Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 618 · 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.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 2 (d) 1
2. 2.A bag has 9 yellow, 3 blue and 2 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 5/14 (b) 9/14 (c) 5/7 (d) 1/3
3. 3.What is the midpoint of the line joining (2, 14) and (8, 2)? (a) (8, 5) (b) (10, 16) (c) (3, 6) (d) (5, 8)
4. 4.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 42 (d) 21
5. 5.What is the distance between the points (8, 9) and (32, 2)? (a) 625 (b) 26 (c) 25 (d) 31
6. 6.What is the 12th term of the AP 6, 11, 16, 21, …? (a) 60 (b) 66 (c) 55 (d) 61
7. 7.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
8. 8.What is the missing term in the AP 20, 29, ?, 47, 56? (a) 39 (b) 47 (c) 38 (d) 37
9. 9.In a class of 45 children, 29 like mangoes, 18 like bananas and 7 like neither. How many like both? (a) 2 (b) 7 (c) 9 (d) 38
10. 10.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 13 (c) 24 (d) 25
11. 11.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 21 (d) 42
12. 12.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 125° (c) 305° (d) 55°
13. 13.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 110° (d) 50°
14. 14.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 65° (b) 120° (c) 125° (d) 115°
15. 15.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 25° (c) 335° (d) 155°
16. 16.In a class of 28 children, 16 like cricket, 9 like football and 9 like neither. How many like both? (a) 6 (b) 19 (c) 9 (d) 7
17. 17.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 16) (d) (x + 1)(x + 72)
18. 18.If a + b = 11 and ab = 18, what is a² + b²? (a) 121 (b) 157 (c) 103 (d) 85
19. 19.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 102 (c) 14 (d) 108
20. 20.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 5° (c) 85° (d) 275°
21. 21.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
22. 22.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 250 (c) 249 (d) 240
23. 23.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
24. 24.What is the smallest prime factor of 143? (a) 11 (b) 13 (c) 1 (d) 2
25. 25.What is the median of 16, 40, 38, 27, 15, 34 and 21? (a) 27 (b) 34 (c) 28 (d) 21
26. 26.In a class of 36 children, 17 like maths, 21 like science and 3 like both. How many like at least one of the two? (a) 38 (b) 32 (c) 36 (d) 35
27. 27.A drawer has lots of white, red, black and green 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) 8
28. 28.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 1 (d) 2
29. 29.In a class of 45 children, 20 like tea, 24 like coffee and 7 like both. How many like neither? (a) 8 (b) 1 (c) 15 (d) 7
30. 30.In a class of 46 children, 25 like mangoes, 28 like bananas and 12 like both. How many like at least one of the two? (a) 46 (b) 41 (c) 29 (d) 53
31. 31.In which quadrant does the point (−6, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
32. 32.What is the smallest prime factor of 203? (a) 1 (b) 29 (c) 7 (d) 2
33. 33.In a class of 43 children, 19 like mangoes, 22 like bananas and 2 like both. How many like neither? (a) 6 (b) 2 (c) 5 (d) 4
34. 34.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 50 (c) 110 (d) 45
35. 35.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 8 (c) 14 (d) 15
36. 36.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 270° (b) 90° (c) 125° (d) 145°
37. 37.What is the midpoint of the line joining (1, 0) and (3, 6)? (a) (2, 3) (b) (4, 6) (c) (3, 2) (d) (1, 3)
38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 11 (b) 12 (c) 10 (d) 3
39. 39.What is the median of 20, 21, 13, 12 and 3? (a) 14 (b) 12 (c) 13 (d) 20
40. 40.In a class of 27 children, 13 like mangoes, 16 like bananas and 8 like both. How many like at least one of the two? (a) 29 (b) 27 (c) 13 (d) 21

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