Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 680 · 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.A drawer has lots of 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) 3 (b) 2 (c) 6 (d) 4
2. 2.What is the mode of 19, 19, 17, 7, 19, 14 and 7? (a) 19 (b) 17 (c) 14 (d) 7
3. 3.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) 14 (c) 22 (d) 21
4. 4.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 100° (b) 230° (c) 50° (d) 130°
5. 5.What are the roots of x² − 6x + 8 = 0? (a) 2 and 5 (b) 1 and 8 (c) 1 and 5 (d) 2 and 4
6. 6.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 85° (d) 86°
7. 7.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
8. 8.In a class of 24 children, 14 like tea, 13 like coffee and 9 like both. How many like only tea? (a) 4 (b) 14 (c) 11 (d) 5
9. 9.In a class of 25 children, 13 like tea, 17 like coffee and 7 like both. How many like at least one of the two? (a) 25 (b) 23 (c) 30 (d) 16
10. 10.What is the midpoint of the line joining (4, 1) and (12, 7)? (a) (16, 8) (b) (8, 4) (c) (4, 8) (d) (4, 3)
11. 11.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 160° (b) 115° (c) 95° (d) 85°
12. 12.What is the mode of 19, 19, 3, 5, 5, 19 and 11? (a) 11 (b) 3 (c) 19 (d) 5
13. 13.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
14. 14.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 24 (c) 75 (d) 72
15. 15.What is the mean of 6, 14, 13, 8, 18 and 13? (a) 14 (b) 12 (c) 13 (d) 11
16. 16.What is the smallest prime factor of 133? (a) 7 (b) 19 (c) 1 (d) 2
17. 17.What are the roots of x² − 9x + 20 = 0? (a) 4 and 5 (b) 1 and 8 (c) 2 and 10 (d) 1 and 20
18. 18.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 132 (d) 144
19. 19.Using (a − b)² = a² − 2ab + b², what is 85²? (a) 9025 (b) 8075 (c) 7235 (d) 7225
20. 20.What is the product of the roots of x² − 13x + 36 = 0? (a) 36 (b) 37 (c) 35 (d) 13
21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 18 (d) 17
22. 22.What is the prime factorisation of 35? (a) 5 × 7 (b) 5 × 7² (c) 5³ × 7 (d) 5² × 7
23. 23.A bag has 9 blue, 4 yellow and 9 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 13/22 (b) 9/22 (c) 1/3 (d) 9/13
24. 24.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 21 (d) 28
25. 25.What is the 15th term of the AP 12, 19, 26, 33, …? (a) 98 (b) 117 (c) 110 (d) 105
26. 26.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/8 (c) 3/4 (d) 1/8
27. 27.A drawer has lots of green, red, 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) 5 (b) 4 (c) 2 (d) 8
28. 28.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 85° (c) 95° (d) 170°
29. 29.In a class of 47 children, 19 like dance, 26 like music and 6 like both. How many like only dance? (a) 13 (b) 19 (c) 20 (d) 21
30. 30.What is the mean of 11, 9, 19 and 9? (a) 11 (b) 13 (c) 12 (d) 16
31. 31.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 190 (c) 37 (d) 361
32. 32.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
33. 33.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 1)(x + 16) (d) (x + 8)(x + 9)
34. 34.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 34 (b) 129 (c) 258 (d) 144
35. 35.The mean of 9 numbers is 14. When the number 4 is added to them, what is the new mean? (a) 12 (b) 14 (c) 13 (d) 9
36. 36.A bag has 7 white, 4 red and 9 green balls. One ball is taken out without looking. What is the probability that it is white? (a) 13/20 (b) 7/20 (c) 7/13 (d) 1/3
37. 37.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 21° (c) 20° (d) 160°
38. 38.In which quadrant does the point (−2, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
39. 39.A bag has 12 red balls and 11 white 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) 12 (c) 13 (d) 23
40. 40.What is the mean of 10, 14, 8 and 8? (a) 9 (b) 8 (c) 11 (d) 10

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