Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 132 · 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 sum of all the whole numbers from 1 to 12? (a) 78 (b) 66 (c) 72 (d) 156
2. 2.If a + b = 20 and ab = 99, what is a² + b²? (a) 598 (b) 202 (c) 301 (d) 400
3. 3.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
4. 4.There are 3 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) 12 (b) 24 (c) 15 (d) 7
5. 5.What is the median of 1, 5, 28, 17 and 20? (a) 20 (b) 17 (c) 5 (d) 28
6. 6.In a class of 45 children, 27 like maths, 19 like science and 11 like both. How many like only maths? (a) 8 (b) 16 (c) 26 (d) 27
7. 7.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 255° (c) 105° (d) 150°
8. 8.What is the midpoint of the line joining (5, 8) and (7, 10)? (a) (12, 18) (b) (6, 9) (c) (9, 6) (d) (1, 1)
9. 9.A bag has 9 green, 7 yellow and 9 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 19/25 (b) 1/3 (c) 7/25 (d) 18/25
10. 10.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
11. 11.A bag has 12 black balls and 5 green 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) 6 (c) 2 (d) 17
12. 12.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) 45 (c) 14 (d) 42
13. 13.There are 4 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) 16 (b) 12 (c) 6 (d) 8
14. 14.In a class of 31 children, 7 like maths, 18 like science and 9 like neither. How many like both? (a) 22 (b) 4 (c) 9 (d) 3
15. 15.What is the mean of 17, 6, 18, 2, 11 and 18? (a) 11 (b) 13 (c) 14 (d) 12
16. 16.A bag has 12 blue balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 13 (d) 21
17. 17.What is the midpoint of the line joining (7, 10) and (19, 14)? (a) (6, 2) (b) (13, 12) (c) (12, 13) (d) (26, 24)
18. 18.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
19. 19.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 120 (d) 25
20. 20.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/8 (c) 1/8 (d) 3/4
21. 21.What is the distance between the points (6, 0) and (22, 12)? (a) 28 (b) 20 (c) 21 (d) 400
22. 22.What is the median of 31, 16, 26, 3 and 32? (a) 16 (b) 27 (c) 26 (d) 31
23. 23.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
24. 24.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1225 (b) 1575 (c) 2025 (d) 1235
25. 25.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 30° (b) 85° (c) 125° (d) 150°
26. 26.In a class of 34 children, 25 like cricket, 10 like football and 5 like neither. How many like both? (a) 5 (b) 29 (c) 6 (d) 1
27. 27.A bag has 4 yellow, 5 blue and 3 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 3/4 (c) 1/12 (d) 2/3
28. 28.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) 13 (b) 24 (c) 12 (d) 25
29. 29.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 37 (c) 49 (d) 36
30. 30.What is the distance between the points (0, 9) and (8, 3)? (a) 11 (b) 14 (c) 10 (d) 100
31. 31.A bag has 5 white balls and 10 black 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) 6 (c) 11 (d) 2
32. 32.A bag has 3 white balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 5 (c) 2 (d) 7
33. 33.What is the 11th term of the AP 4, 10, 16, 22, …? (a) 66 (b) 60 (c) 70 (d) 64
34. 34.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 132 (d) 121
35. 35.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) 14 (b) 21 (c) 22 (d) 15
36. 36.In a class of 34 children, 19 like dance, 18 like music and 4 like neither. How many like both? (a) 4 (b) 3 (c) 30 (d) 7
37. 37.In a class of 34 children, 14 like tea, 19 like coffee and 2 like both. How many like at least one of the two? (a) 29 (b) 33 (c) 34 (d) 31
38. 38.What is the distance between the points (3, 17) and (12, 5)? (a) 225 (b) 16 (c) 21 (d) 15
39. 39.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 39 (d) 12
40. 40.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 130° (c) 50° (d) 35°

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