Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 811 · 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 mean of 19, 16, 18 and 19? (a) 17 (b) 24 (c) 19 (d) 18
2. 2.What is the mean of 18, 15, 14, 20, 19 and 22? (a) 19 (b) 20 (c) 18 (d) 17
3. 3.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
4. 4.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
5. 5.A bag has 4 white, 2 blue and 9 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 2/15 (b) 13/15 (c) 1/3 (d) 2/13
6. 6.If a + b = 15 and ab = 56, what is a² + b²? (a) 337 (b) 113 (c) 225 (d) 169
7. 7.What is the distance between the points (3, 0) and (11, 15)? (a) 289 (b) 23 (c) 17 (d) 18
8. 8.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 85° (b) 160° (c) 95° (d) 105°
9. 9.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 23 (b) 22 (c) 24 (d) 26
10. 10.A bag has 11 green balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 22 (b) 2 (c) 12 (d) 13
11. 11.A bag has 5 white balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 6 (b) 10 (c) 2 (d) 7
12. 12.A drawer has lots of white, 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) 4 (d) 6
13. 13.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 120° (c) 30° (d) 60°
14. 14.A bag has 8 blue balls and 3 black 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) 11 (c) 9 (d) 4
15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
16. 16.A bag has 4 white balls and 5 green 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) 2 (c) 5 (d) 9
17. 17.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 40 (b) 308 (c) 175 (d) 154
18. 18.What is the 22nd term of the AP 1, 8, 15, 22, …? (a) 148 (b) 147 (c) 155 (d) 154
19. 19.How many factors does 74 have? (a) 5 (b) 2 (c) 4 (d) 3
20. 20.A bag has 5 red balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 14 (c) 6 (d) 7
21. 21.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 30° (c) 150° (d) 60°
22. 22.A drawer has lots of yellow, red 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) 2 (b) 3 (c) 6 (d) 4
23. 23.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x + 1)(x + 72)
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 4/11 (c) 5/36 (d) 1/9
25. 25.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
26. 26.What is the midpoint of the line joining (8, 0) and (12, 4)? (a) (2, 2) (b) (10, 2) (c) (20, 4) (d) (2, 10)
27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 16 (b) 15 (c) 17 (d) 5
28. 28.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 94 sq cm (b) 47 sq cm (c) 60 sq cm (d) 188 sq cm
29. 29.A bag has 9 red balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 4 (d) 12
30. 30.What is the distance between the points (1, 27) and (8, 3)? (a) 31 (b) 25 (c) 625 (d) 26
31. 31.A bag has 9 red balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 11 (b) 10 (c) 2 (d) 14
32. 32.In a class of 41 children, 17 like mangoes, 18 like bananas and 4 like both. How many like at least one of the two? (a) 41 (b) 27 (c) 35 (d) 31
33. 33.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 15 (b) 22 (c) 14 (d) 21
34. 34.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 144 (d) 132
35. 35.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 6 (d) 3
36. 36.The mean of 3 numbers is 21. When the number 25 is added to them, what is the new mean? (a) 23 (b) 22 (c) 24 (d) 21
37. 37.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 120° (b) 140° (c) 160° (d) 60°
38. 38.What is the product of the roots of x² − 10x + 24 = 0? (a) 23 (b) 24 (c) 10 (d) 25
39. 39.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 62 (c) 54 (d) 44
40. 40.Which is the correct factorisation of x² + 10x + 24? (a) (x − 4)(x − 6) (b) (x + 4)(x + 6) (c) (x + 1)(x + 9) (d) (x + 1)(x + 24)

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