Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 590 · 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 sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 154 (d) 136
2. 2.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 66 (c) 76 (d) 75
3. 3.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 49 sq cm (c) 343 sq cm (d) 196 sq cm
4. 4.A bag has 6 yellow, 2 white and 2 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 4/5 (c) 1/5 (d) 9/10
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
6. 6.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
7. 7.How many factors does 50 have? (a) 6 (b) 7 (c) 4 (d) 5
8. 8.The mean of 8 numbers is 39. When the number 21 is added to them, what is the new mean? (a) 38 (b) 39 (c) 37 (d) 30
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 2/11 (d) 1/12
10. 10.What is the missing term in the AP 12, 16, 20, ?, 28? (a) 23 (b) 25 (c) 28 (d) 24
11. 11.What is the distance between the points (0, 15) and (8, 9)? (a) 100 (b) 10 (c) 14 (d) 11
12. 12.A drawer has lots of yellow 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) 2 (b) 4 (c) 5 (d) 3
13. 13.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
14. 14.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 20 (d) 10
15. 15.What is the median of 17, 31, 25, 23 and 24? (a) 26 (b) 24 (c) 23 (d) 25
16. 16.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
17. 17.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 80° (b) 160° (c) 260° (d) 100°
18. 18.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 120° (c) 60° (d) 30°
19. 19.In a class of 21 children, 5 like tea, 11 like coffee and 7 like neither. How many like both? (a) 3 (b) 7 (c) 2 (d) 14
20. 20.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 9 (d) 7
21. 21.In which quadrant does the point (−1, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
22. 22.In a class of 38 children, 17 like tea, 27 like coffee and 8 like both. How many like neither? (a) 10 (b) 8 (c) 3 (d) 2
23. 23.What is the mean of 18, 13, 12 and 5? (a) 16 (b) 12 (c) 13 (d) 11
24. 24.If a + b = 17 and ab = 60, what is (a − b)²? (a) 169 (b) 49 (c) 289 (d) 7
25. 25.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
26. 26.What is the distance between the points (2, 21) and (14, 5)? (a) 21 (b) 400 (c) 28 (d) 20
27. 27.What is the median of 31, 1, 17, 39 and 24? (a) 25 (b) 17 (c) 24 (d) 31
28. 28.The mean of 7 numbers is 16. When the number 40 is added to them, what is the new mean? (a) 20 (b) 16 (c) 19 (d) 28
29. 29.How many factors does 21 have? (a) 5 (b) 3 (c) 2 (d) 4
30. 30.A bag has 11 black balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 23 (c) 13 (d) 2
31. 31.In a class of 33 children, 10 like dance, 17 like music and 2 like both. How many like at least one of the two? (a) 33 (b) 23 (c) 27 (d) 25
32. 32.4 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) 16 (b) 12 (c) 6 (d) 8
33. 33.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/3 (c) 1/4 (d) 2/3
34. 34.A drawer has lots of green, black, yellow and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 2 (d) 8
35. 35.What is the mean of 14, 11, 5 and 14? (a) 11 (b) 13 (c) 12 (d) 10
36. 36.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
37. 37.A bag has 9 blue balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 10 (b) 11 (c) 2 (d) 15
38. 38.Using (a − b)² = a² − 2ab + b², what is 86²? (a) 8084 (b) 7406 (c) 8836 (d) 7396
39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 4 (d) 2
40. 40.What is the mean of 15, 10, 19, 4 and 12? (a) 15 (b) 12 (c) 10 (d) 13

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