Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 228 · 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.A bag has 3 red balls and 4 black 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) 7 (d) 5
2. 2.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 7 (c) 63 (d) 21
3. 3.A drawer has lots of 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) 4 (b) 5 (c) 3 (d) 2
4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
5. 5.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 105 (d) 182
6. 6.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 224 (c) 219 (d) 229
7. 7.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 242 (c) 255 (d) 246
8. 8.What is the midpoint of the line joining (7, 3) and (11, 1)? (a) (18, 4) (b) (2, 9) (c) (2, 1) (d) (9, 2)
9. 9.What is the midpoint of the line joining (2, 4) and (6, 10)? (a) (8, 14) (b) (4, 7) (c) (7, 4) (d) (2, 3)
10. 10.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 71° (c) 70° (d) 110°
11. 11.In which quadrant does the point (−3, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
12. 12.What is the mean of 5, 5, 13 and 9? (a) 7 (b) 8 (c) 9 (d) 10
13. 13.A bag has 4 red balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 5 (c) 2 (d) 8
14. 14.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
15. 15.A bag has 5 blue, 9 white and 2 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 5/11 (b) 1/3 (c) 11/16 (d) 5/16
16. 16.In a class of 24 children, 15 like maths, 16 like science and 12 like both. How many like neither? (a) 6 (b) 12 (c) 5 (d) 17
17. 17.In which quadrant does the point (5, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
18. 18.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 270° (c) 155° (d) 90°
19. 19.What is the median of 24, 33, 10, 35 and 8? (a) 10 (b) 24 (c) 33 (d) 22
20. 20.A drawer has lots of red, yellow 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
21. 21.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 75° (d) 15°
22. 22.In a class of 22 children, 12 like mangoes, 10 like bananas and 6 like both. How many like at least one of the two? (a) 22 (b) 17 (c) 10 (d) 16
23. 23.How many factors does 45 have? (a) 5 (b) 7 (c) 6 (d) 4
24. 24.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/4 (b) 5/6 (c) 2/3 (d) 1/3
25. 25.If a + b = 7 and ab = 6, what is a² + b²? (a) 43 (b) 37 (c) 61 (d) 49
26. 26.What is the mode of 19, 13, 10, 16, 19, 13 and 13? (a) 19 (b) 13 (c) 10 (d) 16
27. 27.What is the midpoint of the line joining (8, 3) and (12, 13)? (a) (8, 10) (b) (10, 8) (c) (2, 5) (d) (20, 16)
28. 28.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
29. 29.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 2/3 (c) 1/3 (d) 5/6
30. 30.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
31. 31.A bag has 9 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 14 (c) 2 (d) 10
32. 32.In a class of 27 children, 16 like maths, 11 like science and 5 like both. How many like only maths? (a) 11 (b) 5 (c) 6 (d) 16
33. 33.What is the sum of the roots of x² − 16x + 63 = 0? (a) 15 (b) 63 (c) 16 (d) 17
34. 34.What is the midpoint of the line joining (10, 9) and (20, 19)? (a) (30, 28) (b) (14, 15) (c) (5, 5) (d) (15, 14)
35. 35.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2 × 5⁴ (c) 2⁵ × 5 (d) 2³ × 5
36. 36.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 144 (d) 66
37. 37.What is the midpoint of the line joining (10, 14) and (12, 2)? (a) (22, 16) (b) (8, 11) (c) (11, 8) (d) (1, 6)
38. 38.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 1/4 (c) 3/8 (d) 5/8
39. 39.In a class of 46 children, 27 like maths, 27 like science and 10 like both. How many like only maths? (a) 17 (b) 10 (c) 27 (d) 19
40. 40.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times

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