Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 981 · 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.What is the mean of 12, 4, 11, 19, 13 and 25? (a) 12 (b) 15 (c) 14 (d) 13
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
3. 3.In a class of 41 children, 21 like dance, 18 like music and 2 like both. How many like neither? (a) 6 (b) 4 (c) 5 (d) 2
4. 4.In a class of 35 children, 17 like dance, 18 like music and 10 like both. How many like only dance? (a) 17 (b) 7 (c) 10 (d) 8
5. 5.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 15 (d) 4
7. 7.If a + b = 14 and ab = 33, what is a² + b²? (a) 196 (b) 163 (c) 130 (d) 262
8. 8.A bag has 7 yellow, 4 red and 9 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 7/13 (b) 7/20 (c) 13/20 (d) 1/3
9. 9.If a + b = 17 and ab = 66, what is (a − b)²? (a) 25 (b) 5 (c) 289 (d) 157
10. 10.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
11. 11.What is the mean of 3, 9, 17, 17, 2 and 6? (a) 9 (b) 8 (c) 10 (d) 11
12. 12.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/3 (c) 2/3 (d) 1/2
13. 13.A bag has 12 black balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 16 (b) 2 (c) 13 (d) 14
14. 14.What is the mode of 7, 5, 5, 2, 9, 2 and 2? (a) 7 (b) 9 (c) 5 (d) 2
15. 15.In a class of 41 children, 18 like maths, 25 like science and 5 like both. How many like neither? (a) 8 (b) 5 (c) 4 (d) 3
16. 16.In a class of 35 children, 24 like maths, 9 like science and 4 like both. How many like only maths? (a) 20 (b) 24 (c) 26 (d) 5
17. 17.In a class of 50 children, 27 like tea, 22 like coffee and 9 like both. How many like at least one of the two? (a) 49 (b) 40 (c) 50 (d) 31
18. 18.What are the roots of x² − 17x + 72 = 0? (a) 1 and 16 (b) 2 and 36 (c) 1 and 72 (d) 8 and 9
19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 3 (b) 5 (c) 2 (d) 4
20. 20.A bag has 3 red, 6 yellow and 2 green balls. One ball is taken out without looking. What is the probability that it is red? (a) 3/8 (b) 1/3 (c) 8/11 (d) 3/11
21. 21.What is the smallest prime factor of 133? (a) 7 (b) 2 (c) 1 (d) 19
22. 22.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 75 (b) 140 (c) 70 (d) 24
23. 23.The mean of 5 numbers is 40. When the number 46 is added to them, what is the new mean? (a) 41 (b) 42 (c) 43 (d) 40
24. 24.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 35° (d) 125°
25. 25.In a class of 30 children, 7 like dance, 18 like music and 2 like both. How many like at least one of the two? (a) 21 (b) 30 (c) 23 (d) 25
26. 26.Which term of the AP 16, 19, 22, 25, … is 49? (a) 13th (b) 14th (c) 11th (d) 12th
27. 27.A drawer has lots of yellow, blue, black, white 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) 6 (c) 10 (d) 5
28. 28.What is the prime factorisation of 14? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2 × 7
29. 29.What is the midpoint of the line joining (6, 1) and (10, 7)? (a) (16, 8) (b) (2, 3) (c) (8, 4) (d) (4, 8)
30. 30.A drawer has lots of yellow, green, black 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) 8 (b) 2 (c) 5 (d) 4
31. 31.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) 24 (b) 13 (c) 25 (d) 12
32. 32.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 352 (b) 176 (c) 179 (d) 31
33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 18 (d) 19
34. 34.A bag has 11 black balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 16 (b) 12 (c) 13 (d) 2
35. 35.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
36. 36.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 44 (c) 62 (d) 54
37. 37.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 100° (d) 80°
38. 38.How many prime numbers are there between 50 and 70? (a) 6 (b) 5 (c) 3 (d) 4
39. 39.How many factors does 23 have? (a) 2 (b) 1 (c) 3 (d) 4
40. 40.What is the smallest prime factor of 247? (a) 2 (b) 1 (c) 13 (d) 19

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