Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 737 · 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.In a class of 34 children, 16 like maths, 19 like science and 3 like both. How many like only maths? (a) 13 (b) 15 (c) 16 (d) 3
2. 2.Using (a − b)² = a² − 2ab + b², what is 58²? (a) 3844 (b) 3374 (c) 3596 (d) 3364
3. 3.What is the mean of 8, 10, 12, 12, 13 and 23? (a) 13 (b) 14 (c) 15 (d) 12
4. 4.Which term of the AP 11, 13, 15, 17, … is 33? (a) 11th (b) 14th (c) 12th (d) 13th
5. 5.A bag has 7 blue balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 15 (d) 9
6. 6.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 961 (b) 901 (c) 971 (d) 841
7. 7.A drawer has lots of yellow 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) 5 (d) 4
8. 8.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2² × 5 (d) 2 × 5³
9. 9.A bag has 9 green, 4 white and 9 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 7/11 (b) 13/22 (c) 1/3 (d) 9/22
10. 10.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
11. 11.A bag has 3 white balls and 5 red 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) 6 (d) 2
12. 12.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 70° (d) 35°
13. 13.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 48 (d) 24
14. 14.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 10 (c) 25 (d) 11
15. 15.What is the distance between the points (1, 5) and (7, 13)? (a) 10 (b) 100 (c) 14 (d) 11
16. 16.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5² (c) 3 × 5 (d) 3² × 5
17. 17.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 14 (d) 21
18. 18.A drawer has lots of green 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) 3 (d) 4
19. 19.The mean of 6 numbers is 10. When the number 31 is added to them, what is the new mean? (a) 14 (b) 12 (c) 10 (d) 13
20. 20.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) 12 (b) 24 (c) 25 (d) 13
21. 21.In a class of 24 children, 16 like tea, 11 like coffee and 6 like both. How many like neither? (a) 6 (b) 3 (c) 4 (d) 9
22. 22.In a class of 13 children, 9 like tea, 7 like coffee and 4 like both. How many like only tea? (a) 9 (b) 6 (c) 5 (d) 3
23. 23.How many prime numbers are there between 30 and 60? (a) 8 (b) 7 (c) 9 (d) 6
24. 24.What is the smallest prime factor of 161? (a) 1 (b) 2 (c) 7 (d) 23
25. 25.What is the prime factorisation of 252? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2³ × 3² × 7 (d) 2² × 3² × 7
26. 26.Using (a − b)² = a² − 2ab + b², what is 95²? (a) 9035 (b) 9025 (c) 9975 (d) 11025
27. 27.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
28. 28.4 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 40 (c) 20 (d) 9
29. 29.A bag has 12 green balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 17 (c) 2 (d) 14
30. 30.A drawer has lots of yellow, black 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) 3 (c) 6 (d) 4
31. 31.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7³
32. 32.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 3741 (c) 7656 (d) 3829
33. 33.What is the smallest prime factor of 57? (a) 1 (b) 3 (c) 19 (d) 2
34. 34.What is the mode of 3, 2, 8, 3, 3, 20 and 20? (a) 8 (b) 3 (c) 20 (d) 2
35. 35.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 255° (d) 105°
36. 36.What are the roots of x² − 15x + 56 = 0? (a) 2 and 28 (b) 1 and 14 (c) 1 and 56 (d) 7 and 8
37. 37.What is the smallest prime factor of 51? (a) 3 (b) 1 (c) 17 (d) 2
38. 38.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 120° (c) 135° (d) 60°
39. 39.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 2/3 (c) 1/4 (d) 1/2
40. 40.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 7 (c) 63 (d) 21

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