Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 574 · 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.If a + b = 15 and ab = 44, what is a² + b²? (a) 313 (b) 181 (c) 137 (d) 225
2. 2.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2³ × 3² × 5
3. 3.What is the sum of the roots of x² − 6x + 8 = 0? (a) 7 (b) 8 (c) 6 (d) 5
4. 4.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 20 (d) 45
5. 5.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 6 (c) 9 (d) 18
6. 6.What is the distance between the points (9, 9) and (17, 3)? (a) 10 (b) 100 (c) 11 (d) 14
7. 7.A drawer has lots of white, blue and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 6 (c) 2 (d) 4
8. 8.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 16 (d) 12
9. 9.What is the mode of 9, 14, 10, 9, 10, 9 and 13? (a) 9 (b) 10 (c) 13 (d) 14
10. 10.What is the distance between the points (1, 14) and (25, 7)? (a) 26 (b) 31 (c) 25 (d) 625
11. 11.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 40° (c) 80° (d) 140°
12. 12.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 63 (c) 180 (d) 20
13. 13.What is the distance between the points (9, 10) and (17, 4)? (a) 14 (b) 100 (c) 10 (d) 11
14. 14.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 600 cu cm (d) 400 cu cm
15. 15.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 91 (c) 196 (d) 105
16. 16.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 12 (d) 48
17. 17.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 144 cu cm (d) 217 cu cm
18. 18.If a + b = 18 and ab = 77, what is a² + b²? (a) 324 (b) 478 (c) 170 (d) 247
19. 19.The mean of 9 numbers is 25. When the number 45 is added to them, what is the new mean? (a) 27 (b) 35 (c) 25 (d) 28
20. 20.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 492 (b) 246 (c) 264 (d) 37
21. 21.What is the distance between the points (8, 2) and (24, 14)? (a) 21 (b) 400 (c) 20 (d) 28
22. 22.In a class of 37 children, 17 like dance, 19 like music and 2 like both. How many like at least one of the two? (a) 37 (b) 36 (c) 34 (d) 32
23. 23.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 45° (b) 120° (c) 135° (d) 105°
24. 24.A drawer has lots of yellow 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) 3 (b) 5 (c) 2 (d) 4
25. 25.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) 37 (b) 25 (c) 36 (d) 24
26. 26.How many factors does 32 have? (a) 7 (b) 4 (c) 5 (d) 6
27. 27.How many factors does 69 have? (a) 2 (b) 4 (c) 5 (d) 3
28. 28.What is the mode of 14, 20, 6, 19, 19, 14 and 19? (a) 6 (b) 19 (c) 20 (d) 14
29. 29.A drawer has lots of red, green, black 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) 2 (b) 4 (c) 5 (d) 8
30. 30.There are 4 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) 8 (b) 12 (c) 6 (d) 16
31. 31.What is the smallest prime factor of 143? (a) 13 (b) 11 (c) 2 (d) 1
32. 32.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5²
33. 33.A bag has 6 white balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 13 (d) 8
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/36 (c) 1/12 (d) 1/18
35. 35.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 10 (c) 25 (d) 20
36. 36.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 130° (c) 40° (d) 50°
37. 37.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
38. 38.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 300° (c) 120° (d) 60°
39. 39.What is the 16th term of the AP 5, 13, 21, 29, …? (a) 120 (b) 128 (c) 133 (d) 125
40. 40.What is the sum of the roots of x² − 15x + 54 = 0? (a) 14 (b) 54 (c) 16 (d) 15

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