Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 656 · 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 league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 81 (c) 72 (d) 45
2. 2.A bag has 9 green, 4 white and 6 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 13/19 (b) 6/19 (c) 1/3 (d) 14/19
3. 3.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 125° (b) 80° (c) 155° (d) 25°
4. 4.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 15 (c) 45 (d) 18
5. 5.A bag has 10 blue balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 22 (b) 2 (c) 11 (d) 12
6. 6.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 132 (d) 66
7. 7.A drawer has lots of white, blue, red, black and green 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) 5 (c) 6 (d) 10
8. 8.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 96 (c) 56 (d) 14
9. 9.What is the smallest prime factor of 65? (a) 13 (b) 1 (c) 5 (d) 2
10. 10.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 240 (c) 25 (d) 120
11. 11.Which term of the AP 10, 12, 14, 16, … is 30? (a) 12th (b) 11th (c) 15th (d) 10th
12. 12.Using (a − b)² = a² − 2ab + b², what is 56²? (a) 3584 (b) 4096 (c) 3146 (d) 3136
13. 13.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 135° (c) 91° (d) 90°
14. 14.In a class of 29 children, 21 like dance, 7 like music and 4 like both. How many like at least one of the two? (a) 29 (b) 28 (c) 20 (d) 24
15. 15.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
16. 16.A bag has 3 yellow, 5 green and 6 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 5/14 (c) 5/7 (d) 9/14
17. 17.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 78 (d) 91
18. 18.What is the median of 33, 10, 30, 12, 26, 9 and 20? (a) 26 (b) 20 (c) 12 (d) 21
19. 19.A bag has 11 green balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 21 (b) 2 (c) 13 (d) 12
20. 20.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 170° (b) 160° (c) 30° (d) 10°
21. 21.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 32 (c) 12 (d) 64
22. 22.Using (a − b)² = a² − 2ab + b², what is 65²? (a) 4875 (b) 4235 (c) 4225 (d) 5625
23. 23.Which is the correct factorisation of x² + 11x + 30? (a) (x − 5)(x − 6) (b) (x + 5)(x + 6) (c) (x + 1)(x + 10) (d) (x + 1)(x + 30)
24. 24.What is the midpoint of the line joining (1, 5) and (5, 3)? (a) (6, 8) (b) (4, 3) (c) (3, 4) (d) (2, 1)
25. 25.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 48 (d) 58
26. 26.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 105 (d) 225
27. 27.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 5° (d) 275°
28. 28.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 16 (d) 48
29. 29.If a + b = 6 and ab = 5, what is (a − b)²? (a) 26 (b) 36 (c) 16 (d) 4
30. 30.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2³ × 3 (c) 2² × 3 (d) 2⁴ × 3
31. 31.A drawer has lots of blue, black, green, white 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) 2 (b) 10 (c) 5 (d) 6
32. 32.What is the median of 29, 23, 4, 6, 15, 40 and 28? (a) 15 (b) 6 (c) 23 (d) 28
33. 33.Using (a + b)² = a² + 2ab + b², what is 62²? (a) 3604 (b) 3364 (c) 3844 (d) 3854
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 3/11 (c) 1/12 (d) 1/9
35. 35.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 110° (c) 70° (d) 71°
36. 36.In a class of 24 children, 9 like mangoes, 13 like bananas and 5 like both. How many like at least one of the two? (a) 24 (b) 22 (c) 17 (d) 12
37. 37.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
38. 38.In a class of 20 children, 12 like cricket, 10 like football and 4 like both. How many like at least one of the two? (a) 18 (b) 22 (c) 14 (d) 20
39. 39.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 42 (c) 49 (d) 14
40. 40.If a + b = 15 and ab = 56, what is a² + b²? (a) 169 (b) 113 (c) 225 (d) 337

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