Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 839 · 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. 1.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 45 (c) 55 (d) 90
2. 2.A drawer has lots of blue, white, 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) 8
3. 3.A drawer has lots of yellow, green 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) 6 (b) 4 (c) 2 (d) 3
4. 4.In which quadrant does the point (3, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
5. 5.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 11 (b) 132 (c) 66 (d) 67
6. 6.A bag has 8 red balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 9 (c) 4 (d) 2
7. 7.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 220° (c) 41° (d) 140°
8. 8.In a class of 41 children, 15 like dance, 21 like music and 4 like both. How many like at least one of the two? (a) 36 (b) 41 (c) 32 (d) 28
9. 9.In a class of 32 children, 21 like dance, 13 like music and 7 like both. How many like only dance? (a) 6 (b) 21 (c) 14 (d) 19
10. 10.In a class of 48 children, 28 like tea, 28 like coffee and 10 like both. How many like only tea? (a) 28 (b) 20 (c) 18 (d) 10
11. 11.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 11 (c) 30 (d) 36
12. 12.A bag has 10 blue balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 12 (c) 17 (d) 11
13. 13.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
14. 14.How many prime numbers are there between 50 and 70? (a) 6 (b) 4 (c) 5 (d) 3
15. 15.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 361 (b) 360 (c) 312 (d) 351
16. 16.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
17. 17.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
18. 18.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
19. 19.What is the 39th term of the AP 13, 22, 31, 40, …? (a) 342 (b) 351 (c) 364 (d) 355
20. 20.What is the mean of 9, 18, 3, 17, 14 and 11? (a) 12 (b) 14 (c) 13 (d) 11
21. 21.A bag has 6 red 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) 7 (d) 9
22. 22.A bag has 4 green 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) 5 (c) 8 (d) 6
23. 23.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) 5 (c) 2 (d) 3
24. 24.A bag has 9 blue balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 10 (c) 2 (d) 20
25. 25.What is the smallest prime factor of 55? (a) 2 (b) 1 (c) 5 (d) 11
26. 26.What is the midpoint of the line joining (8, 4) and (16, 0)? (a) (2, 12) (b) (4, 2) (c) (24, 4) (d) (12, 2)
27. 27.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) 5 (b) 4 (c) 2 (d) 3
28. 28.A bag has 6 blue balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 7 (d) 4
29. 29.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 104 (c) 114 (d) 113
30. 30.In which quadrant does the point (5, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
31. 31.Which term of the AP 16, 18, 20, 22, … is 70? (a) 28th (b) 27th (c) 35th (d) 29th
32. 32.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 10 (b) 48 (c) 45 (d) 90
33. 33.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 42 (c) 45 (d) 14
34. 34.In a class of 31 children, 13 like tea, 17 like coffee and 5 like neither. How many like both? (a) 3 (b) 4 (c) 5 (d) 26
35. 35.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
36. 36.In a class of 39 children, 14 like cricket, 29 like football and 10 like both. How many like only cricket? (a) 4 (b) 10 (c) 14 (d) 19
37. 37.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 112 (c) 103 (d) 94
38. 38.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) 125 times (c) 25 times (d) 10 times
39. 39.What is the product of the roots of x² − 16x + 63 = 0? (a) 16 (b) 62 (c) 63 (d) 64
40. 40.A bag has 8 black balls and 4 blue 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) 9 (c) 12 (d) 5

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