Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 134 · 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.The mean of 9 numbers is 19. When the number 9 is added to them, what is the new mean? (a) 14 (b) 18 (c) 19 (d) 17
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/6 (c) 6/11 (d) 1/11
3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
4. 4.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 80° (c) 100° (d) 10°
5. 5.What is the mean of 12, 17, 18, 4 and 4? (a) 12 (b) 10 (c) 13 (d) 11
6. 6.What is the median of 36, 24, 13, 20 and 38? (a) 20 (b) 36 (c) 13 (d) 24
7. 7.In a class of 38 children, 17 like mangoes, 24 like bananas and 11 like both. How many like at least one of the two? (a) 30 (b) 38 (c) 41 (d) 19
8. 8.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 90 (d) 45
9. 9.In a class of 33 children, 26 like cricket, 15 like football and 10 like both. How many like at least one of the two? (a) 41 (b) 21 (c) 31 (d) 33
10. 10.A drawer has lots of blue, black, red 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) 5 (b) 4 (c) 8 (d) 2
11. 11.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 156 (c) 78 (d) 169
12. 12.What is the mean of 10, 11, 11 and 16? (a) 11 (b) 12 (c) 13 (d) 16
13. 13.A drawer has lots of white, black, blue, green and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 2 (d) 5
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/36 (c) 1/12 (d) 1/11
15. 15.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 18 (c) 81 (d) 72
16. 16.Which term of the AP 7, 10, 13, 16, … is 31? (a) 9th (b) 11th (c) 8th (d) 10th
17. 17.In a class of 25 children, 15 like maths, 12 like science and 4 like both. How many like only maths? (a) 11 (b) 8 (c) 13 (d) 15
18. 18.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 21 (d) 42
19. 19.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 49 (c) 42 (d) 21
20. 20.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 150 cu cm (d) 100 cu cm
21. 21.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 6)(x + 7) (c) (x − 6)(x − 7) (d) (x + 1)(x + 12)
22. 22.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
23. 23.In a class of 42 children, 23 like dance, 18 like music and 9 like both. How many like only dance? (a) 24 (b) 14 (c) 23 (d) 9
24. 24.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
25. 25.In a class of 31 children, 14 like mangoes, 23 like bananas and 10 like both. How many like at least one of the two? (a) 27 (b) 31 (c) 17 (d) 37
26. 26.In a class of 53 children, 30 like dance, 29 like music and 6 like neither. How many like both? (a) 13 (b) 47 (c) 12 (d) 6
27. 27.The mean of 3 numbers is 22. When the number 30 is added to them, what is the new mean? (a) 25 (b) 26 (c) 22 (d) 24
28. 28.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 12 (b) 9 (c) 7 (d) 8
29. 29.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 15° (c) 105° (d) 75°
30. 30.In a class of 43 children, 18 like mangoes, 32 like bananas and 12 like both. How many like only mangoes? (a) 6 (b) 18 (c) 11 (d) 20
31. 31.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 24 (c) 16 (d) 10
32. 32.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 70° (c) 40° (d) 110°
33. 33.What is the mean of 2, 13, 19 and 10? (a) 10 (b) 12 (c) 11 (d) 13
34. 34.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 64 (b) 40 (c) 12 (d) 32
35. 35.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
36. 36.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
37. 37.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 195 (c) 208 (d) 204
38. 38.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 48 (d) 24
39. 39.In a class of 35 children, 12 like dance, 21 like music and 5 like both. How many like neither? (a) 5 (b) 12 (c) 7 (d) 2
40. 40.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 12 (b) 9 (c) 10 (d) 11

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