Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 491 · 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.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/4 (c) 1/8 (d) 7/8
2. 2.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 456 (c) 457 (d) 447
3. 3.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/3 (c) 3/4 (d) 1/2
4. 4.A bag has 12 white balls and 3 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) 13 (c) 4 (d) 15
5. 5.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 150° (c) 25° (d) 15°
6. 6.A bag has 4 white, 2 green and 2 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 3/8 (b) 1/4 (c) 3/4 (d) 1/3
7. 7.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 105° (b) 145° (c) 75° (d) 140°
8. 8.What is the prime factorisation of 90? (a) 2 × 3² × 5² (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5
9. 9.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x − 8)(x − 9)
10. 10.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 110° (b) 290° (c) 145° (d) 70°
11. 11.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 35° (b) 90° (c) 145° (d) 125°
12. 12.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2 × 3² × 5 (d) 2² × 3² × 5
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
14. 14.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 160° (b) 60° (c) 140° (d) 120°
15. 15.What is the 10th term of the AP 12, 17, 22, 27, …? (a) 62 (b) 50 (c) 45 (d) 57
16. 16.How many factors does 27 have? (a) 5 (b) 3 (c) 2 (d) 4
17. 17.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
18. 18.A drawer has lots of blue, black, red 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) 8 (b) 2 (c) 5 (d) 4
19. 19.What is the smallest prime factor of 119? (a) 1 (b) 17 (c) 2 (d) 7
20. 20.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 42 (c) 49 (d) 14
21. 21.In a class of 40 children, 30 like maths, 19 like science and 12 like both. How many like at least one of the two? (a) 25 (b) 49 (c) 40 (d) 37
22. 22.In a class of 34 children, 12 like cricket, 23 like football and 8 like both. How many like neither? (a) 15 (b) 6 (c) 7 (d) 8
23. 23.Using (a − b)² = a² − 2ab + b², what is 86²? (a) 7406 (b) 8084 (c) 7396 (d) 8836
24. 24.A bag has 12 white balls and 13 red 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) 13 (c) 14 (d) 25
25. 25.What is the 11th term of the AP 14, 21, 28, 35, …? (a) 91 (b) 77 (c) 70 (d) 84
26. 26.How many prime numbers are there between 70 and 90? (a) 6 (b) 5 (c) 7 (d) 4
27. 27.What is the mean of 10, 12, 5, 15, 2 and 16? (a) 10 (b) 11 (c) 9 (d) 12
28. 28.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
29. 29.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 28 (b) 26 (c) 27 (d) 32
30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 17 (b) 18 (c) 19 (d) 8
31. 31.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) 15 (c) 8 (d) 7
32. 32.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 45 (c) 36 (d) 81
33. 33.In a class of 19 children, 9 like cricket, 8 like football and 4 like both. How many like neither? (a) 10 (b) 4 (c) 6 (d) 2
34. 34.How many factors does 59 have? (a) 3 (b) 2 (c) 1 (d) 4
35. 35.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 16 sq cm (c) 97 sq cm (d) 96 sq cm
36. 36.A drawer has lots of red, yellow 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) 6 (b) 3 (c) 4 (d) 2
37. 37.What is the mode of 8, 18, 13, 8, 8, 18 and 1? (a) 1 (b) 8 (c) 18 (d) 13
38. 38.In a class of 40 children, 23 like maths, 25 like science and 2 like neither. How many like both? (a) 8 (b) 2 (c) 10 (d) 38
39. 39.What is the product of the roots of x² − 15x + 56 = 0? (a) 55 (b) 57 (c) 15 (d) 56
40. 40.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 8 (c) 24 (d) 27

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