Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 339 · 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.How many factors does 85 have? (a) 2 (b) 3 (c) 5 (d) 4
2. 2.What is the mean of 8, 5, 17, 8 and 12? (a) 10 (b) 9 (c) 12 (d) 11
3. 3.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
4. 4.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
5. 5.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 30° (b) 110° (c) 150° (d) 100°
6. 6.What are the roots of x² − 14x + 48 = 0? (a) 6 and 8 (b) 1 and 13 (c) 1 and 48 (d) 2 and 24
7. 7.In a class of 30 children, 7 like cricket, 20 like football and 4 like both. How many like at least one of the two? (a) 27 (b) 19 (c) 30 (d) 23
8. 8.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 20° (b) 160° (c) 60° (d) 140°
9. 9.How many prime numbers are there between 70 and 100? (a) 5 (b) 6 (c) 8 (d) 7
10. 10.What is the mode of 1, 15, 1, 1, 18, 18 and 2? (a) 15 (b) 2 (c) 18 (d) 1
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) 13 (c) 24 (d) 12
12. 12.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 24 sq cm (b) 26 sq cm (c) 52 sq cm (d) 104 sq cm
13. 13.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
14. 14.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
15. 15.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 4 (d) 1
16. 16.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 120° (d) 60°
17. 17.In a class of 49 children, 22 like mangoes, 25 like bananas and 9 like neither. How many like both? (a) 8 (b) 7 (c) 9 (d) 40
18. 18.In a class of 37 children, 19 like maths, 18 like science and 9 like both. How many like at least one of the two? (a) 28 (b) 19 (c) 37 (d) 29
19. 19.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 32 (c) 10 (d) 16
20. 20.If a + b = 13 and ab = 40, what is (a − b)²? (a) 9 (b) 89 (c) 3 (d) 169
21. 21.What is the mean of 5, 10, 5, 5, 8 and 9? (a) 7 (b) 8 (c) 9 (d) 6
22. 22.What is the median of 40, 2, 31, 27 and 18? (a) 28 (b) 27 (c) 31 (d) 18
23. 23.In a class of 38 children, 21 like mangoes, 25 like bananas and 2 like neither. How many like both? (a) 2 (b) 36 (c) 10 (d) 8
24. 24.What is the mean of 8, 2, 15 and 15? (a) 9 (b) 8 (c) 10 (d) 11
25. 25.What is the mode of 20, 10, 12, 17, 10, 12 and 10? (a) 12 (b) 20 (c) 17 (d) 10
26. 26.A bag has 2 white, 3 green and 5 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/10 (b) 3/5 (c) 1/3 (d) 1/2
27. 27.Using (a + b)² = a² + 2ab + b², what is 102²? (a) 9604 (b) 10414 (c) 10004 (d) 10404
28. 28.If a + b = 11 and ab = 10, what is a² + b²? (a) 111 (b) 141 (c) 101 (d) 121
29. 29.In a class of 14 children, 8 like maths, 7 like science and 3 like both. How many like only maths? (a) 7 (b) 8 (c) 4 (d) 5
30. 30.The mean of 4 numbers is 15. When the number 35 is added to them, what is the new mean? (a) 19 (b) 25 (c) 20 (d) 15
31. 31.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 108 (c) 36 (d) 39
32. 32.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 165 (b) 324 (c) 162 (d) 30
33. 33.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 56 (d) 28
34. 34.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 49 sq cm (c) 196 sq cm (d) 294 sq cm
35. 35.What is the mode of 13, 7, 9, 9, 9, 6 and 13? (a) 6 (b) 9 (c) 7 (d) 13
36. 36.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 18 (b) 9 (c) 6 (d) 12
37. 37.What is the distance between the points (5, 8) and (20, 0)? (a) 18 (b) 289 (c) 17 (d) 23
38. 38.What is the mean of 6, 15, 3, 15, 18 and 9? (a) 12 (b) 11 (c) 10 (d) 13
39. 39.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 1/8 (c) 1/4 (d) 3/4
40. 40.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 132 (c) 66 (d) 24

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