Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 437 · 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.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 2 (d) 3
2. 2.Using (a − b)² = a² − 2ab + b², what is 65²? (a) 4225 (b) 5625 (c) 4875 (d) 4235
3. 3.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
4. 4.There are 5 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 40 (c) 25 (d) 9
5. 5.Two angles of a triangle are 20° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 160° (c) 55° (d) 125°
6. 6.A drawer has lots of white, green, red, 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) 5 (c) 2 (d) 6
7. 7.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 24 (c) 37 (d) 36
8. 8.How many factors does 118 have? (a) 2 (b) 4 (c) 5 (d) 3
9. 9.Using (a − b)² = a² − 2ab + b², what is 39²? (a) 1521 (b) 1681 (c) 1531 (d) 1599
10. 10.The mean of 5 numbers is 33. When the number 21 is added to them, what is the new mean? (a) 32 (b) 27 (c) 31 (d) 33
11. 11.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2³ × 3 × 5
12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
13. 13.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 75° (b) 35° (c) 140° (d) 145°
14. 14.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) 39 (b) 36 (c) 12 (d) 108
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/9 (c) 5/36 (d) 1/11
16. 16.Using (a + b)² = a² + 2ab + b², what is 101²? (a) 10211 (b) 9801 (c) 10001 (d) 10201
17. 17.How many factors does 83 have? (a) 2 (b) 3 (c) 4 (d) 1
18. 18.In a class of 36 children, 14 like maths, 21 like science and 8 like both. How many like at least one of the two? (a) 27 (b) 19 (c) 36 (d) 35
19. 19.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 16 (c) 12 (d) 48
20. 20.What is the mode of 11, 5, 5, 5, 13, 17 and 13? (a) 17 (b) 13 (c) 11 (d) 5
21. 21.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 20° (b) 160° (c) 130° (d) 70°
22. 22.A bag has 10 red balls and 12 blue 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) 13 (c) 11 (d) 22
23. 23.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
24. 24.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 55° (c) 46° (d) 90°
25. 25.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
26. 26.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 81 (c) 18 (d) 72
27. 27.What is the smallest prime factor of 95? (a) 2 (b) 1 (c) 5 (d) 19
28. 28.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 215° (c) 145° (d) 36°
29. 29.A bag has 7 blue balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 7 (d) 8
30. 30.What is the mode of 15, 19, 17, 1, 1, 15 and 1? (a) 15 (b) 17 (c) 1 (d) 19
31. 31.A bag has 4 black balls and 7 red 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) 11 (c) 8 (d) 5
32. 32.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
34. 34.What is the mean of 16, 6, 13, 14, 14 and 21? (a) 13 (b) 14 (c) 15 (d) 12
35. 35.What is the mean of 15, 13, 3, 7 and 7? (a) 10 (b) 11 (c) 9 (d) 8
36. 36.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
37. 37.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 595 (c) 585 (d) 468
38. 38.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 1/5 (c) 5/6 (d) 1/3
39. 39.What is the mean of 13, 12, 14, 9 and 22? (a) 15 (b) 16 (c) 14 (d) 13
40. 40.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 559 (b) 558 (c) 549 (d) 444

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