Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 954 · 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 area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 1/6 (c) 5/11 (d) 5/36
3. 3.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
4. 4.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
5. 5.What is the median of 18, 15, 4, 20, 11, 8 and 6? (a) 15 (b) 8 (c) 11 (d) 20
6. 6.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 221 (b) 216 (c) 44 (d) 432
7. 7.In a class of 39 children, 14 like cricket, 18 like football and 2 like both. How many like neither? (a) 9 (b) 11 (c) 7 (d) 2
8. 8.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
9. 9.In which quadrant does the point (−7, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 4 (b) 7 (c) 5 (d) 6
11. 11.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 25° (c) 35° (d) 50°
12. 12.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 1596 (c) 1654 (d) 3306
13. 13.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 16 sq cm (c) 97 sq cm (d) 96 sq cm
14. 14.A bag has 9 yellow balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 19 (b) 10 (c) 11 (d) 2
15. 15.What is the mean of 3, 20, 20, 17 and 20? (a) 15 (b) 17 (c) 16 (d) 20
16. 16.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 8101 (b) 7921 (c) 8281 (d) 8291
17. 17.How many factors does 55 have? (a) 4 (b) 3 (c) 5 (d) 2
18. 18.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 55 (c) 110 (d) 121
19. 19.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4
20. 20.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 186 (c) 194 (d) 185
21. 21.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 28 (d) 21
22. 22.What is the mean of 17, 3, 2, 16 and 12? (a) 9 (b) 12 (c) 10 (d) 11
23. 23.What is the midpoint of the line joining (0, 1) and (6, 9)? (a) (3, 5) (b) (3, 4) (c) (5, 3) (d) (6, 10)
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 1/11 (c) 3/11 (d) 1/12
25. 25.A drawer has lots of red, green 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) 4 (b) 2 (c) 3 (d) 6
26. 26.The mean of 5 numbers is 23. When the number 17 is added to them, what is the new mean? (a) 21 (b) 20 (c) 22 (d) 23
27. 27.What is the mode of 16, 7, 1, 2, 16, 16 and 1? (a) 16 (b) 1 (c) 7 (d) 2
28. 28.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 190 (b) 27 (c) 180 (d) 360
29. 29.A drawer has lots of red, green, white 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) 2 (b) 4 (c) 8 (d) 5
30. 30.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
31. 31.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) 42 (b) 14 (c) 126 (d) 45
32. 32.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 262 (c) 286 (d) 285
33. 33.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 114 (b) 66 (c) 17 (d) 57
34. 34.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 110 (c) 121 (d) 55
35. 35.A drawer has lots of black 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) 3 (b) 5 (c) 2 (d) 4
36. 36.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 3/5 (c) 5/8 (d) 1/4
37. 37.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
38. 38.A bag has 6 yellow balls and 8 blue 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) 9 (c) 14 (d) 2
39. 39.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 132 (d) 144
40. 40.The mean of 5 numbers is 17. When the number 29 is added to them, what is the new mean? (a) 20 (b) 19 (c) 17 (d) 23

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