Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 670 · 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 team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 90 (d) 45
2. 2.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 61° (d) 30°
3. 3.What is the midpoint of the line joining (8, 8) and (18, 14)? (a) (11, 13) (b) (5, 3) (c) (26, 22) (d) (13, 11)
4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
5. 5.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/4 (c) 1/7 (d) 1/8
6. 6.A bag has 3 red, 9 green and 3 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 2/5 (c) 2/3 (d) 3/5
7. 7.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 155° (d) 135°
8. 8.What is the 34th term of the AP 17, 23, 29, 35, …? (a) 221 (b) 198 (c) 204 (d) 215
9. 9.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 21 (c) 30 (d) 36
10. 10.A bag has 10 blue balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 22 (b) 2 (c) 11 (d) 12
11. 11.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 126 (c) 144 (d) 135
12. 12.What is the median of 14, 1, 4, 35 and 18? (a) 15 (b) 18 (c) 14 (d) 4
13. 13.In a class of 29 children, 21 like maths, 9 like science and 4 like both. How many like neither? (a) 2 (b) 4 (c) 7 (d) 3
14. 14.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 50° (d) 40°
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 3/11 (c) 1/12 (d) 1/9
16. 16.A drawer has lots of red, green, 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) 2 (b) 4 (c) 8 (d) 5
17. 17.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) 36 (b) 39 (c) 108 (d) 12
18. 18.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
19. 19.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 6) (b) (x + 1)(x + 10) (c) (x − 2)(x − 5) (d) (x + 2)(x + 5)
20. 20.In which quadrant does the point (4, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
21. 21.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 55 (d) 121
22. 22.If a + b = 15 and ab = 56, what is (a − b)²? (a) 225 (b) 1 (c) 169 (d) 113
23. 23.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 1331 sq cm (c) 484 sq cm (d) 121 sq cm
24. 24.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/3 (b) 2/3 (c) 1/4 (d) 5/6
25. 25.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 16 sq cm (c) 4 sq cm (d) 8 sq cm
26. 26.How many factors does 99 have? (a) 4 (b) 6 (c) 7 (d) 5
27. 27.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
28. 28.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
29. 29.A bag has 5 yellow, 4 red and 6 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 2/3 (b) 2/5 (c) 3/5 (d) 1/3
30. 30.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 8 (c) 14 (d) 15
31. 31.If a + b = 9 and ab = 8, what is a² + b²? (a) 65 (b) 81 (c) 97 (d) 73
32. 32.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
33. 33.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 135° (b) 115° (c) 110° (d) 45°
34. 34.What is the distance between the points (2, 10) and (14, 1)? (a) 16 (b) 225 (c) 15 (d) 21
35. 35.Which term of the AP 13, 18, 23, 28, … is 163? (a) 32nd (b) 33rd (c) 30th (d) 31st
36. 36.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 115° (d) 155°
37. 37.A bag has 5 red balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 14 (c) 2 (d) 6
38. 38.A bag has 12 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 13 (c) 18 (d) 14
39. 39.What is the distance between the points (8, 0) and (20, 9)? (a) 225 (b) 16 (c) 21 (d) 15
40. 40.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 41° (d) 220°

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