Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 633 · 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 mean of 14, 4, 15, 19, 4 and 16? (a) 14 (b) 12 (c) 11 (d) 13
2. 2.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 132 (d) 24
3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 4 (b) 5 (c) 2 (d) 3
4. 4.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 33 (b) 201 (c) 198 (d) 396
5. 5.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 28 (c) 64 (d) 56
6. 6.A bag has 4 green 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
7. 7.In a class of 32 children, 15 like maths, 22 like science and 10 like both. How many like at least one of the two? (a) 27 (b) 37 (c) 17 (d) 32
8. 8.What is the midpoint of the line joining (7, 0) and (15, 12)? (a) (4, 6) (b) (6, 11) (c) (11, 6) (d) (22, 12)
9. 9.What is the distance between the points (4, 7) and (8, 4)? (a) 5 (b) 7 (c) 25 (d) 6
10. 10.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 136 (c) 154 (d) 145
11. 11.A drawer has lots of red, blue, green, yellow and black 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) 5 (d) 6
12. 12.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 55 (d) 121
13. 13.In which quadrant does the point (−6, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 2 (d) 4
15. 15.What is the product of the roots of x² − 11x + 30 = 0? (a) 11 (b) 31 (c) 30 (d) 29
16. 16.What is the 17th term of the AP 17, 23, 29, 35, …? (a) 96 (b) 113 (c) 102 (d) 119
17. 17.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 36 (c) 37 (d) 48
18. 18.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 13 (d) 7
19. 19.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 48 sq cm (b) 176 sq cm (c) 88 sq cm (d) 44 sq cm
20. 20.In a class of 19 children, 7 like maths, 6 like science and 3 like both. How many like neither? (a) 3 (b) 12 (c) 6 (d) 9
21. 21.There are 6 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 36 (b) 12 (c) 42 (d) 72
22. 22.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) 15 (c) 22 (d) 14
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/6 (c) 1/11 (d) 5/11
24. 24.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 21 sq cm (b) 18 sq cm (c) 84 sq cm (d) 42 sq cm
25. 25.A bag has 6 blue balls and 5 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) 6 (c) 11 (d) 7
26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 8 (b) 7 (c) 5 (d) 4
27. 27.What is the 38th term of the AP 3, 8, 13, 18, …? (a) 185 (b) 193 (c) 190 (d) 188
28. 28.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 90 sq cm (b) 50 sq cm (c) 45 sq cm (d) 180 sq cm
29. 29.If a + b = 20 and ab = 99, what is (a − b)²? (a) 202 (b) 4 (c) 400 (d) 2
30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 3 (d) 1
31. 31.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 20 (c) 30 (d) 15
32. 32.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 12 (c) 70 (d) 42
33. 33.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 173 (c) 182 (d) 174
34. 34.The mean of 6 numbers is 16. When the number 9 is added to them, what is the new mean? (a) 14 (b) 17 (c) 15 (d) 16
35. 35.How many factors does 57 have? (a) 2 (b) 4 (c) 3 (d) 5
36. 36.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 135° (c) 100° (d) 125°
37. 37.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x + 1)(x + 72)
38. 38.Which is the correct factorisation of x² + 11x + 24? (a) (x + 3)(x + 8) (b) (x + 1)(x + 24) (c) (x + 1)(x + 10) (d) (x − 3)(x − 8)
39. 39.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 150° (b) 255° (c) 105° (d) 75°
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11

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