Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 68 · 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.In a class of 38 children, 8 like cricket, 25 like football and 5 like both. How many like only cricket? (a) 3 (b) 8 (c) 13 (d) 20
2. 2.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 2/3 (b) 5/6 (c) 1/4 (d) 1/3
3. 3.How many factors does 37 have? (a) 2 (b) 4 (c) 1 (d) 3
4. 4.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
5. 5.A drawer has lots of red, blue and white 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
6. 6.What is the distance between the points (5, 8) and (29, 1)? (a) 26 (b) 25 (c) 625 (d) 31
7. 7.What is the mean of 7, 7, 20 and 6? (a) 9 (b) 8 (c) 11 (d) 10
8. 8.A bag has 4 blue, 7 yellow and 9 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 11/20 (b) 9/11 (c) 1/3 (d) 9/20
9. 9.How many prime numbers are there between 40 and 60? (a) 7 (b) 6 (c) 5 (d) 4
10. 10.In a class of 42 children, 18 like dance, 21 like music and 5 like both. How many like at least one of the two? (a) 34 (b) 29 (c) 39 (d) 42
11. 11.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
12. 12.What is the 35th term of the AP 19, 23, 27, 31, …? (a) 159 (b) 140 (c) 136 (d) 155
13. 13.What is the sum of all the whole numbers from 1 to 17? (a) 154 (b) 136 (c) 153 (d) 306
14. 14.What is the 31st term of the AP 1, 9, 17, 25, …? (a) 240 (b) 248 (c) 249 (d) 241
15. 15.Which is the correct factorisation of x² + 11x + 28? (a) (x + 1)(x + 28) (b) (x + 1)(x + 10) (c) (x + 4)(x + 7) (d) (x − 4)(x − 7)
16. 16.What is the mean of 10, 20, 19, 2 and 14? (a) 14 (b) 12 (c) 13 (d) 15
17. 17.What are the roots of x² − 15x + 56 = 0? (a) 2 and 28 (b) 1 and 56 (c) 7 and 8 (d) 1 and 14
18. 18.What is the distance between the points (2, 8) and (14, 13)? (a) 13 (b) 169 (c) 14 (d) 17
19. 19.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 8 sq cm (c) 16 sq cm (d) 24 sq cm
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
21. 21.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 30° (d) 60°
22. 22.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) 16 times (c) 4 times (d) 8 times
23. 23.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 7/8 (c) 1/8 (d) 1/7
24. 24.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 102 (c) 93 (d) 94
25. 25.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 3/5 (c) 1/4 (d) 5/8
26. 26.A bag has 10 red balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 11 (b) 18 (c) 12 (d) 2
27. 27.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 253 (b) 38 (c) 506 (d) 256
28. 28.In a class of 41 children, 17 like mangoes, 26 like bananas and 10 like both. How many like only mangoes? (a) 16 (b) 15 (c) 17 (d) 7
29. 29.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) 21 (d) 14
30. 30.In a class of 32 children, 18 like tea, 16 like coffee and 10 like neither. How many like both? (a) 2 (b) 12 (c) 10 (d) 22
31. 31.A drawer has lots of black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 3 (d) 2
32. 32.A bag has 10 blue balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 12 (c) 11 (d) 22
33. 33.Which is the correct factorisation of x² + 7x + 12? (a) (x + 1)(x + 6) (b) (x + 3)(x + 4) (c) (x − 3)(x − 4) (d) (x + 1)(x + 12)
34. 34.If a + b = 12 and ab = 35, what is (a − b)²? (a) 74 (b) 144 (c) 2 (d) 4
35. 35.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
36. 36.If a + b = 16 and ab = 48, what is (a − b)²? (a) 64 (b) 256 (c) 160 (d) 8
37. 37.What is the midpoint of the line joining (2, 6) and (14, 16)? (a) (6, 5) (b) (11, 8) (c) (8, 11) (d) (16, 22)
38. 38.What is the distance between the points (4, 12) and (10, 4)? (a) 100 (b) 11 (c) 10 (d) 14
39. 39.How many prime numbers are there between 20 and 30? (a) 3 (b) 4 (c) 2 (d) 1
40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 6 (d) 4

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