Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 208 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/11 (d) 1/9
2. 2.A cuboid is 8 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 15 cu cm (b) 40 cu cm (c) 132 cu cm (d) 80 cu cm
3. 3.How many prime numbers are there between 10 and 20? (a) 4 (b) 5 (c) 3 (d) 6
4. 4.A drawer has lots of green, black, 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) 4 (c) 8 (d) 2
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/12 (c) 1/11 (d) 1/18
6. 6.What is the median of 27, 11, 4, 5 and 8? (a) 11 (b) 8 (c) 5 (d) 4
7. 7.What is the midpoint of the line joining (10, 6) and (12, 2)? (a) (11, 4) (b) (4, 11) (c) (22, 8) (d) (1, 2)
8. 8.In a class of 25 children, 9 like mangoes, 17 like bananas and 3 like both. How many like only mangoes? (a) 9 (b) 6 (c) 8 (d) 14
9. 9.How many factors does 47 have? (a) 2 (b) 1 (c) 3 (d) 4
10. 10.In a class of 28 children, 10 like maths, 18 like science and 6 like both. How many like at least one of the two? (a) 22 (b) 28 (c) 16 (d) 23
11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 5 (b) 4 (c) 3 (d) 2
12. 12.The mean of 7 numbers is 14. When the number 6 is added to them, what is the new mean? (a) 13 (b) 12 (c) 10 (d) 14
13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
14. 14.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 16 (c) 56 (d) 64
15. 15.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) 36 (b) 24 (c) 37 (d) 25
16. 16.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 81 (c) 45 (d) 72
17. 17.What is the mode of 18, 10, 5, 5, 5, 18 and 17? (a) 5 (b) 18 (c) 17 (d) 10
18. 18.A bag has 7 green balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 9 (d) 8
19. 19.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 130° (b) 90° (c) 270° (d) 140°
20. 20.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 15 (c) 18 (d) 5
21. 21.What is the 10th term of the AP 16, 19, 22, 25, …? (a) 30 (b) 46 (c) 27 (d) 43
22. 22.In a class of 35 children, 22 like dance, 9 like music and 3 like both. How many like only dance? (a) 6 (b) 22 (c) 19 (d) 26
23. 23.A bag has 7 red, 4 green and 9 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 17/20 (b) 1/5 (c) 1/3 (d) 4/5
24. 24.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 110° (b) 100° (c) 30° (d) 150°
25. 25.The mean of 7 numbers is 38. When the number 22 is added to them, what is the new mean? (a) 38 (b) 37 (c) 30 (d) 36
26. 26.What is the mean of 5, 2, 10, 5 and 23? (a) 8 (b) 11 (c) 9 (d) 10
27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 5 (d) 3
28. 28.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 120° (d) 60°
29. 29.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
30. 30.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 48 (d) 24
31. 31.A bag has 12 green balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 21 (c) 10 (d) 2
32. 32.A drawer has lots of red 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) 4 (c) 3 (d) 2
33. 33.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 150° (b) 70° (c) 40° (d) 140°
34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 19 (d) 9
35. 35.In a class of 33 children, 7 like mangoes, 23 like bananas and 4 like both. How many like only mangoes? (a) 19 (b) 10 (c) 3 (d) 7
36. 36.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
37. 37.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 120 (d) 25
38. 38.What is the mean of 11, 6, 13, 6, 12 and 6? (a) 11 (b) 8 (c) 10 (d) 9
39. 39.How many factors does 73 have? (a) 3 (b) 2 (c) 4 (d) 1
40. 40.What is the distance between the points (6, 17) and (12, 9)? (a) 100 (b) 11 (c) 14 (d) 10

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