joining (1, 3) and (11, 7)? (a) (5, 2) (b) (12, 10) (c) (6, 5) (d) (5, 6)
21. 21.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
22. 22.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 65° (d) 50°
23. 23.What is the median of 31, 28, 16, 23 and 15? (a) 28 (b) 16 (c) 24 (d) 23
24. 24.In a class of 24 children, 14 like maths, 10 like science and 5 like neither. How many like both? (a) 5 (b) 19 (c) 4 (d) 6
25. 25.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 144 (c) 132 (d) 66
26. 26.In a class of 26 children, 11 like mangoes, 7 like bananas and 2 like both. How many like neither? (a) 10 (b) 2 (c) 8 (d) 12
27. 27.In a class of 28 children, 14 like cricket, 21 like football and 10 like both. How many like only cricket? (a) 14 (b) 4 (c) 7 (d) 11
28. 28.In a class of 32 children, 19 like dance, 17 like music and 5 like both. How many like at least one of the two? (a) 32 (b) 36 (c) 31 (d) 26
29. 29.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 344 (b) 172 (c) 39 (d) 192
30. 30.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
31. 31.Which is the correct factorisation of x² + 6x + 8? (a) (x + 1)(x + 5) (b) (x + 1)(x + 8) (c) (x + 2)(x + 4) (d) (x − 2)(x − 4)
32. 32.A bag has 3 yellow, 5 white and 7 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 3/5 (b) 1/3 (c) 7/15 (d) 8/15
33. 33.In a class of 31 children, 20 like mangoes, 10 like bananas and 6 like both. How many like at least one of the two? (a) 24 (b) 18 (c) 30 (d) 31
34. 34.A bag has 6 yellow balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 2 (c) 7 (d) 16
35. 35.In a class of 41 children, 17 like dance, 20 like music and 6 like both. How many like only dance? (a) 14 (b) 17 (c) 11 (d) 21
36. 36.What is the midpoint of the line joining (5, 2) and (9, 6)? (a) (7, 4) (b) (2, 2) (c) (14, 8) (d) (4, 7)
37. 37.What is the midpoint of the line joining (2, 4) and (10, 2)? (a) (6, 3) (b) (12, 6) (c) (4, 1) (d) (3, 6)
38. 38.A bag has 5 red, 6 yellow and 2 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 8/13 (b) 1/3 (c) 5/13 (d) 9/13
39. 39.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) 11 (b) 36 (c) 33 (d) 99
40. 40.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) 14 (b) 8 (c) 15 (d) 7

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