Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 996 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/9 (c) 1/11 (d) 4/11
2. 2.What is the median of 6, 40, 23, 19, 15, 28 and 10? (a) 15 (b) 19 (c) 23 (d) 20
3. 3.In which quadrant does the point (−8, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
4. 4.A bag has 3 white balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 2 (c) 13 (d) 15
5. 5.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
6. 6.A bag has 2 red, 7 white and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 10/11 (c) 2/11 (d) 9/11
7. 7.What is the product of the roots of x² − 10x + 16 = 0? (a) 10 (b) 15 (c) 17 (d) 16
8. 8.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 135° (c) 225° (d) 45°
9. 9.What is the midpoint of the line joining (2, 22) and (6, 10)? (a) (8, 32) (b) (2, 6) (c) (16, 4) (d) (4, 16)
10. 10.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 30 (d) 12
11. 11.A bag has 10 red balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 11 (c) 21 (d) 12
12. 12.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 48 (c) 80 (d) 13
13. 13.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 230° (b) 50° (c) 130° (d) 100°
14. 14.How many factors does 29 have? (a) 3 (b) 1 (c) 4 (d) 2
15. 15.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 60° (d) 120°
16. 16.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/3 (d) 1/4
17. 17.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
18. 18.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 76 (c) 86 (d) 94
19. 19.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁴ × 3² (c) 2² × 3⁴ (d) 2⁵ × 3²
20. 20.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 160° (b) 60° (c) 40° (d) 140°
21. 21.A bag has 7 red balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 8 (c) 2 (d) 9
22. 22.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
23. 23.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
24. 24.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/4 (c) 1/3 (d) 1/2
25. 25.What is the prime factorisation of 36? (a) 2² × 3² (b) 2² × 3³ (c) 2³ × 3² (d) 2 × 3²
26. 26.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
27. 27.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
28. 28.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
29. 29.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
30. 30.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 506 (d) 253
31. 31.In a class of 40 children, 27 like maths, 15 like science and 6 like neither. How many like both? (a) 6 (b) 8 (c) 34 (d) 2
32. 32.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
33. 33.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 400 sq cm (c) 600 sq cm (d) 1000 sq cm
34. 34.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) 207 (c) 69 (d) 23
35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 6 (d) 17
36. 36.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 9) (b) (x + 1)(x + 24) (c) (x − 4)(x − 6) (d) (x + 4)(x + 6)
37. 37.What is the 16th term of the AP 1, 8, 15, 22, …? (a) 105 (b) 113 (c) 112 (d) 106
38. 38.In a class of 35 children, 17 like tea, 21 like coffee and 8 like both. How many like only tea? (a) 17 (b) 13 (c) 14 (d) 9
39. 39.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 17 (c) 73 (d) 72
40. 40.A bag has 12 blue balls and 8 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) 20 (c) 13 (d) 9

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