Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 131 · 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 book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 297 (c) 288 (d) 270
2. 2.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
3. 3.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) 13 (c) 24 (d) 25
4. 4.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 78 (c) 156 (d) 91
5. 5.A bag has 11 blue balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 22 (b) 12 (c) 2 (d) 13
6. 6.What is the 33rd term of the AP 3, 10, 17, 24, …? (a) 224 (b) 234 (c) 227 (d) 231
7. 7.In which quadrant does the point (2, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
8. 8.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 2/3 (c) 1/4 (d) 1/2
9. 9.How many factors does 59 have? (a) 1 (b) 4 (c) 2 (d) 3
10. 10.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x + 1)(x + 15) (c) (x + 7)(x + 9) (d) (x − 7)(x − 9)
11. 11.A bag has 8 white balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 9 (c) 14 (d) 2
12. 12.How many factors does 70 have? (a) 6 (b) 8 (c) 9 (d) 7
13. 13.How many prime numbers are there between 20 and 30? (a) 4 (b) 3 (c) 2 (d) 1
14. 14.What is the mean of 18, 18, 9, 5 and 20? (a) 13 (b) 16 (c) 14 (d) 15
15. 15.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 22 (d) 15
16. 16.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
17. 17.A drawer has lots of white, black 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) 6 (d) 3
18. 18.A drawer has lots of white, yellow, green, blue 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) 10 (b) 6 (c) 5 (d) 2
19. 19.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 325 (c) 338 (d) 351
20. 20.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 105° (b) 75° (c) 135° (d) 120°
21. 21.A bag has 4 white balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 4 (c) 5 (d) 7
22. 22.In a class of 38 children, 12 like maths, 25 like science and 6 like both. How many like only maths? (a) 12 (b) 6 (c) 13 (d) 19
23. 23.What is the mean of 7, 19, 10 and 16? (a) 12 (b) 15 (c) 13 (d) 14
24. 24.How many factors does 67 have? (a) 3 (b) 2 (c) 1 (d) 4
25. 25.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
26. 26.How many prime numbers are there between 60 and 70? (a) 4 (b) 1 (c) 2 (d) 3
27. 27.What is the median of 16, 10, 37, 3 and 38? (a) 10 (b) 37 (c) 17 (d) 16
28. 28.In a class of 23 children, 9 like maths, 10 like science and 2 like both. How many like neither? (a) 8 (b) 4 (c) 2 (d) 6
29. 29.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 45 (d) 81
30. 30.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
31. 31.In which quadrant does the point (−5, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
32. 32.In a class of 47 children, 28 like mangoes, 22 like bananas and 9 like neither. How many like both? (a) 3 (b) 38 (c) 9 (d) 12
33. 33.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 240 (d) 120
34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
35. 35.How many factors does 53 have? (a) 4 (b) 3 (c) 1 (d) 2
36. 36.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 36 (d) 30
37. 37.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
38. 38.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
39. 39.In a class of 46 children, 28 like mangoes, 24 like bananas and 8 like both. How many like at least one of the two? (a) 44 (b) 52 (c) 46 (d) 36
40. 40.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 120° (c) 300° (d) 30°

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