Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 728 · 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 bag has 7 blue, 6 white and 2 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 8/15 (b) 1/3 (c) 7/15 (d) 7/8
2. 2.In a class of 32 children, 23 like maths, 11 like science and 8 like both. How many like neither? (a) 6 (b) 14 (c) 8 (d) 7
3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 4 (b) 7 (c) 5 (d) 6
4. 4.A bag has 8 yellow balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 15 (c) 10 (d) 2
5. 5.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 16 (d) 48
6. 6.What is the prime factorisation of 35? (a) 5² × 7 (b) 5³ × 7 (c) 5 × 7² (d) 5 × 7
7. 7.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) 36 (c) 49 (d) 37
8. 8.In a class of 21 children, 10 like mangoes, 16 like bananas and 7 like both. How many like neither? (a) 2 (b) 9 (c) 3 (d) 7
9. 9.Using (a − b)² = a² − 2ab + b², what is 85²? (a) 7235 (b) 7225 (c) 8075 (d) 9025
10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 2 (b) 5 (c) 3 (d) 4
11. 11.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 135° (c) 91° (d) 90°
12. 12.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 30 (d) 12
13. 13.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 66 (d) 189
14. 14.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
15. 15.A drawer has lots of green, white, black and red 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) 8 (c) 2 (d) 4
16. 16.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 120 (d) 25
17. 17.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 130 (b) 65 (c) 70 (d) 11
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 2/11 (c) 1/18 (d) 1/12
19. 19.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 70° (b) 140° (c) 71° (d) 110°
20. 20.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
21. 21.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 10 (b) 11 (c) 9 (d) 8
23. 23.In a class of 36 children, 31 like dance, 15 like music and 2 like neither. How many like both? (a) 2 (b) 10 (c) 12 (d) 34
24. 24.In a class of 30 children, 12 like tea, 16 like coffee and 9 like neither. How many like both? (a) 9 (b) 7 (c) 8 (d) 21
25. 25.What is the product of the roots of x² − 10x + 16 = 0? (a) 10 (b) 17 (c) 15 (d) 16
26. 26.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 72 (d) 36
27. 27.What is the 11th term of the AP 3, 8, 13, 18, …? (a) 58 (b) 50 (c) 55 (d) 53
28. 28.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1591 (b) 1379 (c) 1849 (d) 1369
29. 29.How many factors does 50 have? (a) 4 (b) 5 (c) 6 (d) 7
30. 30.In which quadrant does the point (3, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
31. 31.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 95° (b) 115° (c) 85° (d) 150°
32. 32.How many factors does 117 have? (a) 4 (b) 6 (c) 5 (d) 7
33. 33.What is the 30th term of the AP 6, 10, 14, 18, …? (a) 116 (b) 120 (c) 126 (d) 122
34. 34.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 240 (d) 120
35. 35.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
36. 36.How many prime numbers are there between 40 and 70? (a) 7 (b) 6 (c) 8 (d) 9
37. 37.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 86° (c) 95° (d) 265°
38. 38.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 3 (d) 12
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
40. 40.In a class of 38 children, 21 like maths, 19 like science and 12 like both. How many like at least one of the two? (a) 38 (b) 16 (c) 40 (d) 28

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