Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 780 · 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.What is the mean of 3, 15, 17, 12, 9 and 22? (a) 15 (b) 12 (c) 13 (d) 14
2. 2.In a class of 26 children, 16 like maths, 16 like science and 8 like both. How many like only maths? (a) 9 (b) 10 (c) 16 (d) 8
3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
4. 4.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 98 (c) 88 (d) 97
5. 5.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
7. 7.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 40° (d) 50°
8. 8.What is the distance between the points (6, 5) and (9, 9)? (a) 5 (b) 25 (c) 7 (d) 6
9. 9.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) 12 (b) 25 (c) 24 (d) 13
10. 10.What are the roots of x² − 13x + 40 = 0? (a) 1 and 12 (b) 1 and 40 (c) 5 and 8 (d) 2 and 20
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
12. 12.A bag has 8 yellow balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 2 (c) 10 (d) 12
13. 13.What is the mean of 2, 18, 2, 18 and 20? (a) 12 (b) 15 (c) 10 (d) 13
14. 14.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
15. 15.What is the smallest prime factor of 35? (a) 1 (b) 5 (c) 2 (d) 7
16. 16.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 121 (d) 55
17. 17.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/4 (c) 1/3 (d) 5/6
18. 18.In which quadrant does the point (−7, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
19. 19.A bag has 5 yellow balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 6 (b) 13 (c) 7 (d) 2
20. 20.A bag has 8 yellow balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 10 (c) 17 (d) 9
21. 21.A bag has 12 blue balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 19 (c) 8 (d) 2
22. 22.What is the 28th term of the AP 3, 10, 17, 24, …? (a) 192 (b) 189 (c) 196 (d) 199
23. 23.In a class of 31 children, 19 like tea, 12 like coffee and 4 like both. How many like only tea? (a) 19 (b) 8 (c) 4 (d) 15
24. 24.A bag has 4 red balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 6 (b) 2 (c) 5 (d) 11
25. 25.In a class of 54 children, 27 like mangoes, 28 like bananas and 8 like neither. How many like both? (a) 1 (b) 46 (c) 8 (d) 9
26. 26.A bag has 11 red balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 23 (b) 2 (c) 13 (d) 12
27. 27.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 639 (b) 630 (c) 640 (d) 498
28. 28.What is the smallest prime factor of 55? (a) 11 (b) 5 (c) 2 (d) 1
29. 29.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 10° (b) 160° (c) 30° (d) 170°
30. 30.What is the mode of 11, 3, 3, 17, 11, 3 and 5? (a) 11 (b) 5 (c) 17 (d) 3
31. 31.A bag has 10 blue balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 12 (b) 20 (c) 2 (d) 11
32. 32.What are the roots of x² − 16x + 63 = 0? (a) 1 and 15 (b) 1 and 63 (c) 3 and 21 (d) 7 and 9
33. 33.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
34. 34.What is the mode of 1, 19, 1, 19, 19, 12 and 8? (a) 8 (b) 12 (c) 19 (d) 1
35. 35.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 40° (c) 310° (d) 130°
36. 36.What is the missing term in the AP 15, ?, 29, 36, 43? (a) 29 (b) 23 (c) 21 (d) 22
37. 37.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
38. 38.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 350 (c) 418 (d) 417
39. 39.What is the median of 9, 26, 3, 13 and 29? (a) 3 (b) 16 (c) 26 (d) 13
40. 40.What is the 15th term of the AP 20, 28, 36, 44, …? (a) 112 (b) 120 (c) 140 (d) 132

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