Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 447 · 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 2, 9, 3, 14, 9 and 5? (a) 6 (b) 7 (c) 8 (d) 9
2. 2.What is the mean of 20, 9, 14, 5 and 22? (a) 13 (b) 14 (c) 15 (d) 16
3. 3.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/4 (d) 1/3
4. 4.In a class of 37 children, 12 like cricket, 21 like football and 2 like both. How many like at least one of the two? (a) 31 (b) 29 (c) 33 (d) 37
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 1/9 (c) 1/12 (d) 3/11
6. 6.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 6 (d) 3
7. 7.What is the mean of 14, 13, 13 and 4? (a) 13 (b) 11 (c) 10 (d) 12
8. 8.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
9. 9.A bag has 4 green, 5 blue and 5 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 2/5 (b) 5/7 (c) 1/3 (d) 2/7
10. 10.In a class of 34 children, 17 like tea, 18 like coffee and 10 like both. How many like neither? (a) 19 (b) 8 (c) 9 (d) 10
11. 11.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 92 (c) 78 (d) 182
12. 12.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 2/3 (d) 1/2
13. 13.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 110° (c) 35° (d) 290°
14. 14.In which quadrant does the point (−7, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
15. 15.Which term of the AP 3, 11, 19, 27, … is 107? (a) 15th (b) 13th (c) 16th (d) 14th
16. 16.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 85° (b) 95° (c) 145° (d) 130°
17. 17.What is the distance between the points (8, 5) and (17, 17)? (a) 16 (b) 21 (c) 15 (d) 225
18. 18.In a class of 36 children, 29 like cricket, 15 like football and 9 like both. How many like neither? (a) 2 (b) 10 (c) 1 (d) 9
19. 19.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 120° (b) 115° (c) 125° (d) 60°
20. 20.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/4 (c) 7/8 (d) 1/8
21. 21.A bag has 3 yellow balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 4 (d) 10
22. 22.A bag has 8 white, 7 yellow and 9 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 7/24 (b) 1/3 (c) 7/17 (d) 17/24
23. 23.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 25 (c) 10 (d) 21
24. 24.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 32) (b) (x + 1)(x + 11) (c) (x + 4)(x + 8) (d) (x − 4)(x − 8)
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 1/6 (c) 5/11 (d) 5/36
26. 26.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 30° (b) 100° (c) 110° (d) 150°
27. 27.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
28. 28.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 85° (d) 5°
29. 29.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 144 (d) 66
30. 30.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 75° (d) 115°
31. 31.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/6 (c) 1/3 (d) 1/5
32. 32.In a class of 34 children, 16 like dance, 18 like music and 5 like both. How many like at least one of the two? (a) 24 (b) 29 (c) 30 (d) 34
33. 33.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 42 (d) 21
34. 34.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 105° (d) 110°
35. 35.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 12 (d) 13
36. 36.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 75° (b) 160° (c) 125° (d) 105°
37. 37.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 60° (d) 120°
38. 38.A bag has 9 blue, 2 red and 7 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 11/18 (b) 1/3 (c) 7/11 (d) 7/18
39. 39.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
40. 40.What is the midpoint of the line joining (1, 5) and (7, 3)? (a) (3, 1) (b) (8, 8) (c) (4, 4) (d) (5, 4)

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