Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 822 · 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 drawer has lots of red 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) 4 (b) 3 (c) 2 (d) 5
2. 2.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 336 (c) 296 (d) 327
3. 3.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 36 (c) 99 (d) 33
4. 4.In a class of 33 children, 22 like tea, 9 like coffee and 6 like both. How many like at least one of the two? (a) 31 (b) 19 (c) 33 (d) 25
5. 5.The mean of 4 numbers is 33. When the number 28 is added to them, what is the new mean? (a) 34 (b) 31 (c) 33 (d) 32
6. 6.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 100° (b) 65° (c) 115° (d) 145°
7. 7.In a class of 28 children, 6 like cricket, 17 like football and 3 like both. How many like at least one of the two? (a) 17 (b) 28 (c) 23 (d) 20
8. 8.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 7/8 (c) 1/7 (d) 1/4
9. 9.The mean of 8 numbers is 32. When the number 23 is added to them, what is the new mean? (a) 30 (b) 33 (c) 32 (d) 31
10. 10.If a + b = 7 and ab = 10, what is a² + b²? (a) 29 (b) 69 (c) 39 (d) 49
11. 11.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) 12 (b) 24 (c) 25 (d) 13
12. 12.A bag has 8 blue balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 12 (c) 9 (d) 10
13. 13.The mean of 8 numbers is 32. When the number 59 is added to them, what is the new mean? (a) 34 (b) 32 (c) 35 (d) 36
14. 14.A bag has 7 blue balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 8 (c) 16 (d) 9
15. 15.In a class of 38 children, 22 like cricket, 22 like football and 11 like both. How many like at least one of the two? (a) 22 (b) 44 (c) 38 (d) 33
16. 16.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
17. 17.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 1/3 (c) 1/6 (d) 5/6
18. 18.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 37 (b) 48 (c) 36 (d) 49
19. 19.What is the distance between the points (4, 9) and (7, 5)? (a) 5 (b) 25 (c) 7 (d) 6
20. 20.A drawer has lots of yellow, blue 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) 4 (b) 3 (c) 6 (d) 2
21. 21.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 328 (c) 375 (d) 384
22. 22.What is the median of 21, 32, 17, 40, 11, 24 and 14? (a) 40 (b) 21 (c) 17 (d) 24
23. 23.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
24. 24.Using (a + b)² = a² + 2ab + b², what is 72²? (a) 5194 (b) 5184 (c) 4624 (d) 4904
25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 2 (b) 4 (c) 5 (d) 3
26. 26.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 384 (b) 204 (c) 192 (d) 27
27. 27.What is the median of 21, 31, 28, 39, 6, 34 and 9? (a) 39 (b) 31 (c) 28 (d) 24
28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 15 (b) 14 (c) 5 (d) 16
29. 29.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 120° (b) 145° (c) 95° (d) 85°
30. 30.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 144 (c) 66 (d) 132
31. 31.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 49 (d) 28
32. 32.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 190° (c) 10° (d) 95°
33. 33.What is the mean of 8, 18, 3, 16, 10 and 11? (a) 11 (b) 10 (c) 13 (d) 12
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
35. 35.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 27) (b) (x + 3)(x + 9) (c) (x + 1)(x + 11) (d) (x − 3)(x − 9)
36. 36.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 231 (b) 462 (c) 253 (d) 41
37. 37.If a + b = 20 and ab = 96, what is (a − b)²? (a) 208 (b) 400 (c) 4 (d) 16
38. 38.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 245 (b) 242 (c) 484 (d) 37
39. 39.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) 14 (b) 7 (c) 15 (d) 8
40. 40.The mean of 3 numbers is 27. When the number 15 is added to them, what is the new mean? (a) 25 (b) 27 (c) 24 (d) 21

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