Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 643 · 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 the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
2. 2.If a + b = 20 and ab = 99, what is a² + b²? (a) 301 (b) 202 (c) 598 (d) 400
3. 3.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 25 (b) 23 (c) 22 (d) 24
4. 4.What is the distance between the points (7, 7) and (22, 15)? (a) 289 (b) 18 (c) 23 (d) 17
5. 5.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
6. 6.A bag has 2 green, 4 yellow and 4 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/10 (b) 1/3 (c) 3/5 (d) 2/5
7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
8. 8.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 470 (b) 46 (c) 235 (d) 260
9. 9.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 15 (b) 6 (c) 17 (d) 16
11. 11.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 20) (b) (x + 4)(x + 5) (c) (x + 1)(x + 8) (d) (x − 4)(x − 5)
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 7/36 (c) 1/6 (d) 6/11
13. 13.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) 7 (b) 14 (c) 15 (d) 8
14. 14.What is the midpoint of the line joining (8, 2) and (20, 10)? (a) (14, 6) (b) (6, 4) (c) (6, 14) (d) (28, 12)
15. 15.In a class of 39 children, 15 like tea, 26 like coffee and 7 like both. How many like only tea? (a) 19 (b) 15 (c) 8 (d) 13
16. 16.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 52 (c) 44 (d) 34
17. 17.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 15° (d) 30°
18. 18.What is the midpoint of the line joining (0, 10) and (6, 8)? (a) (3, 9) (b) (6, 18) (c) (3, 1) (d) (9, 3)
19. 19.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 25° (d) 50°
20. 20.What is the mean of 18, 13, 3, 13, 13 and 18? (a) 12 (b) 15 (c) 13 (d) 14
21. 21.In a class of 30 children, 17 like cricket, 12 like football and 3 like both. How many like only cricket? (a) 18 (b) 9 (c) 17 (d) 14
22. 22.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 298 (c) 339 (d) 340
23. 23.In which quadrant does the point (−4, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
24. 24.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 676 (b) 1166 (c) 916 (d) 1156
25. 25.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 199 (c) 189 (d) 204
26. 26.How many factors does 99 have? (a) 5 (b) 4 (c) 6 (d) 7
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
28. 28.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 522 (b) 49 (c) 266 (d) 261
29. 29.What is the distance between the points (8, 32) and (15, 8)? (a) 26 (b) 25 (c) 31 (d) 625
30. 30.In which quadrant does the point (−7, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
31. 31.What is the mean of 10, 9, 2, 20 and 24? (a) 14 (b) 12 (c) 15 (d) 13
32. 32.A drawer has lots of black, red, white 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) 2 (b) 4 (c) 5 (d) 8
33. 33.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
34. 34.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 21 (c) 25 (d) 10
35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 16 (d) 15
36. 36.In a class of 31 children, 23 like tea, 17 like coffee and 10 like both. How many like neither? (a) 1 (b) 11 (c) 10 (d) 2
37. 37.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 190 (c) 198 (d) 180
38. 38.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 324 (c) 325 (d) 315
39. 39.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 40 (c) 49 (d) 58
40. 40.What is the median of 16, 22, 34, 30 and 5? (a) 30 (b) 34 (c) 22 (d) 16

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