Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 244 · 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 white, green, black, 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) 6 (c) 2 (d) 10
2. 2.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 105 (d) 91
3. 3.Which is the correct factorisation of x² + 5x + 6? (a) (x − 2)(x − 3) (b) (x + 1)(x + 6) (c) (x + 2)(x + 3) (d) (x + 1)(x + 4)
4. 4.What is the 11th term of the AP 9, 15, 21, 27, …? (a) 60 (b) 75 (c) 66 (d) 69
5. 5.A drawer has lots of green 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) 3 (c) 5 (d) 4
6. 6.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 20 (b) 22 (c) 19 (d) 21
7. 7.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
8. 8.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 24 (d) 48
9. 9.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 1/5 (c) 5/6 (d) 1/6
10. 10.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 10 (d) 20
11. 11.What is the mean of 11, 15, 14, 20 and 10? (a) 13 (b) 15 (c) 16 (d) 14
12. 12.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 240 (d) 25
13. 13.What is the missing term in the AP 17, 21, 25, ?, 33? (a) 28 (b) 29 (c) 33 (d) 30
14. 14.In which quadrant does the point (5, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
15. 15.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
16. 16.How many prime numbers are there between 60 and 70? (a) 2 (b) 1 (c) 3 (d) 4
17. 17.A drawer has lots of 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) 2 (b) 5 (c) 3 (d) 4
18. 18.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 65° (b) 115° (c) 135° (d) 160°
19. 19.A bag has 10 yellow balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 2 (c) 11 (d) 10
20. 20.In which quadrant does the point (4, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
21. 21.What are the roots of x² − 7x + 12 = 0? (a) 1 and 6 (b) 3 and 4 (c) 1 and 12 (d) 2 and 6
22. 22.A drawer has lots of white and black 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) 4 (d) 3
23. 23.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 340° (c) 20° (d) 70°
24. 24.In a class of 20 children, 15 like tea, 15 like coffee and 11 like both. How many like at least one of the two? (a) 20 (b) 8 (c) 19 (d) 30
25. 25.In a class of 37 children, 24 like maths, 9 like science and 8 like neither. How many like both? (a) 8 (b) 29 (c) 4 (d) 5
26. 26.What is the smallest prime factor of 95? (a) 5 (b) 2 (c) 1 (d) 19
27. 27.A bag has 5 green balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 7 (b) 8 (c) 6 (d) 2
28. 28.What is the midpoint of the line joining (0, 0) and (2, 2)? (a) (2, 2) (b) (1, 2) (c) (2, 1) (d) (1, 1)
29. 29.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 135° (b) 120° (c) 105° (d) 45°
30. 30.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
31. 31.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 120° (c) 121° (d) 60°
32. 32.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 150° (d) 135°
33. 33.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 45 (c) 81 (d) 36
34. 34.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 120° (c) 30° (d) 61°
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/11 (c) 1/12 (d) 1/18
36. 36.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7² (c) 3³ × 7 (d) 3 × 7
37. 37.A bag has 4 red, 6 white and 3 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 10/13 (c) 3/13 (d) 11/13
38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 2 (b) 1 (c) 3 (d) 4
39. 39.What is the midpoint of the line joining (2, 21) and (6, 9)? (a) (8, 30) (b) (2, 6) (c) (4, 15) (d) (15, 4)
40. 40.What is the midpoint of the line joining (9, 0) and (11, 8)? (a) (20, 8) (b) (10, 4) (c) (4, 10) (d) (1, 4)

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