Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 707 · 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 smallest prime factor of 209? (a) 1 (b) 2 (c) 11 (d) 19
2. 2.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
3. 3.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 100° (d) 50°
4. 4.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/3 (c) 1/4 (d) 1/2
5. 5.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 354 (c) 364 (d) 314
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 1/12 (c) 2/11 (d) 1/11
7. 7.What is the mean of 8, 7, 13 and 20? (a) 12 (b) 11 (c) 13 (d) 16
8. 8.The mean of 9 numbers is 25. When the number 65 is added to them, what is the new mean? (a) 29 (b) 25 (c) 30 (d) 45
9. 9.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 9 (c) 30 (d) 27
10. 10.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 16 (c) 48 (d) 144
11. 11.Using (a + b)² = a² + 2ab + b², what is 52²? (a) 2304 (b) 2704 (c) 2504 (d) 2714
12. 12.A drawer has lots of red 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) 3 (c) 5 (d) 4
13. 13.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
14. 14.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 912 (b) 456 (c) 492 (d) 71
15. 15.A bag has 7 blue, 6 white and 5 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 7/11 (b) 1/3 (c) 7/18 (d) 11/18
16. 16.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 155° (b) 120° (c) 85° (d) 60°
17. 17.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) 36 (b) 37 (c) 24 (d) 25
18. 18.How many factors does 49 have? (a) 1 (b) 2 (c) 4 (d) 3
19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 17 (b) 18 (c) 8 (d) 19
20. 20.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 75° (d) 30°
21. 21.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 1/4 (c) 3/8 (d) 5/8
22. 22.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 11 (d) 2
23. 23.A bag has 6 white balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 14 (c) 7 (d) 2
24. 24.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
25. 25.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
26. 26.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
27. 27.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
28. 28.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 117 (c) 39 (d) 42
29. 29.A cuboid is 7 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 376 sq cm (b) 168 sq cm (c) 94 sq cm (d) 188 sq cm
30. 30.Which term of the AP 19, 23, 27, 31, … is 175? (a) 41st (b) 40th (c) 42nd (d) 39th
31. 31.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 76° (b) 255° (c) 105° (d) 75°
32. 32.What is the distance between the points (6, 9) and (18, 18)? (a) 15 (b) 16 (c) 21 (d) 225
33. 33.There are 3 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) 6 (b) 5 (c) 9 (d) 12
34. 34.In which quadrant does the point (9, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
35. 35.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 140° (c) 120° (d) 80°
36. 36.What is the mean of 4, 6, 18, 9, 4 and 7? (a) 7 (b) 8 (c) 10 (d) 9
37. 37.What is the mode of 9, 9, 13, 1, 13, 13 and 2? (a) 1 (b) 9 (c) 2 (d) 13
38. 38.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
39. 39.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 50° (c) 140° (d) 40°
40. 40.A drawer has lots of red 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) 3 (b) 2 (c) 4 (d) 5

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