Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 487 · 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 prime factorisation of 252? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2² × 3² × 7 (d) 2³ × 3² × 7
2. 2.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 25 (d) 10
3. 3.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
4. 4.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 40° (d) 110°
5. 5.There are 4 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) 16 (b) 12 (c) 7 (d) 24
6. 6.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 85° (d) 145°
7. 7.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 155° (d) 75°
8. 8.What is the median of 2, 10, 28, 4 and 8? (a) 4 (b) 28 (c) 8 (d) 10
9. 9.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 15 (d) 21
10. 10.A bag has 5 black balls and 11 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) 6 (c) 16 (d) 12
11. 11.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 150° (b) 75° (c) 255° (d) 105°
12. 12.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 140 (c) 131 (d) 132
13. 13.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 11 (c) 56 (d) 28
14. 14.A drawer has lots of blue and red 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
15. 15.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 42 (c) 45 (d) 14
16. 16.In which quadrant does the point (9, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
17. 17.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 225 (c) 120 (d) 210
18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 20 (d) 18
19. 19.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 135° (b) 45° (c) 270° (d) 90°
20. 20.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) 2 (b) 5 (c) 4 (d) 3
21. 21.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
22. 22.How many factors does 111 have? (a) 5 (b) 4 (c) 3 (d) 2
23. 23.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) 10 (b) 32 (c) 24 (d) 16
24. 24.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
25. 25.A bag has 8 red balls and 6 yellow 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) 14 (d) 9
26. 26.In a class of 31 children, 20 like cricket, 13 like football and 9 like both. How many like neither? (a) 9 (b) 8 (c) 7 (d) 16
27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
28. 28.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 3/4 (c) 1/4 (d) 1/2
29. 29.What is the mean of 11, 3, 13, 20 and 18? (a) 15 (b) 12 (c) 14 (d) 13
30. 30.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 741 (c) 780 (d) 1560
31. 31.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 80° (b) 115° (c) 145° (d) 100°
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) 10 times (c) 125 times (d) 25 times
33. 33.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 115° (d) 65°
34. 34.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 75° (c) 105° (d) 145°
35. 35.What is the midpoint of the line joining (0, 7) and (2, 17)? (a) (1, 12) (b) (1, 5) (c) (2, 24) (d) (12, 1)
36. 36.There are 5 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) 20 (b) 30 (c) 15 (d) 8
37. 37.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 75° (c) 140° (d) 105°
38. 38.In a class of 48 children, 25 like tea, 21 like coffee and 6 like both. How many like at least one of the two? (a) 46 (b) 40 (c) 48 (d) 34
39. 39.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 117 (c) 126 (d) 108
40. 40.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 24 (d) 16

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