Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 597 · 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 class of 30 children, 26 like tea, 15 like coffee and 12 like both. How many like at least one of the two? (a) 29 (b) 41 (c) 17 (d) 30
2. 2.What is the 24th term of the AP 13, 20, 27, 34, …? (a) 168 (b) 181 (c) 161 (d) 174
3. 3.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 30° (c) 20° (d) 140°
4. 4.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 210 (c) 120 (d) 105
5. 5.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2⁴ × 3² (c) 2³ × 3² (d) 2² × 3⁴
6. 6.In a class of 36 children, 16 like mangoes, 22 like bananas and 11 like both. How many like neither? (a) 20 (b) 11 (c) 9 (d) 10
7. 7.A bag has 5 black balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 17 (c) 13 (d) 2
8. 8.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) 13 (c) 24 (d) 25
9. 9.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 85° (d) 135°
10. 10.A bag has 3 red balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 10 (d) 4
11. 11.If a + b = 19 and ab = 90, what is a² + b²? (a) 541 (b) 271 (c) 181 (d) 361
12. 12.In a class of 27 children, 16 like maths, 12 like science and 3 like both. How many like only maths? (a) 9 (b) 15 (c) 13 (d) 16
13. 13.Which term of the AP 14, 19, 24, 29, … is 119? (a) 22nd (b) 24th (c) 23rd (d) 21st
14. 14.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 45 (c) 90 (d) 20
15. 15.What is the median of 19, 20, 30, 4, 22, 7 and 34? (a) 22 (b) 4 (c) 19 (d) 20
16. 16.A bag has 9 white, 9 red and 2 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/10 (b) 1/3 (c) 19/20 (d) 9/10
17. 17.In a class of 28 children, 19 like tea, 7 like coffee and 4 like neither. How many like both? (a) 4 (b) 24 (c) 2 (d) 3
18. 18.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
19. 19.A bag has 4 red, 9 yellow and 6 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 15/19 (b) 4/19 (c) 1/3 (d) 4/15
20. 20.Which term of the AP 10, 14, 18, 22, … is 50? (a) 12th (b) 10th (c) 11th (d) 13th
21. 21.A bag has 6 white, 2 yellow and 6 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 3/7 (b) 9/14 (c) 4/7 (d) 1/3
22. 22.The mean of 5 numbers is 28. When the number 22 is added to them, what is the new mean? (a) 27 (b) 25 (c) 26 (d) 28
23. 23.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) 15 (b) 8 (c) 7 (d) 14
24. 24.What is the mode of 19, 9, 1, 4, 9, 19 and 19? (a) 1 (b) 4 (c) 19 (d) 9
25. 25.How many factors does 109 have? (a) 4 (b) 1 (c) 2 (d) 3
26. 26.What is the smallest prime factor of 377? (a) 2 (b) 29 (c) 13 (d) 1
27. 27.A bag has 2 red, 8 white and 7 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 15/17 (b) 2/17 (c) 2/15 (d) 1/3
28. 28.A drawer has lots of blue, red, green, black 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) 10 (b) 2 (c) 5 (d) 6
29. 29.In a class of 52 children, 23 like mangoes, 27 like bananas and 8 like both. How many like at least one of the two? (a) 50 (b) 52 (c) 34 (d) 42
30. 30.What is the sum of the roots of x² − 5x + 6 = 0? (a) 5 (b) 6 (c) 7 (d) 4
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/11 (d) 1/12
32. 32.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 66 (d) 132
33. 33.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) 21 (d) 15
34. 34.In a class of 26 children, 16 like tea, 10 like coffee and 5 like neither. How many like both? (a) 21 (b) 6 (c) 4 (d) 5
35. 35.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
36. 36.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
37. 37.Using (a + b)² = a² + 2ab + b², what is 53²? (a) 2509 (b) 2809 (c) 2819 (d) 2209
38. 38.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 50° (d) 320°
39. 39.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 16 sq cm (d) 96 sq cm
40. 40.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 45 (c) 48 (d) 15

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