Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 984 · 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 the first 6 terms of the AP 8, 14, 20, …? (a) 138 (b) 38 (c) 276 (d) 156
2. 2.What is the 23rd term of the AP 6, 15, 24, 33, …? (a) 213 (b) 198 (c) 207 (d) 204
3. 3.A drawer has lots of white 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) 5 (c) 4 (d) 3
4. 4.What is the smallest prime factor of 65? (a) 2 (b) 1 (c) 5 (d) 13
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
6. 6.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
7. 7.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
8. 8.In a class of 30 children, 16 like mangoes, 19 like bananas and 7 like both. How many like only mangoes? (a) 11 (b) 9 (c) 16 (d) 12
9. 9.A cuboid is 7 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 94 sq cm (b) 376 sq cm (c) 188 sq cm (d) 168 sq cm
10. 10.What is the mean of 9, 16, 3, 2, 17 and 7? (a) 8 (b) 10 (c) 11 (d) 9
11. 11.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) 25 (b) 24 (c) 12 (d) 13
12. 12.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 121 (c) 112 (d) 122
13. 13.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 18 (c) 12 (d) 9
14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 17 (d) 8
15. 15.What is the 27th term of the AP 20, 25, 30, 35, …? (a) 155 (b) 130 (c) 135 (d) 150
16. 16.If a + b = 5 and ab = 4, what is (a − b)²? (a) 3 (b) 25 (c) 9 (d) 17
17. 17.What is the smallest prime factor of 133? (a) 1 (b) 2 (c) 19 (d) 7
18. 18.If a + b = 18 and ab = 77, what is a² + b²? (a) 478 (b) 247 (c) 170 (d) 324
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/9 (c) 1/12 (d) 1/11
20. 20.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
21. 21.What are the roots of x² − 17x + 72 = 0? (a) 1 and 16 (b) 1 and 72 (c) 8 and 9 (d) 2 and 36
22. 22.Using (a − b)² = a² − 2ab + b², what is 85²? (a) 8075 (b) 9025 (c) 7235 (d) 7225
23. 23.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) 16 (b) 10 (c) 32 (d) 24
24. 24.A bag has 11 red balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 19 (d) 12
25. 25.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 100° (c) 280° (d) 80°
26. 26.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 210 (c) 105 (d) 225
27. 27.What is the midpoint of the line joining (1, 2) and (7, 6)? (a) (4, 4) (b) (5, 4) (c) (8, 8) (d) (3, 2)
28. 28.What is the 38th term of the AP 1, 10, 19, 28, …? (a) 342 (b) 334 (c) 333 (d) 343
29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 4 (b) 7 (c) 6 (d) 5
30. 30.A bag has 6 blue balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 7 (c) 8 (d) 11
31. 31.A bag has 6 green, 8 red and 8 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 4/11 (c) 4/7 (d) 7/11
32. 32.A bag has 6 blue balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 7 (c) 8 (d) 11
33. 33.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 48 cu cm (b) 10 cu cm (c) 9 cu cm (d) 20 cu cm
34. 34.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 50° (d) 100°
35. 35.What is the mode of 15, 13, 15, 13, 13, 11 and 14? (a) 14 (b) 15 (c) 11 (d) 13
36. 36.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
37. 37.What is the midpoint of the line joining (9, 8) and (13, 10)? (a) (2, 1) (b) (9, 11) (c) (11, 9) (d) (22, 18)
38. 38.In a class of 29 children, 9 like mangoes, 17 like bananas and 2 like both. How many like neither? (a) 3 (b) 2 (c) 5 (d) 7
39. 39.A bag has 6 blue, 5 red and 2 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 7/13 (b) 6/13 (c) 1/3 (d) 6/7
40. 40.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 55° (b) 130° (c) 105° (d) 125°

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