Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 814 · 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. 1.4 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 8 (b) 32 (c) 20 (d) 16
2. 2.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
3. 3.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/4
4. 4.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 14) (b) (x − 6)(x − 9) (c) (x + 1)(x + 54) (d) (x + 6)(x + 9)
5. 5.In a class of 27 children, 18 like tea, 19 like coffee and 12 like both. How many like at least one of the two? (a) 27 (b) 13 (c) 37 (d) 25
6. 6.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 16 (d) 12
7. 7.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
8. 8.In a class of 31 children, 16 like dance, 25 like music and 1 like neither. How many like both? (a) 1 (b) 11 (c) 30 (d) 10
9. 9.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 48 (c) 51 (d) 144
10. 10.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 25° (d) 50°
11. 11.A bag has 4 blue balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 6 (b) 2 (c) 12 (d) 5
12. 12.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 36 (d) 18
13. 13.How many factors does 103 have? (a) 3 (b) 1 (c) 2 (d) 4
14. 14.A cuboid is 12 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 171 sq cm (b) 324 sq cm (c) 684 sq cm (d) 342 sq cm
15. 15.Using (a − b)² = a² − 2ab + b², what is 65²? (a) 4875 (b) 5625 (c) 4235 (d) 4225
16. 16.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 812 (c) 406 (d) 392
17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 16 (b) 15 (c) 17 (d) 6
18. 18.How many prime numbers are there between 40 and 60? (a) 7 (b) 4 (c) 5 (d) 6
19. 19.If a + b = 3 and ab = 2, what is a² + b²? (a) 13 (b) 9 (c) 7 (d) 5
20. 20.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 3/8 (c) 7/8 (d) 1/4
21. 21.In a class of 33 children, 19 like cricket, 12 like football and 8 like both. How many like at least one of the two? (a) 15 (b) 31 (c) 33 (d) 23
22. 22.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 25° (d) 205°
23. 23.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2³ × 5 (c) 2 × 5⁴ (d) 2⁴ × 5
24. 24.A drawer has lots of red, black, 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) 2 (b) 8 (c) 5 (d) 4
25. 25.A bag has 10 blue balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 11 (c) 16 (d) 12
26. 26.How many prime numbers are there between 20 and 30? (a) 2 (b) 1 (c) 3 (d) 4
27. 27.How many factors does 24 have? (a) 7 (b) 8 (c) 6 (d) 9
28. 28.What is the median of 11, 40, 36, 3, 7, 16 and 27? (a) 16 (b) 20 (c) 3 (d) 27
29. 29.The mean of 8 numbers is 34. When the number 25 is added to them, what is the new mean? (a) 34 (b) 33 (c) 35 (d) 32
30. 30.A bag has 6 red, 6 white and 5 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 5/17 (b) 1/3 (c) 13/17 (d) 12/17
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/11 (c) 1/18 (d) 1/36
32. 32.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 7 (c) 12 (d) 24
33. 33.A drawer has lots of yellow, red, green and blue 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) 4 (c) 2 (d) 5
34. 34.In a class of 50 children, 27 like tea, 25 like coffee and 9 like both. How many like only tea? (a) 27 (b) 18 (c) 16 (d) 25
35. 35.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
36. 36.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 14 (c) 42 (d) 21
37. 37.What is the 13th term of the AP 18, 25, 32, 39, …? (a) 102 (b) 91 (c) 84 (d) 109
38. 38.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 22 (b) 92 (c) 104 (d) 184
39. 39.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 100° (b) 150° (c) 70° (d) 110°
40. 40.If a + b = 17 and ab = 66, what is (a − b)²? (a) 5 (b) 25 (c) 157 (d) 289

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