Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 405 · 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 red, blue, white 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) 4 (c) 8 (d) 5
2. 2.What is the midpoint of the line joining (8, 1) and (18, 3)? (a) (13, 2) (b) (2, 13) (c) (5, 1) (d) (26, 4)
3. 3.What is the median of 30, 26, 4, 9 and 23? (a) 4 (b) 26 (c) 23 (d) 9
4. 4.What is the prime factorisation of 14? (a) 2 × 7 (b) 2 × 7² (c) 2² × 7 (d) 2³ × 7
5. 5.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 122 (c) 113 (d) 114
6. 6.In a class of 44 children, 26 like dance, 21 like music and 10 like both. How many like at least one of the two? (a) 37 (b) 44 (c) 27 (d) 47
7. 7.If a + b = 12 and ab = 32, what is a² + b²? (a) 112 (b) 144 (c) 208 (d) 80
8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 14 (b) 12 (c) 15 (d) 9
9. 9.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 100° (b) 150° (c) 80° (d) 110°
10. 10.A drawer has lots of yellow, blue, white, red 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) 2 (b) 5 (c) 10 (d) 6
11. 11.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 45 (c) 100 (d) 90
12. 12.What is the 35th term of the AP 4, 10, 16, 22, …? (a) 214 (b) 204 (c) 208 (d) 210
13. 13.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) 14 (b) 15 (c) 22 (d) 21
14. 14.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 210 (c) 212 (d) 201
15. 15.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 30° (c) 165° (d) 16°
16. 16.A bag has 8 blue balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 13 (c) 10 (d) 9
17. 17.A bag has 2 blue, 6 green and 6 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 4/7 (c) 3/7 (d) 9/14
18. 18.What is the 35th term of the AP 17, 22, 27, 32, …? (a) 175 (b) 170 (c) 187 (d) 192
19. 19.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 155° (c) 80° (d) 125°
20. 20.How many factors does 28 have? (a) 6 (b) 5 (c) 4 (d) 7
21. 21.What is the mean of 4, 7, 10, 18 and 6? (a) 11 (b) 10 (c) 9 (d) 8
22. 22.The mean of 9 numbers is 40. When the number 70 is added to them, what is the new mean? (a) 40 (b) 55 (c) 44 (d) 43
23. 23.In a class of 17 children, 7 like cricket, 11 like football and 3 like both. How many like neither? (a) 2 (b) 1 (c) 3 (d) 5
24. 24.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 335° (c) 65° (d) 155°
25. 25.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
26. 26.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
27. 27.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7 (d) 3 × 5 × 7²
28. 28.What is the mode of 7, 3, 4, 4, 7, 1 and 4? (a) 4 (b) 1 (c) 7 (d) 3
29. 29.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 8125 (b) 7225 (c) 9035 (d) 9025
30. 30.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4
31. 31.What is the mean of 20, 6, 18, 5 and 11? (a) 13 (b) 10 (c) 12 (d) 15
32. 32.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 294 cu cm (d) 343 cu cm
33. 33.Using (a + b)² = a² + 2ab + b², what is 63²? (a) 3609 (b) 3979 (c) 3249 (d) 3969
34. 34.In which quadrant does the point (−2, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
35. 35.How many factors does 86 have? (a) 3 (b) 5 (c) 2 (d) 4
36. 36.What is the mean of 17, 2, 4 and 13? (a) 12 (b) 10 (c) 8 (d) 9
37. 37.Which is the correct factorisation of x² + 11x + 28? (a) (x + 1)(x + 10) (b) (x + 4)(x + 7) (c) (x − 4)(x − 7) (d) (x + 1)(x + 28)
38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 8 (b) 5 (c) 6 (d) 7
39. 39.What is the mode of 4, 13, 13, 6, 4, 13 and 8? (a) 8 (b) 6 (c) 13 (d) 4
40. 40.Which is the correct factorisation of x² + 13x + 42? (a) (x − 6)(x − 7) (b) (x + 6)(x + 7) (c) (x + 1)(x + 12) (d) (x + 1)(x + 42)

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