Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 268 · 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 17 children, 10 like tea, 7 like coffee and 4 like neither. How many like both? (a) 3 (b) 4 (c) 5 (d) 13
2. 2.A drawer has lots of yellow, black, white 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) 4 (b) 8 (c) 2 (d) 5
3. 3.A bag has 6 white balls and 9 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) 15 (c) 10 (d) 7
4. 4.A bag has 4 yellow balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 2 (c) 6 (d) 16
5. 5.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 120 sq cm (b) 164 sq cm (c) 82 sq cm (d) 328 sq cm
6. 6.What is the mode of 7, 2, 2, 10, 2, 18 and 7? (a) 2 (b) 10 (c) 7 (d) 18
7. 7.In which quadrant does the point (9, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
8. 8.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 66 (d) 189
9. 9.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/4 (c) 3/4 (d) 1/3
10. 10.What is the distance between the points (4, 18) and (20, 6)? (a) 400 (b) 21 (c) 28 (d) 20
11. 11.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
12. 12.In a class of 41 children, 25 like mangoes, 25 like bananas and 11 like both. How many like neither? (a) 3 (b) 11 (c) 13 (d) 2
13. 13.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 70° (c) 20° (d) 160°
14. 14.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 20 (d) 10
15. 15.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 90° (b) 270° (c) 145° (d) 125°
16. 16.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 487 (c) 486 (d) 396
17. 17.A drawer has lots of red, 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) 6 (b) 3 (c) 4 (d) 2
18. 18.If a + b = 14 and ab = 40, what is (a − b)²? (a) 116 (b) 196 (c) 36 (d) 6
19. 19.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
20. 20.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
21. 21.In a class of 24 children, 9 like cricket, 11 like football and 5 like both. How many like neither? (a) 5 (b) 9 (c) 4 (d) 14
22. 22.In a class of 29 children, 8 like mangoes, 17 like bananas and 3 like both. How many like at least one of the two? (a) 29 (b) 19 (c) 25 (d) 22
23. 23.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 120 (d) 225
24. 24.In a class of 31 children, 18 like dance, 15 like music and 7 like neither. How many like both? (a) 24 (b) 9 (c) 2 (d) 7
25. 25.Which is the correct factorisation of x² + 6x + 8? (a) (x + 1)(x + 5) (b) (x + 2)(x + 4) (c) (x + 1)(x + 8) (d) (x − 2)(x − 4)
26. 26.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 60 (c) 11 (d) 35
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
28. 28.In a class of 27 children, 18 like dance, 11 like music and 4 like both. How many like at least one of the two? (a) 25 (b) 21 (c) 27 (d) 29
29. 29.If a + b = 12 and ab = 11, what is a² + b²? (a) 166 (b) 133 (c) 144 (d) 122
30. 30.What is the median of 10, 11, 2, 1 and 7? (a) 10 (b) 8 (c) 7 (d) 2
31. 31.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 36 (c) 39 (d) 108
32. 32.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
33. 33.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
34. 34.What is the median of 16, 2, 31, 27, 34, 7 and 36? (a) 16 (b) 28 (c) 27 (d) 31
35. 35.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
36. 36.If a + b = 8 and ab = 12, what is a² + b²? (a) 64 (b) 88 (c) 40 (d) 52
37. 37.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/3 (b) 1/5 (c) 5/6 (d) 1/6
38. 38.A bag has 6 white balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 7 (b) 2 (c) 16 (d) 8
39. 39.A bag has 12 blue balls and 9 white 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) 21 (c) 10 (d) 13
40. 40.What is the distance between the points (5, 16) and (17, 7)? (a) 16 (b) 15 (c) 225 (d) 21

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