Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 354 · 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 39 children, 16 like tea, 25 like coffee and 7 like both. How many like only tea? (a) 16 (b) 18 (c) 14 (d) 9
2. 2.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) 25 (b) 24 (c) 13 (d) 12
3. 3.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4
4. 4.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 15 (d) 30
5. 5.A bag has 11 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) 2 (c) 23 (d) 12
6. 6.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
7. 7.In a class of 55 children, 26 like mangoes, 28 like bananas and 9 like both. How many like only mangoes? (a) 27 (b) 26 (c) 19 (d) 17
8. 8.In a class of 52 children, 27 like tea, 27 like coffee and 12 like both. How many like only tea? (a) 15 (b) 25 (c) 12 (d) 27
9. 9.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 165° (c) 16° (d) 15°
10. 10.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 6 cu cm (b) 8 cu cm (c) 18 cu cm (d) 42 cu cm
11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 4 (b) 5 (c) 2 (d) 3
12. 12.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 112 (b) 104 (c) 20 (d) 208
13. 13.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 85° (c) 5° (d) 95°
14. 14.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 13 (c) 42 (d) 117
15. 15.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 150° (d) 125°
16. 16.A drawer has lots of blue, 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) 2 (c) 3 (d) 6
17. 17.A drawer has lots of green, yellow and black 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) 3 (c) 4 (d) 2
18. 18.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 51 (c) 48 (d) 16
19. 19.A bag has 6 yellow balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 7 (c) 15 (d) 8
20. 20.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
21. 21.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) 24 (b) 37 (c) 36 (d) 25
22. 22.In a class of 32 children, 23 like mangoes, 10 like bananas and 3 like both. How many like at least one of the two? (a) 27 (b) 32 (c) 30 (d) 33
23. 23.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 245 (b) 47 (c) 270 (d) 490
24. 24.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 45 (d) 20
25. 25.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 15 (d) 10
26. 26.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 24) (b) (x + 1)(x + 9) (c) (x + 4)(x + 6) (d) (x − 4)(x − 6)
27. 27.In a class of 30 children, 20 like tea, 17 like coffee and 10 like both. How many like neither? (a) 13 (b) 3 (c) 10 (d) 4
28. 28.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 155° (b) 70° (c) 135° (d) 45°
29. 29.What is the mode of 19, 11, 4, 9, 19, 4 and 4? (a) 4 (b) 9 (c) 11 (d) 19
30. 30.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 120 (c) 102 (d) 204
31. 31.How many factors does 12 have? (a) 5 (b) 7 (c) 6 (d) 4
32. 32.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
33. 33.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
34. 34.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
35. 35.A bag has 5 red balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 11 (b) 6 (c) 7 (d) 2
36. 36.A bag has 3 white balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 4 (c) 10 (d) 5
37. 37.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 235° (d) 56°
38. 38.How many prime numbers are there between 50 and 80? (a) 6 (b) 9 (c) 7 (d) 8
39. 39.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 125° (d) 80°
40. 40.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 27 (c) 81 (d) 30

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