Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 14 · 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 prime factorisation of 20? (a) 2 × 5 (b) 2² × 5 (c) 2 × 5² (d) 2³ × 5
2. 2.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 45 (c) 55 (d) 90
3. 3.How many factors does 29 have? (a) 3 (b) 2 (c) 1 (d) 4
4. 4.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
5. 5.What is the mean of 9, 2, 15 and 10? (a) 10 (b) 12 (c) 8 (d) 9
6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
7. 7.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 30 (b) 23 (c) 22 (d) 21
8. 8.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
9. 9.How many prime numbers are there between 60 and 90? (a) 9 (b) 8 (c) 7 (d) 6
10. 10.Using (a + b)² = a² + 2ab + b², what is 64²? (a) 4096 (b) 4106 (c) 3136 (d) 3616
11. 11.In a class of 30 children, 10 like maths, 17 like science and 5 like both. How many like only maths? (a) 12 (b) 10 (c) 13 (d) 5
12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
13. 13.A bag has 5 red balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 5 (c) 9 (d) 6
14. 14.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
15. 15.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
16. 16.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
17. 17.How many factors does 74 have? (a) 2 (b) 4 (c) 3 (d) 5
18. 18.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 432 (c) 360 (d) 423
19. 19.A bag has 10 blue balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 7 (c) 11 (d) 2
20. 20.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
21. 21.A bag has 11 blue balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 12 (c) 15 (d) 2
22. 22.In a class of 43 children, 25 like tea, 24 like coffee and 10 like both. How many like only tea? (a) 25 (b) 15 (c) 14 (d) 19
23. 23.A bag has 8 black balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 9 (c) 19 (d) 10
24. 24.A drawer has lots of blue, 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) 3 (b) 2 (c) 6 (d) 4
25. 25.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 100 (c) 20 (d) 45
26. 26.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 115° (b) 270° (c) 155° (d) 90°
27. 27.What is the midpoint of the line joining (3, 1) and (13, 13)? (a) (16, 14) (b) (8, 7) (c) (5, 6) (d) (7, 8)
28. 28.A drawer has lots of yellow 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) 4 (c) 3 (d) 5
29. 29.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
30. 30.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
31. 31.A bag has 7 green, 4 blue and 3 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 2/5 (c) 2/7 (d) 5/7
32. 32.What is the midpoint of the line joining (2, 2) and (6, 12)? (a) (8, 14) (b) (2, 5) (c) (7, 4) (d) (4, 7)
33. 33.A bag has 8 red balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 10 (b) 2 (c) 9 (d) 19
34. 34.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.What is the median of 17, 25, 3, 5 and 40? (a) 18 (b) 3 (c) 17 (d) 25
36. 36.In a class of 31 children, 15 like mangoes, 23 like bananas and 12 like both. How many like only mangoes? (a) 11 (b) 8 (c) 15 (d) 3
37. 37.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 2 (d) 11
38. 38.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 10° (d) 80°
39. 39.Using (a + b)² = a² + 2ab + b², what is 104²? (a) 10016 (b) 9216 (c) 10816 (d) 10826
40. 40.What is the distance between the points (3, 2) and (11, 17)? (a) 17 (b) 289 (c) 18 (d) 23

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