Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 102 · 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 19 have? (a) 4 (b) 2 (c) 3 (d) 1
2. 2.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 27 (c) 81 (d) 9
3. 3.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) 22 (b) 14 (c) 21 (d) 15
4. 4.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 24 (b) 160 (c) 80 (d) 90
5. 5.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
6. 6.In a class of 40 children, 16 like cricket, 23 like football and 5 like both. How many like neither? (a) 6 (b) 1 (c) 11 (d) 5
7. 7.3 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) 9 (b) 6 (c) 5 (d) 12
8. 8.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 121 (d) 55
9. 9.In a class of 44 children, 24 like cricket, 24 like football and 6 like both. How many like neither? (a) 3 (b) 6 (c) 8 (d) 2
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
11. 11.What is the smallest prime factor of 319? (a) 1 (b) 2 (c) 11 (d) 29
12. 12.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 48 (d) 12
13. 13.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 130° (b) 125° (c) 105° (d) 50°
14. 14.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
15. 15.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 130° (b) 80° (c) 150° (d) 100°
16. 16.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 45° (b) 110° (c) 135° (d) 115°
17. 17.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) 28 (d) 56
18. 18.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 15 (b) 16 (c) 4 (d) 14
20. 20.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 24 (c) 25 (d) 36
21. 21.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 172 (d) 163
22. 22.What is the mode of 16, 16, 5, 5, 10, 1 and 16? (a) 1 (b) 5 (c) 16 (d) 10
23. 23.What is the mean of 6, 8, 12, 14, 4 and 4? (a) 10 (b) 8 (c) 7 (d) 9
24. 24.What is the median of 40, 5, 37, 35 and 30? (a) 36 (b) 30 (c) 37 (d) 35
25. 25.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
26. 26.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 75° (d) 150°
27. 27.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 10 (b) 19 (c) 11 (d) 9
28. 28.In a class of 34 children, 23 like cricket, 14 like football and 6 like neither. How many like both? (a) 6 (b) 28 (c) 3 (d) 9
29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
30. 30.In a class of 46 children, 19 like tea, 19 like coffee and 2 like both. How many like neither? (a) 10 (b) 2 (c) 12 (d) 8
31. 31.In a class of 28 children, 8 like cricket, 14 like football and 8 like neither. How many like both? (a) 3 (b) 8 (c) 20 (d) 2
32. 32.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 15° (c) 165° (d) 16°
33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 5 (b) 6 (c) 7 (d) 4
34. 34.What is the midpoint of the line joining (0, 4) and (6, 12)? (a) (6, 16) (b) (8, 3) (c) (3, 4) (d) (3, 8)
35. 35.How many factors does 83 have? (a) 4 (b) 1 (c) 3 (d) 2
36. 36.If a + b = 17 and ab = 66, what is a² + b²? (a) 223 (b) 421 (c) 157 (d) 289
37. 37.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 315° (c) 135° (d) 45°
38. 38.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 650 (c) 325 (d) 625
39. 39.A bag has 3 red balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 5 (c) 7 (d) 2
40. 40.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 100° (b) 135° (c) 45° (d) 125°

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