Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 492 · 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.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 7/8 (c) 1/8 (d) 1/4
2. 2.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 125 (b) 116 (c) 134 (d) 126
3. 3.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 85° (b) 145° (c) 130° (d) 95°
4. 4.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 161 (c) 152 (d) 170
5. 5.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 6 (d) 12
6. 6.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 150° (b) 100° (c) 110° (d) 30°
7. 7.What is the distance between the points (5, 4) and (10, 16)? (a) 17 (b) 13 (c) 169 (d) 14
8. 8.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 200° (d) 21°
9. 9.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) 25 (b) 13 (c) 12 (d) 24
10. 10.Which is the correct factorisation of x² + 9x + 14? (a) (x − 2)(x − 7) (b) (x + 1)(x + 14) (c) (x + 2)(x + 7) (d) (x + 1)(x + 8)
11. 11.A bag has 5 black balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 17 (b) 6 (c) 7 (d) 2
12. 12.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/2 (c) 1/3 (d) 2/3
13. 13.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 155° (c) 45° (d) 160°
14. 14.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) 8 (b) 15 (c) 14 (d) 7
15. 15.What is the smallest prime factor of 115? (a) 23 (b) 1 (c) 5 (d) 2
16. 16.In a class of 26 children, 13 like mangoes, 18 like bananas and 9 like both. How many like neither? (a) 13 (b) 9 (c) 5 (d) 4
17. 17.A bag has 2 green, 2 red and 4 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 7/8 (c) 1/4 (d) 3/4
18. 18.What is the product of the roots of x² − 6x + 8 = 0? (a) 7 (b) 6 (c) 9 (d) 8
19. 19.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 48 (d) 12
20. 20.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 24 (c) 25 (d) 36
21. 21.How many prime numbers are there between 70 and 80? (a) 4 (b) 2 (c) 3 (d) 5
22. 22.A bag has 3 blue balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 4 (b) 2 (c) 5 (d) 13
23. 23.A bag has 12 green balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 20 (d) 13
24. 24.In a class of 39 children, 16 like tea, 21 like coffee and 3 like both. How many like at least one of the two? (a) 37 (b) 34 (c) 31 (d) 39
25. 25.What is the 38th term of the AP 18, 26, 34, 42, …? (a) 314 (b) 322 (c) 296 (d) 304
26. 26.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 43 (b) 212 (c) 414 (d) 207
27. 27.Which term of the AP 6, 13, 20, 27, … is 62? (a) 11th (b) 8th (c) 9th (d) 10th
28. 28.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
29. 29.What is the midpoint of the line joining (5, 10) and (17, 2)? (a) (22, 12) (b) (11, 6) (c) (6, 4) (d) (6, 11)
30. 30.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 105 (c) 91 (d) 182
31. 31.In a class of 25 children, 9 like tea, 18 like coffee and 6 like both. How many like only tea? (a) 9 (b) 7 (c) 12 (d) 3
32. 32.A bag has 4 yellow, 8 white and 5 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 13/17 (b) 4/17 (c) 4/13 (d) 1/3
33. 33.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
34. 34.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 576 cu cm (c) 864 cu cm (d) 1728 cu cm
35. 35.The mean of 8 numbers is 40. When the number 4 is added to them, what is the new mean? (a) 37 (b) 36 (c) 22 (d) 40
36. 36.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) 85° (c) 275° (d) 5°
37. 37.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
38. 38.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
39. 39.What is the distance between the points (2, 13) and (8, 5)? (a) 100 (b) 11 (c) 10 (d) 14
40. 40.Using (a − b)² = a² − 2ab + b², what is 28²? (a) 794 (b) 896 (c) 784 (d) 1024

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