Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 779 · 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 median of 20, 33, 12, 6 and 1? (a) 12 (b) 13 (c) 6 (d) 20
2. 2.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 57 (c) 54 (d) 18
3. 3.How many prime numbers are there between 30 and 50? (a) 5 (b) 6 (c) 7 (d) 4
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
5. 5.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 45° (b) 65° (c) 160° (d) 135°
6. 6.A bag has 3 black balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 5 (b) 4 (c) 2 (d) 6
7. 7.There are 7 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 14 (c) 28 (d) 21
8. 8.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 24 (d) 48
9. 9.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
10. 10.The mean of 8 numbers is 24. When the number 60 is added to them, what is the new mean? (a) 28 (b) 24 (c) 42 (d) 29
11. 11.What is the 13th term of the AP 20, 29, 38, 47, …? (a) 137 (b) 128 (c) 108 (d) 117
12. 12.In a class of 32 children, 16 like tea, 23 like coffee and 8 like both. How many like neither? (a) 1 (b) 8 (c) 2 (d) 9
13. 13.How many prime numbers are there between 50 and 70? (a) 6 (b) 4 (c) 5 (d) 3
14. 14.The mean of 5 numbers is 27. When the number 3 is added to them, what is the new mean? (a) 24 (b) 15 (c) 23 (d) 27
15. 15.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 1/4 (c) 7/8 (d) 1/7
16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 6 (d) 17
17. 17.In a class of 16 children, 5 like dance, 6 like music and 2 like both. How many like at least one of the two? (a) 11 (b) 16 (c) 9 (d) 7
18. 18.What is the smallest prime factor of 341? (a) 11 (b) 2 (c) 1 (d) 31
19. 19.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 156 (c) 78 (d) 169
20. 20.If a + b = 14 and ab = 45, what is a² + b²? (a) 151 (b) 106 (c) 196 (d) 286
21. 21.What is the mean of 4, 8, 6, 16, 15 and 11? (a) 12 (b) 11 (c) 9 (d) 10
22. 22.What is the mode of 5, 5, 12, 4, 4, 5 and 8? (a) 4 (b) 12 (c) 5 (d) 8
23. 23.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 48) (b) (x + 6)(x + 8) (c) (x − 6)(x − 8) (d) (x + 1)(x + 13)
24. 24.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
25. 25.Using (a − b)² = a² − 2ab + b², what is 46²? (a) 2484 (b) 2916 (c) 2116 (d) 2126
26. 26.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
27. 27.In a class of 44 children, 23 like dance, 22 like music and 9 like neither. How many like both? (a) 35 (b) 1 (c) 10 (d) 9
28. 28.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 72 sq cm (b) 108 sq cm (c) 54 sq cm (d) 216 sq cm
29. 29.What is the mean of 15, 15, 5, 3, 19 and 21? (a) 12 (b) 14 (c) 13 (d) 15
30. 30.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 80° (c) 100° (d) 280°
31. 31.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 1)(x + 14) (c) (x + 7)(x + 8) (d) (x + 1)(x + 56)
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 13 (b) 14 (c) 15 (d) 3
33. 33.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
34. 34.The mean of 4 numbers is 25. When the number 10 is added to them, what is the new mean? (a) 21 (b) 22 (c) 23 (d) 25
35. 35.What is the midpoint of the line joining (9, 3) and (13, 9)? (a) (22, 12) (b) (2, 3) (c) (11, 6) (d) (6, 11)
36. 36.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3486 (c) 3487 (d) 3403
37. 37.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 10 (c) 33 (d) 30
38. 38.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 131 (b) 126 (c) 33 (d) 252
39. 39.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 86° (d) 85°
40. 40.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) 24 (b) 36 (c) 37 (d) 25

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