Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 1 · 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.The mean of 3 numbers is 25. When the number 9 is added to them, what is the new mean? (a) 17 (b) 22 (c) 25 (d) 21
2. 2.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 105° (c) 75° (d) 160°
3. 3.The mean of 3 numbers is 25. When the number 41 is added to them, what is the new mean? (a) 29 (b) 33 (c) 25 (d) 30
4. 4.A drawer has lots of white, blue 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) 4 (b) 2 (c) 3 (d) 6
5. 5.What is the distance between the points (2, 20) and (14, 4)? (a) 400 (b) 21 (c) 20 (d) 28
6. 6.In a class of 28 children, 9 like mangoes, 19 like bananas and 6 like neither. How many like both? (a) 6 (b) 22 (c) 7 (d) 5
7. 7.What is the smallest prime factor of 341? (a) 11 (b) 2 (c) 31 (d) 1
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 1/11 (c) 5/36 (d) 4/11
9. 9.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 20 (d) 45
10. 10.What is the mode of 11, 13, 11, 10, 13, 4 and 11? (a) 10 (b) 13 (c) 11 (d) 4
11. 11.How many factors does 102 have? (a) 9 (b) 6 (c) 8 (d) 7
12. 12.What is the midpoint of the line joining (9, 3) and (17, 7)? (a) (4, 2) (b) (13, 5) (c) (5, 13) (d) (26, 10)
13. 13.What is the 33rd term of the AP 4, 7, 10, 13, …? (a) 99 (b) 103 (c) 100 (d) 96
14. 14.In a class of 32 children, 13 like maths, 18 like science and 6 like both. How many like at least one of the two? (a) 31 (b) 32 (c) 19 (d) 25
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 1/11 (c) 1/9 (d) 3/11
16. 16.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
17. 17.A bag has 8 red balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 10 (b) 9 (c) 2 (d) 18
18. 18.What is the smallest prime factor of 51? (a) 1 (b) 2 (c) 17 (d) 3
19. 19.A bag has 4 black balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 5 (d) 9
20. 20.Which is the correct factorisation of x² + 13x + 36? (a) (x + 4)(x + 9) (b) (x + 1)(x + 12) (c) (x − 4)(x − 9) (d) (x + 1)(x + 36)
21. 21.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) 42 (d) 21
22. 22.In a class of 21 children, 14 like tea, 7 like coffee and 3 like neither. How many like both? (a) 3 (b) 18 (c) 4 (d) 2
23. 23.What is the median of 22, 35, 32, 25, 4, 14 and 20? (a) 23 (b) 20 (c) 25 (d) 22
24. 24.A bag has 3 white, 6 blue and 4 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 9/13 (b) 4/13 (c) 4/9 (d) 1/3
25. 25.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 20° (c) 160° (d) 200°
26. 26.What is the prime factorisation of 20? (a) 2² × 5 (b) 2³ × 5 (c) 2 × 5² (d) 2 × 5
27. 27.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 10) (b) (x − 5)(x − 6) (c) (x + 5)(x + 6) (d) (x + 1)(x + 30)
28. 28.What is the 30th term of the AP 5, 7, 9, 11, …? (a) 60 (b) 58 (c) 65 (d) 63
29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 4 (b) 6 (c) 5 (d) 7
30. 30.What is the midpoint of the line joining (7, 17) and (13, 5)? (a) (20, 22) (b) (11, 10) (c) (10, 11) (d) (3, 6)
31. 31.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
32. 32.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
33. 33.A bag has 3 green balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 4 (d) 7
34. 34.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 300 (c) 291 (d) 301
35. 35.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
36. 36.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2³ × 3 × 5
37. 37.If a + b = 16 and ab = 48, what is a² + b²? (a) 256 (b) 208 (c) 160 (d) 352
38. 38.What is the midpoint of the line joining (0, 7) and (12, 11)? (a) (9, 6) (b) (12, 18) (c) (6, 9) (d) (6, 2)
39. 39.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 50° (c) 25° (d) 65°
40. 40.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3

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