Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 731 · 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 22nd term of the AP 20, 26, 32, 38, …? (a) 132 (b) 146 (c) 126 (d) 152
2. 2.How many factors does 28 have? (a) 7 (b) 4 (c) 6 (d) 5
3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 3/11 (c) 1/12 (d) 1/11
4. 4.A bag has 6 green balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 8 (b) 2 (c) 7 (d) 10
5. 5.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 29 (c) 28 (d) 22
6. 6.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
7. 7.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 75° (c) 125° (d) 105°
8. 8.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
9. 9.What are the roots of x² − 17x + 72 = 0? (a) 1 and 16 (b) 8 and 9 (c) 2 and 36 (d) 1 and 72
10. 10.What is the sum of the first 5 terms of the AP 4, 8, 12, …? (a) 120 (b) 60 (c) 70 (d) 20
11. 11.There are 5 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 70 (b) 40 (c) 35 (d) 12
12. 12.What is the mean of 16, 12, 8, 5 and 9? (a) 11 (b) 12 (c) 10 (d) 9
13. 13.In which quadrant does the point (−6, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 59 (d) 465
15. 15.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 130° (c) 51° (d) 50°
16. 16.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 110° (d) 80°
17. 17.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 60° (c) 120° (d) 145°
18. 18.A drawer has lots of white 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) 5 (b) 3 (c) 4 (d) 2
19. 19.What is the mode of 19, 10, 5, 10, 10, 5 and 6? (a) 19 (b) 5 (c) 6 (d) 10
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/36 (c) 1/18 (d) 1/12
21. 21.A bag has 9 green balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 15 (b) 10 (c) 11 (d) 2
22. 22.What is the prime factorisation of 420? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2³ × 3 × 5 × 7
23. 23.Using (a − b)² = a² − 2ab + b², what is 36²? (a) 1306 (b) 1936 (c) 1296 (d) 1584
24. 24.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 135° (c) 160° (d) 45°
25. 25.Which term of the AP 11, 18, 25, 32, … is 284? (a) 41st (b) 42nd (c) 40th (d) 39th
26. 26.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 36 (c) 81 (d) 18
27. 27.How many prime numbers are there between 10 and 40? (a) 9 (b) 8 (c) 7 (d) 10
28. 28.How many factors does 68 have? (a) 6 (b) 5 (c) 7 (d) 4
29. 29.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 80° (d) 155°
30. 30.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 45 (c) 100 (d) 90
31. 31.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 841 (b) 971 (c) 901 (d) 961
32. 32.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 160° (b) 30° (c) 50° (d) 150°
33. 33.A bag has 11 red balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 12 (c) 23 (d) 13
34. 34.In a class of 47 children, 26 like cricket, 20 like football and 7 like both. How many like neither? (a) 7 (b) 1 (c) 8 (d) 15
35. 35.If a + b = 13 and ab = 30, what is (a − b)²? (a) 49 (b) 169 (c) 7 (d) 109
36. 36.What is the midpoint of the line joining (9, 4) and (13, 0)? (a) (2, 2) (b) (2, 11) (c) (11, 2) (d) (22, 4)
37. 37.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 42 (d) 49
38. 38.What is the mean of 4, 3, 2 and 15? (a) 5 (b) 7 (c) 8 (d) 6
39. 39.A drawer has lots of yellow, red, white, 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) 2 (b) 6 (c) 5 (d) 10
40. 40.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 14 (c) 49 (d) 21

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