Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 470 · 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 every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
2. 2.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 12) (b) (x + 1)(x + 40) (c) (x − 5)(x − 8) (d) (x + 5)(x + 8)
3. 3.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 54 (b) 108 (c) 55 (d) 10
4. 4.A bag has 5 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 7 (c) 8 (d) 6
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
6. 6.What is the smallest prime factor of 51? (a) 1 (b) 3 (c) 2 (d) 17
7. 7.If a + b = 9 and ab = 14, what is (a − b)²? (a) 81 (b) 53 (c) 5 (d) 25
8. 8.If a + b = 17 and ab = 72, what is a² + b²? (a) 433 (b) 217 (c) 145 (d) 289
9. 9.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 56 (d) 16
10. 10.What is the distance between the points (2, 11) and (10, 5)? (a) 100 (b) 14 (c) 11 (d) 10
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/12 (c) 1/11 (d) 1/36
12. 12.How many prime numbers are there between 60 and 70? (a) 3 (b) 1 (c) 4 (d) 2
13. 13.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 115° (b) 65° (c) 145° (d) 150°
14. 14.A drawer has lots of black, yellow, red 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) 5 (b) 4 (c) 8 (d) 2
15. 15.In which quadrant does the point (−3, −3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
16. 16.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
17. 17.What is the midpoint of the line joining (3, 9) and (13, 11)? (a) (10, 8) (b) (5, 1) (c) (8, 10) (d) (16, 20)
18. 18.What is the smallest prime factor of 65? (a) 1 (b) 2 (c) 5 (d) 13
19. 19.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
20. 20.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 75° (b) 125° (c) 160° (d) 55°
21. 21.In a class of 39 children, 18 like maths, 26 like science and 7 like both. How many like at least one of the two? (a) 44 (b) 39 (c) 37 (d) 30
22. 22.What is the smallest prime factor of 209? (a) 1 (b) 11 (c) 2 (d) 19
23. 23.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 155° (b) 140° (c) 65° (d) 115°
24. 24.In which quadrant does the point (9, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
25. 25.In a class of 40 children, 19 like maths, 23 like science and 9 like both. How many like at least one of the two? (a) 33 (b) 24 (c) 42 (d) 40
26. 26.In a class of 46 children, 23 like mangoes, 25 like bananas and 6 like both. How many like at least one of the two? (a) 42 (b) 36 (c) 48 (d) 46
27. 27.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 295° (c) 115° (d) 65°
28. 28.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 155° (b) 125° (c) 80° (d) 25°
29. 29.What is the distance between the points (8, 9) and (32, 16)? (a) 625 (b) 25 (c) 26 (d) 31
30. 30.How many factors does 99 have? (a) 6 (b) 7 (c) 5 (d) 4
31. 31.A bag has 4 yellow, 4 red and 6 blue balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 2/7 (c) 5/7 (d) 11/14
32. 32.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 1/4 (c) 3/8 (d) 3/5
33. 33.What is the median of 36, 5, 25, 4, 1, 33 and 11? (a) 5 (b) 25 (c) 4 (d) 11
34. 34.A bag has 2 red, 6 blue and 5 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 6/7 (b) 7/13 (c) 1/3 (d) 6/13
35. 35.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 100 (c) 45 (d) 90
36. 36.A bag has 3 blue, 8 yellow and 5 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 7/8 (b) 3/16 (c) 1/3 (d) 13/16
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 5/11 (c) 5/36 (d) 1/11
38. 38.What is the midpoint of the line joining (0, 10) and (12, 0)? (a) (6, 5) (b) (7, 5) (c) (5, 6) (d) (12, 10)
39. 39.In which quadrant does the point (6, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
40. 40.A drawer has lots of red, blue, black 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) 8 (b) 5 (c) 4 (d) 2

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