Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 105 · 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 black, green and yellow 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) 3 (d) 6
2. 2.In a class of 25 children, 9 like tea, 17 like coffee and 2 like both. How many like at least one of the two? (a) 26 (b) 24 (c) 22 (d) 25
3. 3.A bag has 2 blue, 2 green and 7 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 4/7 (b) 4/11 (c) 1/3 (d) 7/11
4. 4.How many prime numbers are there between 80 and 90? (a) 2 (b) 1 (c) 4 (d) 3
5. 5.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 25 (c) 10 (d) 20
6. 6.How many prime numbers are there between 80 and 100? (a) 4 (b) 3 (c) 5 (d) 2
7. 7.A bag has 6 white balls and 9 red 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) 7 (c) 15 (d) 10
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
9. 9.In a class of 41 children, 22 like maths, 19 like science and 6 like both. How many like neither? (a) 7 (b) 6 (c) 12 (d) 0
10. 10.What is the median of 38, 3, 23, 4 and 28? (a) 4 (b) 23 (c) 24 (d) 28
11. 11.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 78 (c) 169 (d) 91
12. 12.How many factors does 57 have? (a) 3 (b) 5 (c) 2 (d) 4
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/11 (c) 1/12 (d) 3/11
14. 14.If a + b = 8 and ab = 15, what is a² + b²? (a) 64 (b) 49 (c) 34 (d) 94
15. 15.How many prime numbers are there between 70 and 90? (a) 5 (b) 6 (c) 7 (d) 4
16. 16.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 160° (d) 75°
17. 17.In which quadrant does the point (9, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
18. 18.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 190 (d) 200
19. 19.What are the roots of x² − 11x + 30 = 0? (a) 5 and 6 (b) 2 and 15 (c) 1 and 30 (d) 1 and 10
20. 20.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
21. 21.How many factors does 46 have? (a) 5 (b) 2 (c) 4 (d) 3
22. 22.What is the smallest prime factor of 299? (a) 13 (b) 2 (c) 1 (d) 23
23. 23.What is the median of 8, 25, 14, 17, 40, 6 and 11? (a) 15 (b) 14 (c) 11 (d) 17
24. 24.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 145° (c) 215° (d) 35°
25. 25.A bag has 3 white balls and 8 red 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) 11 (d) 4
26. 26.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) 2 (b) 3 (c) 5 (d) 4
27. 27.In which quadrant does the point (−1, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
28. 28.In a class of 31 children, 12 like mangoes, 14 like bananas and 5 like both. How many like neither? (a) 10 (b) 5 (c) 11 (d) 15
29. 29.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 20 (d) 18
31. 31.If a + b = 17 and ab = 72, what is (a − b)²? (a) 1 (b) 217 (c) 145 (d) 289
32. 32.In a class of 32 children, 17 like tea, 21 like coffee and 1 like neither. How many like both? (a) 7 (b) 1 (c) 6 (d) 31
33. 33.If a + b = 19 and ab = 88, what is (a − b)²? (a) 361 (b) 3 (c) 9 (d) 185
34. 34.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 121 (d) 66
35. 35.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 10100 (c) 4950 (d) 5000
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
37. 37.A bag has 4 blue balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 9 (d) 12
38. 38.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 70 (c) 8 (d) 35
39. 39.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/3 (c) 1/2 (d) 3/4
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 3/11 (c) 1/12 (d) 1/11

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