Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 84 · 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.In a class of 54 children, 27 like mangoes, 26 like bananas and 8 like both. How many like only mangoes? (a) 28 (b) 27 (c) 19 (d) 18
2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 6 (b) 7 (c) 9 (d) 8
3. 3.What is the 16th term of the AP 19, 27, 35, 43, …? (a) 139 (b) 120 (c) 147 (d) 128
4. 4.A bag has 6 blue balls and 12 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) 7 (c) 13 (d) 18
5. 5.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 338 (c) 351 (d) 325
6. 6.What is the mode of 3, 3, 16, 3, 20, 20 and 2? (a) 20 (b) 2 (c) 16 (d) 3
7. 7.What is the mean of 5, 10, 2 and 11? (a) 6 (b) 8 (c) 7 (d) 9
8. 8.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 24 (c) 12 (d) 25
9. 9.What is the prime factorisation of 40? (a) 2³ × 5 (b) 2² × 5 (c) 2 × 5³ (d) 2⁴ × 5
10. 10.What is the product of the roots of x² − 17x + 72 = 0? (a) 72 (b) 17 (c) 71 (d) 73
11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 15 (b) 13 (c) 3 (d) 14
12. 12.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 61° (c) 60° (d) 120°
13. 13.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 5 (c) 18 (d) 15
14. 14.What is the median of 24, 6, 5, 13, 3, 28 and 8? (a) 8 (b) 13 (c) 6 (d) 9
15. 15.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x − 7)(x − 8) (c) (x + 1)(x + 56) (d) (x + 7)(x + 8)
16. 16.If a + b = 8 and ab = 15, what is (a − b)²? (a) 2 (b) 4 (c) 34 (d) 64
17. 17.What is the 35th term of the AP 17, 24, 31, 38, …? (a) 245 (b) 255 (c) 238 (d) 262
18. 18.Two angles of a triangle are 50° and 95°. What is the third angle? (a) 130° (b) 35° (c) 85° (d) 145°
19. 19.How many factors does 67 have? (a) 3 (b) 2 (c) 4 (d) 1
20. 20.In a class of 38 children, 15 like mangoes, 31 like bananas and 11 like both. How many like only mangoes? (a) 20 (b) 7 (c) 15 (d) 4
21. 21.In a class of 27 children, 21 like cricket, 14 like football and 2 like neither. How many like both? (a) 2 (b) 10 (c) 25 (d) 8
22. 22.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 25 (c) 37 (d) 24
23. 23.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 6 (d) 3
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
25. 25.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 216 (b) 120 (c) 24 (d) 108
26. 26.A drawer has lots of blue, red, green 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) 8 (b) 2 (c) 5 (d) 4
27. 27.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 255° (b) 150° (c) 105° (d) 75°
28. 28.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 110 (d) 121
29. 29.There are 8 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) 16 (b) 32 (c) 10 (d) 24
30. 30.Using (a + b)² = a² + 2ab + b², what is 104²? (a) 10816 (b) 9216 (c) 10016 (d) 10826
31. 31.What are the roots of x² − 15x + 54 = 0? (a) 2 and 27 (b) 1 and 54 (c) 6 and 9 (d) 1 and 14
32. 32.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
33. 33.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
34. 34.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 110° (c) 155° (d) 70°
35. 35.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 70° (d) 110°
36. 36.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 40 (b) 350 (c) 180 (d) 175
37. 37.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 75° (b) 95° (c) 160° (d) 105°
38. 38.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 60° (d) 120°
39. 39.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/18 (c) 1/11 (d) 1/12

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