Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 246 · 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.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) 8 (c) 14 (d) 15
2. 2.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
3. 3.What is the midpoint of the line joining (8, 6) and (10, 16)? (a) (9, 11) (b) (1, 5) (c) (18, 22) (d) (11, 9)
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
5. 5.A drawer has lots of 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) 3 (c) 4 (d) 5
6. 6.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
7. 7.A bag has 5 blue balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 6 (b) 2 (c) 8 (d) 7
8. 8.What is the midpoint of the line joining (3, 2) and (9, 14)? (a) (3, 6) (b) (8, 6) (c) (6, 8) (d) (12, 16)
9. 9.What is the 14th term of the AP 17, 20, 23, 26, …? (a) 59 (b) 56 (c) 42 (d) 39
10. 10.A bag has 5 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 7 (c) 6 (d) 10
11. 11.In a class of 31 children, 16 like tea, 22 like coffee and 8 like both. How many like neither? (a) 9 (b) 2 (c) 1 (d) 8
12. 12.What is the midpoint of the line joining (6, 15) and (18, 9)? (a) (12, 12) (b) (13, 12) (c) (6, 3) (d) (24, 24)
13. 13.What is the 23rd term of the AP 1, 5, 9, 13, …? (a) 92 (b) 89 (c) 93 (d) 88
14. 14.Using (a + b)² = a² + 2ab + b², what is 43²? (a) 1369 (b) 1609 (c) 1849 (d) 1859
15. 15.What is the midpoint of the line joining (7, 6) and (11, 0)? (a) (2, 3) (b) (18, 6) (c) (9, 3) (d) (3, 9)
16. 16.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 105° (c) 150° (d) 75°
17. 17.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
18. 18.In which quadrant does the point (−9, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
19. 19.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 110 (d) 121
20. 20.In a class of 40 children, 22 like cricket, 16 like football and 3 like both. How many like neither? (a) 8 (b) 2 (c) 5 (d) 3
21. 21.What is the missing term in the AP 14, ?, 18, 20, 22? (a) 18 (b) 15 (c) 17 (d) 16
22. 22.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
23. 23.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
24. 24.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
25. 25.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 28 (d) 49
26. 26.How many factors does 19 have? (a) 4 (b) 3 (c) 2 (d) 1
27. 27.The mean of 5 numbers is 22. When the number 28 is added to them, what is the new mean? (a) 23 (b) 22 (c) 25 (d) 24
28. 28.In a class of 19 children, 7 like mangoes, 7 like bananas and 3 like both. How many like only mangoes? (a) 12 (b) 4 (c) 3 (d) 7
29. 29.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 70° (b) 130° (c) 20° (d) 160°
30. 30.The mean of 8 numbers is 34. When the number 61 is added to them, what is the new mean? (a) 38 (b) 34 (c) 37 (d) 36
31. 31.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
32. 32.A bag has 9 red balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 19 (b) 11 (c) 10 (d) 2
33. 33.What is the midpoint of the line joining (8, 9) and (10, 19)? (a) (14, 9) (b) (1, 5) (c) (9, 14) (d) (18, 28)
34. 34.A drawer has lots of yellow 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) 2 (c) 4 (d) 5
35. 35.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 70 (c) 140 (d) 85
36. 36.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 60 (c) 69 (d) 70
37. 37.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 181 (c) 182 (d) 172
38. 38.A drawer has lots of red 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) 4 (b) 2 (c) 5 (d) 3
39. 39.What is the distance between the points (6, 3) and (21, 11)? (a) 18 (b) 23 (c) 289 (d) 17
40. 40.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25

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