Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 946 · 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 mean of 17, 20, 9, 16, 4 and 18? (a) 15 (b) 14 (c) 13 (d) 12
2. 2.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
3. 3.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 66 (d) 144
4. 4.A bag has 2 red, 4 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/4 (b) 1/3 (c) 3/4 (d) 3/8
5. 5.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 126 (b) 13 (c) 66 (d) 63
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/11 (b) 5/36 (c) 1/6 (d) 1/11
7. 7.A drawer has lots of green, white, blue, red and black 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) 10 (d) 6
8. 8.In a class of 40 children, 22 like tea, 19 like coffee and 10 like neither. How many like both? (a) 30 (b) 11 (c) 1 (d) 10
9. 9.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
10. 10.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
11. 11.A bag has 4 green balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 8 (b) 6 (c) 5 (d) 2
12. 12.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 7 (d) 2
13. 13.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 150° (d) 30°
14. 14.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 132 (d) 144
15. 15.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 127 (c) 136 (d) 128
16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 3 (b) 4 (c) 5 (d) 6
17. 17.What is the smallest prime factor of 253? (a) 23 (b) 1 (c) 11 (d) 2
18. 18.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 5 (d) 7
19. 19.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 70° (d) 80°
20. 20.If a + b = 18 and ab = 77, what is (a − b)²? (a) 170 (b) 16 (c) 324 (d) 4
21. 21.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) 36 (b) 48 (c) 37 (d) 49
22. 22.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 16 (c) 6 (d) 8
23. 23.The mean of 8 numbers is 15. When the number 42 is added to them, what is the new mean? (a) 19 (b) 15 (c) 17 (d) 18
24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
25. 25.What is the mode of 8, 12, 16, 16, 2, 16 and 2? (a) 2 (b) 12 (c) 16 (d) 8
26. 26.What is the 25th term of the AP 11, 15, 19, 23, …? (a) 96 (b) 111 (c) 107 (d) 100
27. 27.In a class of 29 children, 11 like cricket, 20 like football and 4 like both. How many like only cricket? (a) 7 (b) 16 (c) 11 (d) 9
28. 28.In a class of 40 children, 22 like cricket, 18 like football and 4 like both. How many like at least one of the two? (a) 37 (b) 36 (c) 32 (d) 40
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/12 (c) 2/11 (d) 1/18
30. 30.What is the smallest prime factor of 209? (a) 1 (b) 2 (c) 11 (d) 19
31. 31.If a + b = 11 and ab = 18, what is (a − b)²? (a) 7 (b) 49 (c) 121 (d) 85
32. 32.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
33. 33.A drawer has lots of yellow, green and black 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) 2 (c) 4 (d) 3
34. 34.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 255° (b) 75° (c) 150° (d) 105°
35. 35.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 42 (c) 35 (d) 70
36. 36.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 70° (d) 55°
37. 37.How many prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 3 (d) 5
38. 38.If a + b = 21 and ab = 108, what is a² + b²? (a) 657 (b) 441 (c) 225 (d) 333
39. 39.A bag has 12 black balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 14 (b) 2 (c) 21 (d) 13
40. 40.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 33 (b) 210 (c) 120 (d) 105

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