Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 74 · 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 bag has 4 blue balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 9 (c) 5 (d) 6
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 4/11 (c) 5/36 (d) 1/9
3. 3.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 14 (c) 22 (d) 15
4. 4.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 28 (c) 64 (d) 56
5. 5.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
6. 6.In a class of 38 children, 23 like dance, 14 like music and 9 like neither. How many like both? (a) 29 (b) 9 (c) 7 (d) 8
7. 7.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
8. 8.What is the midpoint of the line joining (4, 14) and (8, 4)? (a) (6, 9) (b) (9, 6) (c) (12, 18) (d) (2, 5)
9. 9.Using (a − b)² = a² − 2ab + b², what is 66²? (a) 5476 (b) 4366 (c) 4356 (d) 4884
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/18 (c) 1/12 (d) 2/11
11. 11.What is the 18th term of the AP 12, 17, 22, 27, …? (a) 85 (b) 90 (c) 97 (d) 102
12. 12.What is the mean of 2, 10, 3 and 5? (a) 4 (b) 7 (c) 5 (d) 6
13. 13.The numbers 14 to 22 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) 57 (c) 162 (d) 18
14. 14.What is the mean of 8, 4, 7 and 21? (a) 8 (b) 10 (c) 9 (d) 11
15. 15.What is the median of 35, 13, 8, 30, 31, 17 and 39? (a) 31 (b) 17 (c) 29 (d) 30
16. 16.What are the roots of x² − 16x + 63 = 0? (a) 3 and 21 (b) 7 and 9 (c) 1 and 63 (d) 1 and 15
17. 17.What is the product of the roots of x² − 11x + 28 = 0? (a) 11 (b) 29 (c) 28 (d) 27
18. 18.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 144 (d) 66
19. 19.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 676 (b) 686 (c) 1156 (d) 884
20. 20.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 256 cu cm (d) 512 cu cm
21. 21.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
22. 22.In a class of 29 children, 24 like maths, 16 like science and 12 like both. How many like only maths? (a) 24 (b) 4 (c) 12 (d) 13
23. 23.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
24. 24.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
25. 25.What is the 17th term of the AP 20, 28, 36, 44, …? (a) 128 (b) 136 (c) 156 (d) 148
26. 26.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 64 cu cm (d) 96 cu cm
27. 27.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 120 (d) 240
28. 28.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 120° (c) 30° (d) 150°
29. 29.What is the sum of all the whole numbers from 1 to 28? (a) 406 (b) 378 (c) 392 (d) 812
30. 30.A drawer has lots of blue, red, black, yellow and green 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) 6 (c) 5 (d) 10
31. 31.A cuboid is 12 cm long, 9 cm wide and 8 cm high. What is its volume? (a) 864 cu cm (b) 29 cu cm (c) 108 cu cm (d) 552 cu cm
32. 32.What is the mean of 6, 4, 16 and 10? (a) 10 (b) 9 (c) 12 (d) 8
33. 33.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
34. 34.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 603 (c) 474 (d) 604
35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 8 (b) 6 (c) 7 (d) 5
36. 36.In a class of 41 children, 14 like maths, 22 like science and 3 like both. How many like only maths? (a) 11 (b) 3 (c) 14 (d) 19
37. 37.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 64 sq cm (d) 97 sq cm
38. 38.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
39. 39.What is the median of 12, 8, 31, 40, 15, 7 and 33? (a) 15 (b) 12 (c) 40 (d) 31
40. 40.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 144 (d) 153

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