Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 898 · 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 dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 1/9 (c) 5/36 (d) 4/11
2. 2.What is the smallest prime factor of 39? (a) 13 (b) 2 (c) 3 (d) 1
3. 3.A bag has 5 red balls and 6 yellow 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) 2 (c) 11 (d) 7
4. 4.In a class of 41 children, 18 like dance, 25 like music and 9 like both. How many like at least one of the two? (a) 41 (b) 34 (c) 25 (d) 43
5. 5.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 50° (d) 40°
6. 6.In a class of 36 children, 22 like cricket, 16 like football and 8 like neither. How many like both? (a) 2 (b) 10 (c) 8 (d) 28
7. 7.What is the mode of 2, 15, 15, 7, 7, 7 and 10? (a) 7 (b) 10 (c) 2 (d) 15
8. 8.What is the mean of 6, 17, 11, 17, 8 and 13? (a) 12 (b) 14 (c) 13 (d) 11
9. 9.A bag has 3 black balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 8 (c) 2 (d) 10
10. 10.What is the midpoint of the line joining (4, 1) and (14, 13)? (a) (7, 9) (b) (9, 7) (c) (18, 14) (d) (5, 6)
11. 11.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/3 (c) 1/5 (d) 1/6
12. 12.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 71° (c) 250° (d) 70°
13. 13.A bag has 4 black balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 5 (b) 12 (c) 2 (d) 6
14. 14.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 45° (c) 46° (d) 90°
15. 15.In which quadrant does the point (4, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
16. 16.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 45 (d) 20
17. 17.What is the smallest prime factor of 21? (a) 2 (b) 1 (c) 3 (d) 7
18. 18.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
19. 19.What is the midpoint of the line joining (4, 6) and (16, 4)? (a) (5, 10) (b) (6, 1) (c) (10, 5) (d) (20, 10)
20. 20.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 158 (c) 150 (d) 140
21. 21.Using (a + b)² = a² + 2ab + b², what is 54²? (a) 2916 (b) 2926 (c) 2516 (d) 2116
22. 22.In a class of 40 children, 13 like maths, 23 like science and 4 like both. How many like neither? (a) 9 (b) 8 (c) 12 (d) 4
23. 23.What is the smallest prime factor of 403? (a) 13 (b) 1 (c) 2 (d) 31
24. 24.A drawer has lots of yellow, black, blue, red 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) 5 (b) 10 (c) 2 (d) 6
25. 25.What is the 38th term of the AP 14, 18, 22, 26, …? (a) 162 (b) 166 (c) 148 (d) 152
26. 26.The mean of 6 numbers is 18. When the number 25 is added to them, what is the new mean? (a) 19 (b) 21 (c) 20 (d) 18
27. 27.A bag has 3 black 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) 4 (b) 10 (c) 8 (d) 2
28. 28.In a class of 43 children, 18 like maths, 31 like science and 11 like both. How many like only maths? (a) 20 (b) 12 (c) 18 (d) 7
29. 29.What is the mean of 15, 11, 9, 2 and 18? (a) 11 (b) 12 (c) 10 (d) 13
30. 30.How many prime numbers are there between 60 and 80? (a) 5 (b) 6 (c) 4 (d) 7
31. 31.A bag has 5 yellow, 7 red and 3 green balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/15 (b) 1/3 (c) 11/15 (d) 2/3
32. 32.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 145° (b) 110° (c) 35° (d) 105°
33. 33.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
34. 34.What is the prime factorisation of 126? (a) 2 × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7² (d) 2³ × 3² × 7
35. 35.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 20 (d) 11
36. 36.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2 × 5 × 7 (c) 2 × 5 × 7² (d) 2³ × 5 × 7
37. 37.A bag has 9 red, 2 white and 6 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 8/17 (b) 10/17 (c) 9/17 (d) 1/3
38. 38.What is the distance between the points (3, 9) and (19, 21)? (a) 20 (b) 21 (c) 400 (d) 28
39. 39.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
40. 40.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 22 (d) 110

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