Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 496 · 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.If a + b = 10 and ab = 9, what is a² + b²? (a) 100 (b) 91 (c) 118 (d) 82
2. 2.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
3. 3.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 3/4 (c) 1/3 (d) 1/2
4. 4.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 143 (b) 286 (c) 23 (d) 154
5. 5.In a class of 23 children, 14 like tea, 9 like coffee and 2 like neither. How many like both? (a) 2 (b) 1 (c) 21 (d) 3
6. 6.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 529 (b) 409 (c) 289 (d) 539
7. 7.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 7 (c) 14 (d) 8
8. 8.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 28 (c) 21 (d) 22
9. 9.How many factors does 45 have? (a) 7 (b) 5 (c) 6 (d) 4
10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 5 (d) 3
11. 11.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 121 (d) 55
12. 12.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 50 (b) 30 (c) 10 (d) 25
13. 13.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
14. 14.Which is the correct factorisation of x² + 11x + 30? (a) (x + 5)(x + 6) (b) (x + 1)(x + 10) (c) (x − 5)(x − 6) (d) (x + 1)(x + 30)
15. 15.A drawer has lots of 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) 4 (c) 5 (d) 3
16. 16.Which is the correct factorisation of x² + 9x + 14? (a) (x + 2)(x + 7) (b) (x + 1)(x + 8) (c) (x + 1)(x + 14) (d) (x − 2)(x − 7)
17. 17.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 12 (d) 16
18. 18.A drawer has lots of yellow, 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) 6 (c) 3 (d) 4
19. 19.A cuboid is 11 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 21 cu cm (b) 66 cu cm (c) 264 cu cm (d) 268 cu cm
20. 20.A bag has 7 yellow balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 10 (c) 9 (d) 2
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
22. 22.A drawer has lots of white, red 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) 3 (b) 6 (c) 2 (d) 4
23. 23.If a + b = 9 and ab = 14, what is (a − b)²? (a) 81 (b) 5 (c) 25 (d) 53
24. 24.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 112 (b) 15 (c) 64 (d) 56
25. 25.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
26. 26.What is the 40th term of the AP 3, 8, 13, 18, …? (a) 203 (b) 200 (c) 195 (d) 198
27. 27.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 8 (c) 18 (d) 24
28. 28.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 120 (d) 25
29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 18 (b) 17 (c) 16 (d) 6
30. 30.6 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 8 (b) 24 (c) 12 (d) 18
31. 31.What is the median of 3, 13, 35, 19 and 15? (a) 19 (b) 35 (c) 15 (d) 17
32. 32.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 33 (b) 31 (c) 41 (d) 32
33. 33.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
34. 34.The mean of 3 numbers is 20. When the number 24 is added to them, what is the new mean? (a) 21 (b) 20 (c) 22 (d) 23
35. 35.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 95° (c) 155° (d) 85°
36. 36.In a class of 30 children, 18 like cricket, 15 like football and 8 like both. How many like neither? (a) 5 (b) 6 (c) 8 (d) 13
37. 37.There are 3 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 10 (c) 42 (d) 21
38. 38.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 45 (c) 36 (d) 81
39. 39.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
40. 40.What is the smallest prime factor of 33? (a) 1 (b) 11 (c) 3 (d) 2

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