Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 17 · 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.The mean of 6 numbers is 31. When the number 45 is added to them, what is the new mean? (a) 34 (b) 38 (c) 33 (d) 31
2. 2.How many factors does 12 have? (a) 4 (b) 5 (c) 6 (d) 7
3. 3.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 14 (b) 16 (c) 15 (d) 4
5. 5.How many factors does 87 have? (a) 2 (b) 4 (c) 3 (d) 5
6. 6.What is the median of 35, 38, 4, 34 and 27? (a) 35 (b) 4 (c) 34 (d) 27
7. 7.A drawer has lots of black, red, blue, yellow and green 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) 6 (c) 2 (d) 10
8. 8.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 12 (d) 30
9. 9.If a + b = 10 and ab = 16, what is a² + b²? (a) 84 (b) 68 (c) 132 (d) 100
10. 10.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 9025 (b) 11035 (c) 11025 (d) 10025
11. 11.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 37 (c) 25 (d) 36
12. 12.What is the distance between the points (2, 3) and (17, 11)? (a) 289 (b) 23 (c) 18 (d) 17
13. 13.What is the midpoint of the line joining (2, 16) and (14, 4)? (a) (6, 6) (b) (16, 20) (c) (10, 8) (d) (8, 10)
14. 14.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 81 (d) 72
15. 15.What is the smallest prime factor of 217? (a) 7 (b) 1 (c) 31 (d) 2
16. 16.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 66 (d) 78
17. 17.What is the mode of 20, 9, 1, 9, 13, 1 and 9? (a) 13 (b) 1 (c) 9 (d) 20
18. 18.In a class of 33 children, 12 like tea, 21 like coffee and 9 like neither. How many like both? (a) 10 (b) 8 (c) 9 (d) 24
19. 19.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 130° (b) 115° (c) 245° (d) 65°
20. 20.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 56° (b) 125° (c) 55° (d) 235°
21. 21.In a class of 35 children, 27 like dance, 15 like music and 8 like both. How many like at least one of the two? (a) 34 (b) 42 (c) 26 (d) 35
22. 22.A drawer has lots of red, green, black, blue and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 6 (d) 10
23. 23.A drawer has lots of white, black, yellow and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 4 (c) 5 (d) 8
24. 24.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 253 (b) 462 (c) 231 (d) 41
25. 25.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 105° (b) 75° (c) 140° (d) 145°
26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 1 (b) 4 (c) 3 (d) 2
27. 27.A drawer has lots of white, green, red, black and yellow 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) 6 (c) 10 (d) 2
28. 28.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 160° (c) 20° (d) 70°
29. 29.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
30. 30.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
31. 31.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 125° (c) 56° (d) 55°
32. 32.What is the distance between the points (0, 4) and (4, 7)? (a) 25 (b) 6 (c) 7 (d) 5
33. 33.How many prime numbers are there between 50 and 70? (a) 3 (b) 4 (c) 5 (d) 6
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/11 (c) 1/12 (d) 3/11
35. 35.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 48 (d) 24
36. 36.A bag has 10 white balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 10 (c) 19 (d) 11
37. 37.What are the roots of x² − 10x + 16 = 0? (a) 1 and 16 (b) 1 and 9 (c) 3 and 7 (d) 2 and 8
38. 38.What is the missing term in the AP 4, 9, 14, ?, 24? (a) 19 (b) 20 (c) 18 (d) 24
39. 39.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
40. 40.What is the distance between the points (6, 12) and (10, 9)? (a) 7 (b) 6 (c) 5 (d) 25

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