Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 67 · 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.In a class of 29 children, 8 like tea, 24 like coffee and 5 like both. How many like only tea? (a) 3 (b) 8 (c) 5 (d) 19
2. 2.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 10) (b) (x + 1)(x + 6) (c) (x + 2)(x + 5) (d) (x − 2)(x − 5)
3. 3.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
4. 4.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
5. 5.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 32 sq cm (b) 12 sq cm (c) 64 sq cm (d) 16 sq cm
6. 6.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
7. 7.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 56 (c) 36 (d) 28
8. 8.What is the 36th term of the AP 1, 4, 7, 10, …? (a) 108 (b) 105 (c) 106 (d) 109
9. 9.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
10. 10.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 110 (d) 22
11. 11.The mean of 9 numbers is 20. When the number 10 is added to them, what is the new mean? (a) 15 (b) 19 (c) 18 (d) 20
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/18 (c) 1/11 (d) 1/12
13. 13.What is the median of 17, 3, 27, 33, 13, 10 and 37? (a) 27 (b) 20 (c) 33 (d) 17
14. 14.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 30° (c) 31° (d) 150°
15. 15.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) 10 (b) 90 (c) 33 (d) 30
16. 16.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
17. 17.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 130° (d) 70°
18. 18.In a class of 22 children, 15 like dance, 8 like music and 5 like both. How many like at least one of the two? (a) 23 (b) 13 (c) 18 (d) 22
19. 19.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
20. 20.What is the mean of 4, 11, 4 and 13? (a) 10 (b) 7 (c) 9 (d) 8
21. 21.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 14 (b) 12 (c) 13 (d) 15
22. 22.There are 6 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 36 (c) 18 (d) 24
23. 23.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 36 (d) 81
24. 24.What is the smallest prime factor of 221? (a) 2 (b) 1 (c) 17 (d) 13
25. 25.What is the 27th term of the AP 9, 11, 13, 15, …? (a) 54 (b) 52 (c) 61 (d) 63
26. 26.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 12 (d) 16
27. 27.A bag has 4 red balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 7 (c) 2 (d) 5
28. 28.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 5/6 (c) 1/3 (d) 2/3
29. 29.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) 24 (c) 13 (d) 12
30. 30.In a class of 40 children, 10 like maths, 26 like science and 6 like both. How many like neither? (a) 4 (b) 10 (c) 16 (d) 6
31. 31.In a class of 23 children, 15 like dance, 9 like music and 2 like neither. How many like both? (a) 3 (b) 2 (c) 21 (d) 1
32. 32.Which is the correct factorisation of x² + 12x + 32? (a) (x + 4)(x + 8) (b) (x + 1)(x + 11) (c) (x − 4)(x − 8) (d) (x + 1)(x + 32)
33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 18 (d) 19
34. 34.In a class of 24 children, 14 like cricket, 15 like football and 8 like both. How many like only cricket? (a) 6 (b) 9 (c) 14 (d) 7
35. 35.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
36. 36.If a + b = 15 and ab = 56, what is a² + b²? (a) 225 (b) 337 (c) 169 (d) 113
37. 37.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
38. 38.If a + b = 14 and ab = 33, what is a² + b²? (a) 130 (b) 196 (c) 262 (d) 163
39. 39.The mean of 4 numbers is 22. When the number 2 is added to them, what is the new mean? (a) 22 (b) 12 (c) 19 (d) 18
40. 40.What is the product of the roots of x² − 14x + 45 = 0? (a) 44 (b) 45 (c) 46 (d) 14

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