Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 948 · 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 mode of 20, 6, 6, 12, 20, 1 and 20? (a) 20 (b) 6 (c) 12 (d) 1
2. 2.What is the median of 14, 5, 36, 24 and 12? (a) 12 (b) 36 (c) 14 (d) 24
3. 3.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 285° (c) 105° (d) 75°
4. 4.There are 5 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 25 (b) 20 (c) 9 (d) 40
5. 5.What is the midpoint of the line joining (5, 8) and (11, 10)? (a) (9, 8) (b) (3, 1) (c) (16, 18) (d) (8, 9)
6. 6.A bag has 4 red, 3 green and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 7/9 (c) 2/3 (d) 1/9
7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
8. 8.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 155° (d) 125°
9. 9.What is the median of 26, 32, 24, 38 and 10? (a) 32 (b) 24 (c) 27 (d) 26
10. 10.A bag has 8 white balls and 3 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) 9 (c) 11 (d) 4
11. 11.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 8 times (d) 6 times
12. 12.Using (a + b)² = a² + 2ab + b², what is 43²? (a) 1859 (b) 1369 (c) 1609 (d) 1849
13. 13.How many factors does 62 have? (a) 3 (b) 4 (c) 5 (d) 2
14. 14.3 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 7 (b) 15 (c) 12 (d) 24
15. 15.What is the distance between the points (3, 9) and (7, 6)? (a) 5 (b) 7 (c) 25 (d) 6
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 13 (b) 3 (c) 14 (d) 15
17. 17.In a class of 36 children, 25 like mangoes, 16 like bananas and 6 like both. How many like only mangoes? (a) 25 (b) 10 (c) 20 (d) 19
18. 18.In a class of 37 children, 15 like tea, 26 like coffee and 6 like both. How many like at least one of the two? (a) 37 (b) 41 (c) 35 (d) 29
19. 19.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
20. 20.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 14 (c) 21 (d) 15
21. 21.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 13 (c) 25 (d) 12
22. 22.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 66 (d) 24
23. 23.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 8 sq cm (c) 4 sq cm (d) 24 sq cm
24. 24.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 130° (b) 120° (c) 110° (d) 50°
25. 25.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
26. 26.How many factors does 38 have? (a) 2 (b) 3 (c) 5 (d) 4
27. 27.In a class of 43 children, 23 like mangoes, 29 like bananas and 3 like neither. How many like both? (a) 40 (b) 3 (c) 12 (d) 9
28. 28.What is the prime factorisation of 28? (a) 2 × 7 (b) 2 × 7² (c) 2² × 7 (d) 2³ × 7
29. 29.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 30° (d) 120°
30. 30.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
31. 31.In a class of 28 children, 15 like cricket, 9 like football and 7 like neither. How many like both? (a) 21 (b) 7 (c) 4 (d) 3
32. 32.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
33. 33.How many factors does 15 have? (a) 3 (b) 4 (c) 5 (d) 2
34. 34.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
35. 35.What is the median of 12, 2, 6, 1, 13, 21 and 20? (a) 13 (b) 6 (c) 12 (d) 1
36. 36.What is the midpoint of the line joining (10, 6) and (18, 8)? (a) (28, 14) (b) (7, 14) (c) (14, 7) (d) (4, 1)
37. 37.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 18 (c) 9 (d) 36
38. 38.In a class of 28 children, 16 like tea, 20 like coffee and 12 like both. How many like only tea? (a) 4 (b) 16 (c) 12 (d) 8
39. 39.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
40. 40.What are the roots of x² − 13x + 36 = 0? (a) 1 and 36 (b) 2 and 18 (c) 1 and 12 (d) 4 and 9

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