Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 367 · 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.Two angles of a triangle are 25° and 45°. What is the exterior angle at the third corner? (a) 155° (b) 110° (c) 135° (d) 70°
2. 2.What is the midpoint of the line joining (10, 17) and (14, 9)? (a) (24, 26) (b) (12, 13) (c) (2, 4) (d) (13, 12)
3. 3.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 45 (b) 90 (c) 15 (d) 48
4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 3 (d) 1
5. 5.How many factors does 79 have? (a) 1 (b) 3 (c) 4 (d) 2
6. 6.What is the 16th term of the AP 5, 13, 21, 29, …? (a) 128 (b) 120 (c) 125 (d) 133
7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 53 (d) 729
8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
9. 9.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 110° (d) 50°
10. 10.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x + 1)(x + 14) (c) (x − 7)(x − 8) (d) (x + 7)(x + 8)
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 1/12 (c) 3/11 (d) 1/9
12. 12.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 165° (b) 135° (c) 15° (d) 60°
13. 13.Which is the correct factorisation of x² + 7x + 12? (a) (x + 1)(x + 12) (b) (x + 1)(x + 6) (c) (x − 3)(x − 4) (d) (x + 3)(x + 4)
14. 14.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
15. 15.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 275° (d) 5°
16. 16.In a class of 20 children, 11 like tea, 9 like coffee and 4 like both. How many like only tea? (a) 11 (b) 5 (c) 4 (d) 7
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 day of the week? (a) 15 (b) 21 (c) 22 (d) 14
18. 18.What is the distance between the points (0, 13) and (5, 1)? (a) 17 (b) 169 (c) 14 (d) 13
19. 19.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°
20. 20.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 64 (c) 56 (d) 16
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/18 (c) 1/11 (d) 1/12
22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 16 (d) 5
23. 23.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 95° (c) 155° (d) 85°
24. 24.In a class of 26 children, 10 like cricket, 13 like football and 3 like both. How many like neither? (a) 6 (b) 3 (c) 7 (d) 9
25. 25.If a + b = 14 and ab = 24, what is (a − b)²? (a) 148 (b) 100 (c) 196 (d) 10
26. 26.A bag has 7 black balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 16 (c) 8 (d) 9
27. 27.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 42 (d) 49
28. 28.A bag has 3 red balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 11 (d) 4
29. 29.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 286 (b) 144 (c) 143 (d) 18
30. 30.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
31. 31.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 49 (b) 13 (c) 84 (d) 42
32. 32.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 240 (d) 25
33. 33.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
34. 34.What is the mode of 4, 7, 4, 19, 8, 7 and 7? (a) 8 (b) 4 (c) 7 (d) 19
35. 35.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 66° (c) 65° (d) 130°
36. 36.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 92 (c) 182 (d) 78
37. 37.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) 12 (b) 25 (c) 24 (d) 13
38. 38.In a class of 35 children, 12 like tea, 27 like coffee and 7 like both. How many like only tea? (a) 20 (b) 12 (c) 5 (d) 8
39. 39.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 1)(x + 16) (c) (x − 8)(x − 9) (d) (x + 8)(x + 9)
40. 40.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 40° (c) 70° (d) 110°

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