Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 741 · 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 23 children, 16 like tea, 16 like coffee and 12 like both. How many like at least one of the two? (a) 8 (b) 32 (c) 20 (d) 23
2. 2.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 80° (c) 100° (d) 20°
3. 3.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 1152 (c) 2352 (d) 1176
4. 4.In a class of 38 children, 25 like tea, 21 like coffee and 10 like both. How many like neither? (a) 10 (b) 2 (c) 3 (d) 12
5. 5.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 30 (d) 21
6. 6.What is the mean of 17, 15, 12, 6, 6 and 10? (a) 13 (b) 10 (c) 11 (d) 12
7. 7.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
8. 8.What is the midpoint of the line joining (1, 8) and (9, 18)? (a) (4, 5) (b) (13, 5) (c) (5, 13) (d) (10, 26)
9. 9.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 19 (d) 110
10. 10.What is the mean of 16, 15, 10, 12, 7 and 6? (a) 12 (b) 10 (c) 13 (d) 11
11. 11.What is the median of 20, 23, 38, 8, 33, 28 and 35? (a) 28 (b) 33 (c) 8 (d) 23
12. 12.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
13. 13.A drawer has lots of black, green and yellow 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
14. 14.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 65 (b) 16 (c) 60 (d) 120
15. 15.What is the distance between the points (5, 4) and (13, 10)? (a) 100 (b) 14 (c) 11 (d) 10
16. 16.Using (a − b)² = a² − 2ab + b², what is 95²? (a) 9025 (b) 11025 (c) 9035 (d) 9975
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
18. 18.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 15 (d) 30
19. 19.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°
20. 20.What is the median of 32, 6, 18, 10 and 38? (a) 32 (b) 10 (c) 18 (d) 19
21. 21.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) 3 (b) 6 (c) 4 (d) 2
22. 22.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 86° (d) 265°
23. 23.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) 14 (b) 21 (c) 15 (d) 22
24. 24.Two angles of a triangle are 20° and 110°. What is the exterior angle at the third corner? (a) 160° (b) 50° (c) 130° (d) 70°
25. 25.In a class of 39 children, 19 like dance, 25 like music and 4 like neither. How many like both? (a) 9 (b) 5 (c) 35 (d) 4
26. 26.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 12 (d) 16
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
28. 28.What is the distance between the points (8, 12) and (20, 7)? (a) 17 (b) 13 (c) 169 (d) 14
29. 29.In a class of 24 children, 12 like cricket, 16 like football and 8 like both. How many like neither? (a) 12 (b) 4 (c) 5 (d) 8
30. 30.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 160° (b) 110° (c) 70° (d) 130°
31. 31.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
32. 32.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 8 (c) 7 (d) 15
33. 33.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) 36 (c) 25 (d) 24
34. 34.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 586 (b) 585 (c) 576 (d) 462
35. 35.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
36. 36.In which quadrant does the point (−2, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
37. 37.A drawer has lots of black, blue and yellow 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) 6 (c) 4 (d) 3
38. 38.A bag has 3 red, 2 yellow and 3 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 3/8 (b) 5/8 (c) 3/4 (d) 1/3
39. 39.A cuboid is 5 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 105 cu cm (b) 142 cu cm (c) 106 cu cm (d) 15 cu cm
40. 40.What is the median of 7, 31, 3, 17 and 8? (a) 17 (b) 8 (c) 7 (d) 3

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