Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 232 · 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.A drawer has lots of green, 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) 6 (b) 3 (c) 4 (d) 2
2. 2.What is the 25th term of the AP 1, 6, 11, 16, …? (a) 125 (b) 120 (c) 121 (d) 126
3. 3.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 45 (c) 100 (d) 20
4. 4.A bag has 2 red, 3 blue and 7 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 1/4 (c) 5/6 (d) 3/4
5. 5.In a class of 25 children, 8 like maths, 11 like science and 3 like both. How many like at least one of the two? (a) 13 (b) 19 (c) 16 (d) 25
6. 6.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) 15 (b) 22 (c) 14 (d) 21
7. 7.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 10 (c) 24 (d) 16
8. 8.A bag has 4 white balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 6 (b) 11 (c) 5 (d) 2
9. 9.How many factors does 89 have? (a) 4 (b) 2 (c) 1 (d) 3
10. 10.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 120 (d) 240
11. 11.What is the distance between the points (2, 1) and (17, 9)? (a) 23 (b) 18 (c) 17 (d) 289
12. 12.Two angles of a triangle are 60° and 60°. What is the exterior angle at the third corner? (a) 240° (b) 121° (c) 60° (d) 120°
13. 13.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
14. 14.A drawer has lots of red, green, white, 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) 10 (b) 6 (c) 5 (d) 2
15. 15.A drawer has lots of white, green 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) 2 (b) 3 (c) 6 (d) 4
16. 16.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 120° (b) 95° (c) 145° (d) 85°
17. 17.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
18. 18.Using (a + b)² = a² + 2ab + b², what is 83²? (a) 6889 (b) 6409 (c) 6899 (d) 5929
19. 19.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 49 (d) 28
20. 20.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
21. 21.What is the mean of 3, 19, 15, 15 and 3? (a) 12 (b) 13 (c) 10 (d) 11
22. 22.Which is the correct factorisation of x² + 5x + 6? (a) (x + 1)(x + 6) (b) (x + 2)(x + 3) (c) (x − 2)(x − 3) (d) (x + 1)(x + 4)
23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 15 (d) 72
24. 24.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 105° (d) 75°
25. 25.What is the median of 16, 14, 13, 8, 11, 2 and 34? (a) 14 (b) 13 (c) 11 (d) 8
26. 26.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 15° (b) 165° (c) 90° (d) 105°
27. 27.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
28. 28.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 1)(x + 16) (c) (x − 8)(x − 9) (d) (x + 8)(x + 9)
29. 29.In a class of 37 children, 22 like cricket, 13 like football and 7 like both. How many like neither? (a) 9 (b) 7 (c) 2 (d) 16
30. 30.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 8 (c) 7 (d) 15
31. 31.If a + b = 4 and ab = 3, what is (a − b)²? (a) 4 (b) 2 (c) 16 (d) 10
32. 32.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 160° (c) 20° (d) 80°
33. 33.How many factors does 40 have? (a) 9 (b) 6 (c) 7 (d) 8
34. 34.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 150° (b) 115° (c) 95° (d) 30°
35. 35.The mean of 7 numbers is 29. When the number 45 is added to them, what is the new mean? (a) 31 (b) 32 (c) 37 (d) 29
36. 36.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 121 (d) 55
37. 37.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
38. 38.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 65° (b) 105° (c) 115° (d) 140°
39. 39.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 1/5 (c) 1/3 (d) 5/6
40. 40.How many prime numbers are there between 60 and 90? (a) 7 (b) 8 (c) 9 (d) 6

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