Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 400 · 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.What is the mean of 10, 5, 7 and 10? (a) 9 (b) 8 (c) 7 (d) 10
2. 2.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
3. 3.What is the product of the roots of x² − 13x + 36 = 0? (a) 37 (b) 13 (c) 35 (d) 36
4. 4.What is the missing term in the AP 8, 15, ?, 29, 36? (a) 23 (b) 21 (c) 29 (d) 22
5. 5.A bag has 11 black balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 14 (c) 12 (d) 13
6. 6.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 416 (c) 516 (d) 507
7. 7.A bag has 9 white balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 10 (c) 2 (d) 6
8. 8.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 160° (b) 100° (c) 120° (d) 80°
9. 9.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 135° (c) 315° (d) 136°
10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
11. 11.What is the mode of 6, 7, 9, 6, 3, 6 and 3? (a) 9 (b) 3 (c) 7 (d) 6
12. 12.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5²
13. 13.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 72 (b) 42 (c) 12 (d) 36
14. 14.What is the prime factorisation of 36? (a) 2² × 3² (b) 2 × 3² (c) 2³ × 3² (d) 2² × 3³
15. 15.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 36) (b) (x + 4)(x + 9) (c) (x − 4)(x − 9) (d) (x + 1)(x + 12)
16. 16.What is the prime factorisation of 560? (a) 2³ × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2⁵ × 5 × 7
17. 17.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
18. 18.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) 7 (c) 15 (d) 8
19. 19.A bag has 11 yellow balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 13 (b) 2 (c) 12 (d) 14
20. 20.What is the midpoint of the line joining (0, 13) and (2, 9)? (a) (2, 22) (b) (11, 1) (c) (1, 11) (d) (1, 2)
21. 21.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) 39 (c) 108 (d) 36
22. 22.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
23. 23.A drawer has lots of blue, white 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) 2 (b) 4 (c) 3 (d) 6
24. 24.How many factors does 72 have? (a) 12 (b) 10 (c) 11 (d) 13
25. 25.How many factors does 106 have? (a) 4 (b) 2 (c) 3 (d) 5
26. 26.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 7056 (b) 7066 (c) 6416 (d) 5776
27. 27.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
29. 29.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 49 (d) 42
30. 30.Using (a − b)² = a² − 2ab + b², what is 78²? (a) 6724 (b) 6094 (c) 6084 (d) 6396
31. 31.What is the distance between the points (2, 9) and (17, 17)? (a) 289 (b) 23 (c) 18 (d) 17
32. 32.If a + b = 15 and ab = 54, what is (a − b)²? (a) 225 (b) 117 (c) 9 (d) 3
33. 33.A bag has 9 red balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 11 (c) 10 (d) 12
34. 34.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 160° (b) 115° (c) 65° (d) 135°
35. 35.A bag has 8 red, 5 yellow and 7 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 2/5 (b) 1/3 (c) 13/20 (d) 3/5
36. 36.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 105° (b) 110° (c) 145° (d) 75°
37. 37.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
38. 38.How many factors does 73 have? (a) 3 (b) 2 (c) 1 (d) 4
39. 39.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 3/8 (c) 5/8 (d) 1/4
40. 40.What is the distance between the points (3, 13) and (15, 8)? (a) 13 (b) 17 (c) 169 (d) 14

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