Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 20 · 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 3 white, 3 yellow and 5 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 3/8 (b) 3/11 (c) 1/3 (d) 8/11
2. 2.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 169 (c) 156 (d) 91
3. 3.What is the mean of 6, 2, 14 and 22? (a) 10 (b) 12 (c) 13 (d) 11
4. 4.In a class of 25 children, 8 like cricket, 12 like football and 5 like both. How many like only cricket? (a) 7 (b) 8 (c) 13 (d) 3
5. 5.If a + b = 13 and ab = 22, what is a² + b²? (a) 213 (b) 169 (c) 147 (d) 125
6. 6.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 36 (c) 11 (d) 33
7. 7.A drawer has lots of yellow, black 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) 4 (b) 2 (c) 3 (d) 6
8. 8.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
9. 9.How many factors does 102 have? (a) 9 (b) 7 (c) 6 (d) 8
10. 10.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 11 (c) 28 (d) 56
11. 11.What is the mode of 14, 8, 11, 12, 11, 14 and 14? (a) 11 (b) 14 (c) 8 (d) 12
12. 12.A bag has 7 yellow, 5 white and 9 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 5/21 (c) 17/21 (d) 16/21
13. 13.How many prime numbers are there between 30 and 40? (a) 1 (b) 3 (c) 4 (d) 2
14. 14.A drawer has lots of yellow, red, black 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) 4 (c) 8 (d) 5
15. 15.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 54 (d) 153
16. 16.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
18. 18.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 42 (d) 49
19. 19.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 102 (b) 60 (c) 16 (d) 51
20. 20.In a class of 45 children, 21 like cricket, 27 like football and 9 like neither. How many like both? (a) 9 (b) 12 (c) 36 (d) 3
21. 21.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 16 (d) 12
22. 22.What are the roots of x² − 8x + 15 = 0? (a) 1 and 15 (b) 2 and 6 (c) 1 and 7 (d) 3 and 5
23. 23.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 2 (b) 3 (c) 5 (d) 4
25. 25.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
26. 26.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 105 (c) 120 (d) 225
27. 27.In a class of 49 children, 27 like maths, 24 like science and 10 like both. How many like at least one of the two? (a) 41 (b) 49 (c) 31 (d) 51
28. 28.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 110° (c) 290° (d) 145°
29. 29.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 10° (c) 20° (d) 11°
30. 30.What is the mode of 3, 1, 3, 1, 1, 19 and 13? (a) 13 (b) 19 (c) 1 (d) 3
31. 31.A bag has 6 green, 3 yellow and 4 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 7/13 (c) 6/13 (d) 8/13
32. 32.Using (a − b)² = a² − 2ab + b², what is 77²? (a) 6889 (b) 5929 (c) 6391 (d) 5939
33. 33.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 40° (d) 140°
34. 34.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 50 (b) 14 (c) 100 (d) 55
35. 35.If a + b = 20 and ab = 99, what is a² + b²? (a) 301 (b) 202 (c) 598 (d) 400
36. 36.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 56 (c) 98 (d) 49
37. 37.Which term of the AP 14, 20, 26, 32, … is 224? (a) 37th (b) 38th (c) 35th (d) 36th
38. 38.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
39. 39.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 20 (d) 90
40. 40.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 153 (d) 306

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