Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 663 · 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 fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
2. 2.What is the smallest prime factor of 85? (a) 17 (b) 2 (c) 1 (d) 5
3. 3.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 144 sq cm (c) 36 sq cm (d) 217 sq cm
4. 4.What is the smallest prime factor of 51? (a) 3 (b) 2 (c) 1 (d) 17
5. 5.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 63 (c) 66 (d) 21
6. 6.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 111 (b) 222 (c) 31 (d) 126
7. 7.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 132 (c) 144 (d) 66
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 1/11 (c) 1/9 (d) 3/11
9. 9.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
10. 10.What is the product of the roots of x² − 13x + 42 = 0? (a) 43 (b) 41 (c) 13 (d) 42
11. 11.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 354 (c) 314 (d) 363
12. 12.There are 8 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 32 (c) 10 (d) 16
13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 20 (d) 18
15. 15.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 1653 (c) 3422 (d) 1711
16. 16.In a class of 27 children, 14 like dance, 7 like music and 3 like both. How many like at least one of the two? (a) 18 (b) 27 (c) 21 (d) 15
17. 17.A drawer has lots of red, white, blue, black 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) 10 (b) 2 (c) 5 (d) 6
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
19. 19.In a class of 20 children, 13 like dance, 14 like music and 8 like both. How many like at least one of the two? (a) 27 (b) 20 (c) 19 (d) 11
20. 20.What is the distance between the points (0, 10) and (12, 5)? (a) 17 (b) 14 (c) 169 (d) 13
21. 21.A bag has 5 white balls and 4 green 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) 5 (c) 9 (d) 6
22. 22.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
23. 23.If a + b = 20 and ab = 99, what is a² + b²? (a) 202 (b) 301 (c) 598 (d) 400
24. 24.How many factors does 92 have? (a) 6 (b) 7 (c) 5 (d) 4
25. 25.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 61 (c) 70 (d) 62
26. 26.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 120° (c) 150° (d) 30°
27. 27.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 20° (d) 160°
28. 28.What is the median of 19, 31, 26, 23 and 29? (a) 23 (b) 26 (c) 29 (d) 27
29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 6 (b) 5 (c) 7 (d) 4
30. 30.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2³ × 7 (c) 2⁴ × 7 (d) 2² × 7
31. 31.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/3 (d) 1/4
32. 32.A bag has 6 white balls and 8 green 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) 7 (c) 14 (d) 9
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
34. 34.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 5256 (c) 2556 (d) 2628
35. 35.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 342 (c) 405 (d) 396
36. 36.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 20 (b) 21 (c) 19 (d) 23
37. 37.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
38. 38.The mean of 7 numbers is 20. When the number 12 is added to them, what is the new mean? (a) 18 (b) 20 (c) 19 (d) 16
39. 39.What are the roots of x² − 13x + 42 = 0? (a) 1 and 42 (b) 2 and 21 (c) 6 and 7 (d) 1 and 12
40. 40.What is the 15th term of the AP 6, 9, 12, 15, …? (a) 48 (b) 51 (c) 45 (d) 42

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