Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 480 · 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 midpoint of the line joining (9, 10) and (13, 20)? (a) (15, 11) (b) (2, 5) (c) (22, 30) (d) (11, 15)
2. 2.In a class of 40 children, 25 like cricket, 17 like football and 6 like both. How many like only cricket? (a) 19 (b) 11 (c) 25 (d) 23
3. 3.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
4. 4.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 156 (c) 78 (d) 91
5. 5.What is the smallest prime factor of 377? (a) 1 (b) 13 (c) 2 (d) 29
6. 6.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 318 (c) 370 (d) 360
7. 7.How many prime numbers are there between 30 and 40? (a) 2 (b) 4 (c) 3 (d) 1
8. 8.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 21 (c) 49 (d) 14
9. 9.What is the mode of 14, 14, 1, 1, 4, 14 and 16? (a) 4 (b) 16 (c) 14 (d) 1
10. 10.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 28 (d) 16
11. 11.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 85° (c) 5° (d) 95°
12. 12.What is the 12th term of the AP 16, 19, 22, 25, …? (a) 33 (b) 49 (c) 36 (d) 52
13. 13.What is the 21st term of the AP 12, 15, 18, 21, …? (a) 60 (b) 72 (c) 75 (d) 63
14. 14.A drawer has lots of yellow, red, green, 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) 5 (b) 10 (c) 6 (d) 2
15. 15.In a class of 26 children, 7 like tea, 16 like coffee and 2 like both. How many like at least one of the two? (a) 23 (b) 26 (c) 19 (d) 21
16. 16.What is the mean of 5, 7, 18, 17 and 3? (a) 9 (b) 11 (c) 10 (d) 12
17. 17.In a class of 45 children, 25 like tea, 27 like coffee and 12 like both. How many like at least one of the two? (a) 40 (b) 52 (c) 28 (d) 45
18. 18.What is the 25th term of the AP 5, 12, 19, 26, …? (a) 180 (b) 168 (c) 173 (d) 175
19. 19.A bag has 7 red balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 11 (b) 2 (c) 8 (d) 9
20. 20.What is the sum of the roots of x² − 17x + 72 = 0? (a) 16 (b) 17 (c) 18 (d) 72
21. 21.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/3 (d) 1/4
22. 22.A bag has 5 black 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) 7 (d) 13
23. 23.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 30 (c) 36 (d) 15
24. 24.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 60 (c) 57 (d) 171
25. 25.What is the mean of 16, 17, 16, 14 and 12? (a) 14 (b) 16 (c) 17 (d) 15
26. 26.A bag has 8 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 9 (c) 13 (d) 10
27. 27.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
28. 28.How many prime numbers are there between 20 and 30? (a) 2 (b) 3 (c) 1 (d) 4
29. 29.A bag has 9 red balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 14 (c) 2 (d) 10
30. 30.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 961 (b) 901 (c) 841 (d) 971
31. 31.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 7 (d) 13
32. 32.How many factors does 15 have? (a) 2 (b) 5 (c) 4 (d) 3
33. 33.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 7/8 (c) 1/4 (d) 1/7
34. 34.How many factors does 21 have? (a) 2 (b) 3 (c) 5 (d) 4
35. 35.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 10 (d) 8
36. 36.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 25 (d) 120
37. 37.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 10 (b) 8 (c) 6 (d) 7
38. 38.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) 5 (b) 4 (c) 3 (d) 2
39. 39.What is the 29th term of the AP 15, 24, 33, 42, …? (a) 252 (b) 261 (c) 276 (d) 267
40. 40.A bag has 8 red, 3 green and 7 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 4/9 (b) 11/18 (c) 5/9 (d) 1/3

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