Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 701 · 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 26 children, 8 like mangoes, 19 like bananas and 4 like neither. How many like both? (a) 4 (b) 5 (c) 1 (d) 22
2. 2.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
3. 3.The mean of 3 numbers is 10. When the number 2 is added to them, what is the new mean? (a) 10 (b) 9 (c) 6 (d) 8
4. 4.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 9 (c) 20 (d) 24
5. 5.A drawer has lots of blue 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) 2 (b) 3 (c) 4 (d) 5
6. 6.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 314 (b) 354 (c) 363 (d) 364
7. 7.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
8. 8.In a class of 29 children, 15 like dance, 14 like music and 10 like both. How many like neither? (a) 20 (b) 0 (c) 11 (d) 10
9. 9.How many factors does 51 have? (a) 2 (b) 5 (c) 3 (d) 4
10. 10.What is the distance between the points (9, 0) and (24, 8)? (a) 289 (b) 18 (c) 23 (d) 17
11. 11.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
12. 12.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 15 (b) 17 (c) 16 (d) 20
13. 13.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 84 (b) 17 (c) 77 (d) 154
14. 14.How many prime numbers are there between 80 and 100? (a) 2 (b) 3 (c) 5 (d) 4
15. 15.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 28 (c) 42 (d) 21
16. 16.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/18 (c) 2/11 (d) 1/12
18. 18.A cuboid is 10 cm long, 6 cm wide and 9 cm high. What is its total surface area? (a) 540 sq cm (b) 816 sq cm (c) 204 sq cm (d) 408 sq cm
19. 19.What is the mean of 6, 12, 17 and 17? (a) 14 (b) 15 (c) 12 (d) 13
20. 20.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 219 (c) 210 (d) 220
21. 21.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 39 (c) 12 (d) 36
22. 22.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/2 (c) 1/4 (d) 1/3
23. 23.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
24. 24.What is the mean of 8, 19, 6 and 7? (a) 11 (b) 9 (c) 8 (d) 10
25. 25.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 140° (d) 115°
26. 26.The mean of 6 numbers is 35. When the number 28 is added to them, what is the new mean? (a) 33 (b) 35 (c) 36 (d) 34
27. 27.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 210 (c) 120 (d) 225
28. 28.In which quadrant does the point (−7, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
29. 29.A bag has 9 yellow balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 11 (c) 2 (d) 16
30. 30.A bag has 4 black balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 5 (b) 14 (c) 2 (d) 6
31. 31.A bag has 4 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 6 (b) 5 (c) 9 (d) 2
32. 32.What is the mean of 6, 13, 8 and 17? (a) 10 (b) 12 (c) 13 (d) 11
33. 33.What is the distance between the points (0, 23) and (8, 8)? (a) 289 (b) 17 (c) 23 (d) 18
34. 34.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 523 (c) 522 (d) 420
35. 35.A drawer has lots of red, 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) 4 (b) 2 (c) 8 (d) 5
36. 36.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
37. 37.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 36° (c) 145° (d) 35°
38. 38.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 1/4 (c) 3/8 (d) 1/8
39. 39.If a + b = 10 and ab = 9, what is (a − b)²? (a) 82 (b) 64 (c) 100 (d) 8
40. 40.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm

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