Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 201 · 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 49 children, 27 like cricket, 27 like football and 2 like neither. How many like both? (a) 7 (b) 47 (c) 2 (d) 5
2. 2.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
4. 4.A drawer has lots of red, black, white 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) 5 (b) 2 (c) 8 (d) 4
5. 5.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
6. 6.A cuboid is 9 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 256 cu cm (b) 18 cu cm (c) 21 cu cm (d) 180 cu cm
7. 7.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/8 (c) 1/4 (d) 7/8
8. 8.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 352 (c) 420 (d) 421
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 5/11 (c) 1/11 (d) 5/36
10. 10.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 46° (c) 55° (d) 45°
11. 11.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 105° (b) 75° (c) 115° (d) 140°
12. 12.A drawer has lots of black 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) 5 (b) 3 (c) 2 (d) 4
13. 13.In which quadrant does the point (−5, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
14. 14.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 5/8 (c) 3/5 (d) 1/4
15. 15.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) 24 (b) 12 (c) 25 (d) 13
16. 16.A drawer has lots of red, blue and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 4 (c) 3 (d) 2
17. 17.In a class of 38 children, 15 like cricket, 24 like football and 7 like both. How many like only cricket? (a) 8 (b) 15 (c) 14 (d) 17
18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
19. 19.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 45 (d) 55
20. 20.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 100° (d) 125°
21. 21.A drawer has lots of white, red, black, green 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) 6 (b) 10 (c) 5 (d) 2
22. 22.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
23. 23.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 244 (c) 259 (d) 258
24. 24.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 54 (c) 72 (d) 63
25. 25.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
26. 26.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 7/8 (c) 1/8 (d) 3/8
27. 27.What is the 36th term of the AP 5, 12, 19, 26, …? (a) 257 (b) 245 (c) 252 (d) 250
28. 28.A bag has 8 blue, 4 red and 7 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 11/19 (c) 8/19 (d) 12/19
29. 29.In a class of 29 children, 14 like tea, 11 like coffee and 7 like neither. How many like both? (a) 7 (b) 22 (c) 3 (d) 4
30. 30.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
31. 31.In which quadrant does the point (−3, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
32. 32.A bag has 4 blue balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 4 (c) 2 (d) 5
33. 33.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
34. 34.What is the median of 2, 8, 15, 30, 14, 12 and 13? (a) 30 (b) 14 (c) 13 (d) 12
35. 35.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 250° (b) 140° (c) 70° (d) 110°
36. 36.A bag has 6 green, 3 blue and 2 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 3/8 (c) 3/11 (d) 8/11
37. 37.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 25° (d) 65°
38. 38.In which quadrant does the point (5, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
39. 39.The mean of 5 numbers is 19. When the number 7 is added to them, what is the new mean? (a) 13 (b) 18 (c) 19 (d) 17
40. 40.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 10 (b) 9 (c) 19 (d) 11

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