Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 143 · 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 12, 11, 18, 19 and 5? (a) 14 (b) 15 (c) 13 (d) 12
2. 2.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 285° (c) 15° (d) 105°
3. 3.Using (a + b)² = a² + 2ab + b², what is 42²? (a) 1604 (b) 1764 (c) 1774 (d) 1444
4. 4.What is the distance between the points (6, 2) and (18, 18)? (a) 400 (b) 28 (c) 21 (d) 20
5. 5.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 18 (c) 6 (d) 12
6. 6.What is the prime factorisation of 45? (a) 3 × 5² (b) 3 × 5 (c) 3² × 5 (d) 3³ × 5
7. 7.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
8. 8.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 30° (c) 135° (d) 150°
9. 9.In a class of 43 children, 28 like cricket, 20 like football and 9 like both. How many like only cricket? (a) 19 (b) 11 (c) 28 (d) 23
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 1/11 (c) 2/11 (d) 1/12
11. 11.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 6 times (c) 8 times (d) 2 times
12. 12.In a class of 54 children, 28 like dance, 29 like music and 11 like both. How many like at least one of the two? (a) 54 (b) 35 (c) 46 (d) 57
13. 13.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/4 (c) 1/3 (d) 5/6
14. 14.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 235° (b) 55° (c) 125° (d) 110°
15. 15.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 50° (c) 70° (d) 140°
16. 16.What is the mean of 7, 3, 9 and 9? (a) 6 (b) 7 (c) 8 (d) 9
17. 17.In a class of 33 children, 27 like dance, 15 like music and 2 like neither. How many like both? (a) 31 (b) 9 (c) 2 (d) 11
18. 18.There are 5 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 15 (b) 10 (c) 7 (d) 20
19. 19.What are the roots of x² − 17x + 72 = 0? (a) 1 and 16 (b) 2 and 36 (c) 1 and 72 (d) 8 and 9
20. 20.Which is the correct factorisation of x² + 16x + 63? (a) (x − 7)(x − 9) (b) (x + 1)(x + 15) (c) (x + 7)(x + 9) (d) (x + 1)(x + 63)
21. 21.How many factors does 27 have? (a) 2 (b) 3 (c) 5 (d) 4
22. 22.How many factors does 65 have? (a) 3 (b) 4 (c) 5 (d) 2
23. 23.The numbers 19 to 27 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) 23 (c) 69 (d) 207
24. 24.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 115° (d) 110°
25. 25.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 162 (c) 54 (d) 18
26. 26.A bag has 11 white balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 6 (c) 16 (d) 2
27. 27.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2³ × 3² (c) 2⁴ × 3² (d) 2⁵ × 3²
28. 28.What is the mean of 12, 19, 5 and 20? (a) 16 (b) 13 (c) 14 (d) 15
29. 29.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 24 (c) 34 (d) 33
30. 30.In a class of 31 children, 16 like cricket, 19 like football and 7 like both. How many like neither? (a) 10 (b) 3 (c) 4 (d) 7
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
32. 32.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
33. 33.A bag has 12 green balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 13 (b) 14 (c) 16 (d) 2
34. 34.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 60° (c) 120° (d) 135°
35. 35.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 3906 (c) 1953 (d) 1922
36. 36.Which is the correct factorisation of x² + 14x + 45? (a) (x − 5)(x − 9) (b) (x + 1)(x + 13) (c) (x + 5)(x + 9) (d) (x + 1)(x + 45)
37. 37.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
38. 38.A drawer has lots of yellow, green, black 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) 5 (b) 4 (c) 2 (d) 8
39. 39.A bag has 7 black balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 8 (c) 13 (d) 2
40. 40.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26

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