Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 644 · 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 35? (a) 1 (b) 5 (c) 7 (d) 2
2. 2.A drawer has lots of green, yellow, black, blue 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) 5 (b) 6 (c) 2 (d) 10
3. 3.What is the median of 37, 18, 4, 33, 17, 38 and 9? (a) 18 (b) 19 (c) 33 (d) 17
4. 4.What is the distance between the points (5, 0) and (17, 9)? (a) 225 (b) 21 (c) 16 (d) 15
5. 5.There are 7 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) 9 (b) 28 (c) 14 (d) 21
6. 6.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 35° (c) 215° (d) 145°
7. 7.What is the product of the roots of x² − 7x + 12 = 0? (a) 13 (b) 7 (c) 11 (d) 12
8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 6 (d) 16
9. 9.A drawer has lots of white 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) 5 (b) 2 (c) 4 (d) 3
10. 10.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 130° (c) 40° (d) 50°
11. 11.How many prime numbers are there between 80 and 110? (a) 7 (b) 6 (c) 9 (d) 8
12. 12.A drawer has lots of green and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 3 (d) 2
13. 13.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 60° (c) 120° (d) 70°
14. 14.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 121 (d) 55
15. 15.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 50° (c) 26° (d) 25°
16. 16.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
17. 17.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 120 (c) 105 (d) 240
18. 18.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1235 (b) 1225 (c) 2025 (d) 1575
19. 19.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 35° (b) 105° (c) 110° (d) 145°
20. 20.There are 6 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 84 (c) 13 (d) 42
21. 21.Using (a + b)² = a² + 2ab + b², what is 21²? (a) 401 (b) 451 (c) 441 (d) 361
22. 22.A bag has 6 red balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 9 (c) 2 (d) 14
23. 23.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 29 (c) 22 (d) 28
24. 24.How many prime numbers are there between 80 and 90? (a) 1 (b) 4 (c) 2 (d) 3
25. 25.What is the smallest prime factor of 133? (a) 19 (b) 7 (c) 2 (d) 1
26. 26.A drawer has lots of black 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) 5 (b) 2 (c) 4 (d) 3
27. 27.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 120° (b) 95° (c) 145° (d) 85°
28. 28.The mean of 8 numbers is 29. When the number 38 is added to them, what is the new mean? (a) 31 (b) 29 (c) 30 (d) 32
29. 29.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
30. 30.If a + b = 15 and ab = 44, what is (a − b)²? (a) 49 (b) 225 (c) 7 (d) 137
31. 31.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
32. 32.A bag has 5 yellow balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 7 (c) 6 (d) 16
33. 33.A cuboid is 5 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 40 sq cm (b) 38 sq cm (c) 76 sq cm (d) 152 sq cm
34. 34.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 45 (c) 100 (d) 90
35. 35.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 320° (c) 160° (d) 140°
36. 36.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
37. 37.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 40° (d) 110°
38. 38.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) 22 (b) 14 (c) 15 (d) 21
39. 39.Using (a − b)² = a² − 2ab + b², what is 96²? (a) 9216 (b) 9226 (c) 9984 (d) 10816
40. 40.What is the midpoint of the line joining (10, 15) and (20, 9)? (a) (12, 15) (b) (30, 24) (c) (15, 12) (d) (5, 3)

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