Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 50 · 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 drawer has lots of yellow, blue, green, black 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) 5 (c) 6 (d) 10
2. 2.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 15 (d) 30
3. 3.If a + b = 5 and ab = 6, what is (a − b)²? (a) 13 (b) 25 (c) 19 (d) 1
4. 4.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 130° (b) 270° (c) 140° (d) 90°
5. 5.In a class of 33 children, 24 like cricket, 13 like football and 5 like both. How many like at least one of the two? (a) 37 (b) 33 (c) 32 (d) 27
6. 6.A bag has 5 white, 5 red and 6 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 11/16 (b) 5/16 (c) 1/3 (d) 5/11
7. 7.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
8. 8.What is the mean of 8, 19, 8, 20, 10 and 19? (a) 13 (b) 12 (c) 14 (d) 15
9. 9.In a class of 35 children, 22 like dance, 7 like music and 4 like both. How many like only dance? (a) 22 (b) 28 (c) 18 (d) 3
10. 10.If a + b = 16 and ab = 48, what is a² + b²? (a) 208 (b) 352 (c) 256 (d) 160
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
12. 12.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/4 (c) 2/3 (d) 1/3
13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 18 (d) 8
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
15. 15.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 7 (c) 24 (d) 63
16. 16.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 7/8 (c) 1/4 (d) 1/8
17. 17.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 65° (c) 130° (d) 50°
18. 18.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 66 (c) 198 (d) 22
19. 19.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 320° (c) 160° (d) 20°
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/11 (d) 1/12
21. 21.How many prime numbers are there between 80 and 110? (a) 8 (b) 7 (c) 9 (d) 6
22. 22.A bag has 6 yellow, 7 white and 5 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 7/18 (c) 2/3 (d) 1/2
23. 23.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 1)(x + 16) (d) (x + 8)(x + 9)
24. 24.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
25. 25.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 20 (c) 9 (d) 25
26. 26.A bag has 3 yellow, 3 green and 9 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 13/15 (b) 1/5 (c) 4/5 (d) 1/3
27. 27.A bag has 6 white, 8 yellow and 7 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 13/21 (b) 8/21 (c) 1/3 (d) 8/13
28. 28.In a class of 33 children, 21 like mangoes, 11 like bananas and 2 like both. How many like only mangoes? (a) 19 (b) 21 (c) 22 (d) 9
29. 29.In a class of 20 children, 15 like cricket, 11 like football and 7 like both. How many like at least one of the two? (a) 12 (b) 26 (c) 19 (d) 20
30. 30.What is the sum of the roots of x² − 5x + 6 = 0? (a) 5 (b) 6 (c) 7 (d) 4
31. 31.What is the mode of 3, 3, 10, 7, 3, 10 and 9? (a) 7 (b) 9 (c) 3 (d) 10
32. 32.A drawer has lots of blue 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) 5 (b) 3 (c) 4 (d) 2
33. 33.What is the distance between the points (4, 0) and (12, 6)? (a) 10 (b) 100 (c) 14 (d) 11
34. 34.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 60° (d) 30°
35. 35.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 240 (b) 30 (c) 456 (d) 228
36. 36.If a + b = 21 and ab = 108, what is a² + b²? (a) 657 (b) 441 (c) 333 (d) 225
37. 37.The mean of 4 numbers is 28. When the number 38 is added to them, what is the new mean? (a) 28 (b) 31 (c) 33 (d) 30
38. 38.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 2/3
39. 39.What is the prime factorisation of 63? (a) 3 × 7² (b) 3² × 7 (c) 3 × 7 (d) 3³ × 7
40. 40.In a class of 39 children, 22 like maths, 27 like science and 12 like both. How many like at least one of the two? (a) 37 (b) 39 (c) 25 (d) 49

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