Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 8 · 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 product of the roots of x² − 9x + 18 = 0? (a) 19 (b) 17 (c) 18 (d) 9
2. 2.What is the mode of 8, 8, 4, 8, 9, 4 and 5? (a) 4 (b) 9 (c) 5 (d) 8
3. 3.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 64 (c) 56 (d) 36
4. 4.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 70° (b) 150° (c) 110° (d) 100°
5. 5.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
6. 6.A drawer has lots of white and black 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) 5 (c) 4 (d) 3
7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 13 (d) 49
8. 8.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 1/4 (c) 5/8 (d) 3/5
9. 9.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) 15 (c) 8 (d) 7
10. 10.In which quadrant does the point (8, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
11. 11.How many prime numbers are there between 20 and 50? (a) 7 (b) 9 (c) 8 (d) 6
12. 12.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 4 (d) 2
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 5/36 (c) 1/9 (d) 1/11
14. 14.How many factors does 25 have? (a) 1 (b) 2 (c) 4 (d) 3
15. 15.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 115° (c) 65° (d) 160°
16. 16.What is the mean of 19, 2, 12, 8, 19 and 18? (a) 13 (b) 12 (c) 14 (d) 15
17. 17.What is the mode of 5, 18, 5, 5, 18, 6 and 15? (a) 18 (b) 5 (c) 6 (d) 15
18. 18.In a class of 34 children, 12 like maths, 25 like science and 5 like both. How many like only maths? (a) 7 (b) 12 (c) 9 (d) 20
19. 19.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/11 (c) 1/12 (d) 1/36
21. 21.The mean of 4 numbers is 14. When the number 34 is added to them, what is the new mean? (a) 14 (b) 19 (c) 24 (d) 18
22. 22.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 144 (d) 132
23. 23.What is the distance between the points (1, 11) and (13, 2)? (a) 15 (b) 225 (c) 16 (d) 21
24. 24.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 28 (c) 64 (d) 16
25. 25.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 10 (c) 15 (d) 25
26. 26.What is the mode of 11, 9, 9, 19, 11, 11 and 18? (a) 18 (b) 9 (c) 11 (d) 19
27. 27.The mean of 3 numbers is 14. When the number 6 is added to them, what is the new mean? (a) 13 (b) 10 (c) 14 (d) 12
28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/11 (c) 1/6 (d) 5/11
30. 30.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2³ × 3² × 7 (c) 2 × 3² × 7 (d) 2² × 3² × 7
31. 31.The mean of 6 numbers is 18. When the number 4 is added to them, what is the new mean? (a) 16 (b) 18 (c) 17 (d) 11
32. 32.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
33. 33.What are the roots of x² − 11x + 30 = 0? (a) 2 and 15 (b) 1 and 10 (c) 5 and 6 (d) 1 and 30
34. 34.What is the distance between the points (2, 10) and (8, 2)? (a) 11 (b) 10 (c) 14 (d) 100
35. 35.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 40° (d) 80°
36. 36.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 165° (c) 195° (d) 16°
37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 8 (b) 6 (c) 7 (d) 5
38. 38.What is the midpoint of the line joining (9, 3) and (17, 11)? (a) (4, 4) (b) (7, 13) (c) (13, 7) (d) (26, 14)
39. 39.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) 36 (c) 25 (d) 24
40. 40.What is the midpoint of the line joining (3, 4) and (15, 12)? (a) (8, 9) (b) (18, 16) (c) (6, 4) (d) (9, 8)

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