Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 65 · 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.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
2. 2.A drawer has lots of yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 3 (c) 4 (d) 2
3. 3.A drawer has lots of blue, red, yellow, green and black 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) 6 (c) 5 (d) 10
4. 4.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 27 (b) 170 (c) 85 (d) 90
5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 7 (b) 16 (c) 18 (d) 17
6. 6.What is the 28th term of the AP 10, 17, 24, 31, …? (a) 206 (b) 189 (c) 199 (d) 196
7. 7.The mean of 4 numbers is 40. When the number 25 is added to them, what is the new mean? (a) 38 (b) 36 (c) 37 (d) 40
8. 8.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
9. 9.What is the distance between the points (1, 6) and (4, 10)? (a) 6 (b) 5 (c) 7 (d) 25
10. 10.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 1/12 (d) 2/11
12. 12.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 155° (b) 95° (c) 85° (d) 110°
13. 13.What is the distance between the points (9, 4) and (21, 9)? (a) 13 (b) 14 (c) 17 (d) 169
14. 14.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 24 (d) 48
15. 15.A bag has 9 red balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 2 (c) 18 (d) 11
16. 16.What is the distance between the points (1, 3) and (17, 15)? (a) 400 (b) 21 (c) 28 (d) 20
17. 17.A cuboid is 9 cm long, 8 cm wide and 2 cm high. What is its total surface area? (a) 424 sq cm (b) 144 sq cm (c) 212 sq cm (d) 106 sq cm
18. 18.What is the distance between the points (1, 1) and (17, 13)? (a) 28 (b) 400 (c) 20 (d) 21
19. 19.In a class of 49 children, 22 like cricket, 27 like football and 7 like neither. How many like both? (a) 6 (b) 42 (c) 8 (d) 7
20. 20.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 6 cu cm (b) 42 cu cm (c) 12 cu cm (d) 82 cu cm
21. 21.A drawer has lots of red, yellow, black 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) 4 (b) 5 (c) 2 (d) 8
22. 22.A bag has 4 red balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 5 (c) 6 (d) 2
23. 23.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 80 (c) 40 (d) 13
24. 24.What is the sum of the roots of x² − 9x + 18 = 0? (a) 18 (b) 8 (c) 10 (d) 9
25. 25.What are the roots of x² − 12x + 35 = 0? (a) 2 and 10 (b) 1 and 35 (c) 5 and 7 (d) 1 and 11
26. 26.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 1)(x + 12) (c) (x + 6)(x + 7) (d) (x − 6)(x − 7)
27. 27.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
28. 28.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 90° (b) 60° (c) 150° (d) 120°
29. 29.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 225 (b) 625 (c) 635 (d) 425
30. 30.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 100 (d) 90
31. 31.In a class of 38 children, 24 like dance, 18 like music and 9 like both. How many like at least one of the two? (a) 24 (b) 42 (c) 38 (d) 33
32. 32.There are 3 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 8 (b) 30 (c) 15 (d) 18
33. 33.In a class of 44 children, 22 like maths, 23 like science and 11 like both. How many like neither? (a) 9 (b) 10 (c) 11 (d) 21
34. 34.There are 5 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) 20 (b) 15 (c) 8 (d) 30
35. 35.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 45 (c) 15 (d) 135
36. 36.What is the midpoint of the line joining (8, 4) and (18, 0)? (a) (2, 13) (b) (5, 2) (c) (13, 2) (d) (26, 4)
37. 37.What is the mode of 10, 18, 11, 16, 16, 10 and 16? (a) 16 (b) 11 (c) 10 (d) 18
38. 38.A bag has 5 red, 4 green and 4 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 8/13 (b) 9/13 (c) 5/13 (d) 1/3
39. 39.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
40. 40.What is the distance between the points (1, 7) and (9, 1)? (a) 100 (b) 14 (c) 11 (d) 10

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