Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 51 · 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.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 55 (d) 100
2. 2.A bag has 4 blue, 7 green and 2 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 7/13 (b) 1/3 (c) 8/13 (d) 6/13
3. 3.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 2/3 (b) 1/3 (c) 1/4 (d) 5/6
4. 4.How many factors does 87 have? (a) 5 (b) 4 (c) 3 (d) 2
5. 5.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
6. 6.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 65° (d) 115°
7. 7.The mean of 8 numbers is 37. When the number 73 is added to them, what is the new mean? (a) 55 (b) 37 (c) 41 (d) 42
8. 8.In a class of 34 children, 18 like maths, 10 like science and 9 like neither. How many like both? (a) 3 (b) 25 (c) 4 (d) 9
9. 9.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 9) (b) (x − 2)(x − 8) (c) (x + 1)(x + 16) (d) (x + 2)(x + 8)
10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 17 (b) 8 (c) 18 (d) 19
11. 11.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
12. 12.What is the sum of the roots of x² − 14x + 48 = 0? (a) 48 (b) 14 (c) 13 (d) 15
13. 13.A bag has 9 green, 5 white and 8 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 9/13 (c) 9/22 (d) 13/22
14. 14.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
15. 15.What is the sum of the roots of x² − 9x + 14 = 0? (a) 8 (b) 9 (c) 10 (d) 14
16. 16.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 25 (b) 182 (c) 91 (d) 105
17. 17.If a + b = 10 and ab = 24, what is (a − b)²? (a) 2 (b) 4 (c) 100 (d) 52
18. 18.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
19. 19.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
20. 20.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 1/6 (c) 1/5 (d) 5/6
21. 21.How many factors does 110 have? (a) 6 (b) 9 (c) 7 (d) 8
22. 22.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 12 (d) 30
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 3/11 (c) 1/11 (d) 1/12
24. 24.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 36 (d) 81
25. 25.What is the median of 21, 9, 35, 29 and 19? (a) 29 (b) 35 (c) 21 (d) 19
26. 26.6 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) 42 (b) 12 (c) 72 (d) 36
27. 27.In a class of 33 children, 21 like maths, 13 like science and 3 like both. How many like neither? (a) 2 (b) 5 (c) 1 (d) 3
28. 28.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
29. 29.What is the distance between the points (8, 20) and (13, 8)? (a) 13 (b) 169 (c) 17 (d) 14
30. 30.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 11° (c) 190° (d) 170°
31. 31.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 30° (c) 120° (d) 60°
32. 32.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/2 (c) 1/4 (d) 1/3
33. 33.If a + b = 20 and ab = 99, what is a² + b²? (a) 598 (b) 400 (c) 301 (d) 202
34. 34.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 120° (d) 60°
35. 35.What are the roots of x² − 10x + 21 = 0? (a) 2 and 8 (b) 3 and 7 (c) 1 and 9 (d) 1 and 21
36. 36.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1431 (c) 1485 (d) 1458
37. 37.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 80° (b) 41° (c) 40° (d) 140°
38. 38.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 145° (b) 120° (c) 85° (d) 95°
39. 39.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
40. 40.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 130° (b) 155° (c) 310° (d) 50°

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