Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 53 · 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.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 36 (c) 18 (d) 24
2. 2.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
3. 3.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
4. 4.What is the smallest prime factor of 253? (a) 2 (b) 23 (c) 11 (d) 1
5. 5.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 51 (c) 17 (d) 153
6. 6.If a + b = 14 and ab = 40, what is a² + b²? (a) 196 (b) 116 (c) 276 (d) 156
7. 7.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 36 (c) 28 (d) 64
8. 8.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 80° (c) 100° (d) 20°
9. 9.What is the 34th term of the AP 1, 9, 17, 25, …? (a) 265 (b) 264 (c) 272 (d) 273
10. 10.What is the 39th term of the AP 18, 23, 28, 33, …? (a) 190 (b) 213 (c) 208 (d) 195
11. 11.In which quadrant does the point (3, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
12. 12.What is the mean of 5, 18, 2 and 7? (a) 7 (b) 9 (c) 10 (d) 8
13. 13.The mean of 7 numbers is 39. When the number 71 is added to them, what is the new mean? (a) 43 (b) 44 (c) 39 (d) 55
14. 14.What is the mode of 5, 4, 6, 5, 11, 4 and 5? (a) 4 (b) 11 (c) 6 (d) 5
15. 15.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 418 (c) 510 (d) 520
16. 16.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 21 (d) 49
17. 17.What is the mean of 6, 10, 9 and 3? (a) 9 (b) 7 (c) 6 (d) 8
18. 18.What is the distance between the points (2, 11) and (5, 7)? (a) 25 (b) 6 (c) 7 (d) 5
19. 19.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
20. 20.What is the distance between the points (9, 6) and (12, 2)? (a) 6 (b) 25 (c) 5 (d) 7
21. 21.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
22. 22.5 T-shirts and 5 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) 30 (c) 50 (d) 25
23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 6 (b) 17 (c) 18 (d) 16
24. 24.A drawer has lots of yellow, black, white, 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) 10 (c) 6 (d) 5
25. 25.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 36 (d) 18
26. 26.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 10 (c) 25 (d) 11
27. 27.In a class of 37 children, 28 like maths, 13 like science and 9 like both. How many like only maths? (a) 24 (b) 28 (c) 4 (d) 19
28. 28.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 562 (c) 561 (d) 446
29. 29.What is the mean of 12, 18, 3, 8, 14 and 17? (a) 13 (b) 11 (c) 12 (d) 14
30. 30.What is the mode of 15, 4, 1, 20, 4, 1 and 4? (a) 20 (b) 15 (c) 1 (d) 4
31. 31.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 42 (c) 14 (d) 49
32. 32.A bag has 6 green balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 7 (b) 2 (c) 18 (d) 8
33. 33.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 534 (c) 543 (d) 434
34. 34.A bag has 6 yellow, 5 red and 5 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 11/16 (b) 5/11 (c) 5/16 (d) 1/3
35. 35.What is the mean of 19, 20, 13 and 16? (a) 19 (b) 17 (c) 16 (d) 18
36. 36.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 126 (c) 42 (d) 45
37. 37.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
39. 39.Which term of the AP 20, 25, 30, 35, … is 190? (a) 35th (b) 38th (c) 34th (d) 36th
40. 40.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 204 (c) 195 (d) 208

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