Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 406 · 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.Which is the correct factorisation of x² + 8x + 12? (a) (x − 2)(x − 6) (b) (x + 2)(x + 6) (c) (x + 1)(x + 12) (d) (x + 1)(x + 7)
2. 2.How many factors does 62 have? (a) 2 (b) 3 (c) 5 (d) 4
3. 3.In a class of 27 children, 16 like cricket, 17 like football and 9 like both. How many like neither? (a) 3 (b) 12 (c) 4 (d) 9
4. 4.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 17 (b) 12 (c) 13 (d) 14
5. 5.What is the midpoint of the line joining (2, 15) and (12, 9)? (a) (5, 3) (b) (12, 7) (c) (14, 24) (d) (7, 12)
6. 6.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 3/8 (c) 1/4 (d) 7/8
7. 7.The mean of 5 numbers is 26. When the number 44 is added to them, what is the new mean? (a) 26 (b) 35 (c) 30 (d) 29
8. 8.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 2/3 (d) 1/3
9. 9.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 12 (c) 18 (d) 6
10. 10.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
11. 11.In a class of 45 children, 25 like dance, 31 like music and 12 like both. How many like at least one of the two? (a) 56 (b) 45 (c) 32 (d) 44
12. 12.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
13. 13.What is the 19th term of the AP 11, 16, 21, 26, …? (a) 106 (b) 101 (c) 95 (d) 90
14. 14.What is the mean of 20, 4, 6, 19, 11 and 6? (a) 13 (b) 10 (c) 12 (d) 11
15. 15.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
16. 16.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 55 (c) 45 (d) 90
17. 17.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 105 (d) 91
18. 18.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 465 (c) 497 (d) 496
19. 19.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 230° (b) 50° (c) 100° (d) 130°
20. 20.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 102 (c) 93 (d) 94
21. 21.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
22. 22.What is the product of the roots of x² − 12x + 32 = 0? (a) 32 (b) 12 (c) 33 (d) 31
23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 4 (b) 3 (c) 1 (d) 2
24. 24.A drawer has lots of blue, white, black, red 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) 6 (c) 10 (d) 5
25. 25.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
26. 26.A drawer has lots of yellow, black, 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) 5 (b) 10 (c) 6 (d) 2
27. 27.In a class of 25 children, 11 like maths, 16 like science and 5 like both. How many like only maths? (a) 11 (b) 5 (c) 9 (d) 6
28. 28.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 132 (c) 144 (d) 24
29. 29.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 7 (d) 2
30. 30.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
31. 31.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 220° (d) 41°
32. 32.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 20 (d) 25
33. 33.What is the midpoint of the line joining (5, 2) and (17, 4)? (a) (11, 3) (b) (22, 6) (c) (6, 1) (d) (3, 11)
34. 34.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 30 (c) 21 (d) 36
35. 35.What is the smallest prime factor of 253? (a) 11 (b) 1 (c) 2 (d) 23
36. 36.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 95° (d) 85°
37. 37.In a class of 31 children, 17 like cricket, 13 like football and 5 like both. How many like only cricket? (a) 8 (b) 12 (c) 17 (d) 18
38. 38.How many prime numbers are there between 40 and 60? (a) 5 (b) 6 (c) 4 (d) 7
39. 39.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) 51 (c) 48 (d) 144
40. 40.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 256 sq cm (d) 512 sq cm

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