Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 874 · 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.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 90° (c) 150° (d) 270°
2. 2.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 156 (c) 169 (d) 78
3. 3.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
4. 4.What is the median of 18, 26, 2, 15 and 24? (a) 2 (b) 24 (c) 17 (d) 18
5. 5.In a class of 33 children, 21 like maths, 18 like science and 12 like both. How many like only maths? (a) 15 (b) 6 (c) 9 (d) 21
6. 6.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 25° (c) 130° (d) 310°
7. 7.What is the mode of 7, 10, 18, 18, 10, 18 and 6? (a) 7 (b) 10 (c) 18 (d) 6
8. 8.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 4 (b) 5 (c) 2 (d) 3
10. 10.A drawer has lots of black, white, 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) 8 (b) 2 (c) 4 (d) 5
11. 11.What is the distance between the points (2, 20) and (14, 4)? (a) 20 (b) 21 (c) 28 (d) 400
12. 12.A drawer has lots of yellow 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) 5 (c) 3 (d) 4
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/11 (c) 1/6 (d) 7/36
14. 14.If a + b = 15 and ab = 56, what is (a − b)²? (a) 169 (b) 225 (c) 113 (d) 1
15. 15.A bag has 7 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) 8 (b) 10 (c) 2 (d) 4
16. 16.What is the mode of 14, 10, 10, 14, 5, 6 and 14? (a) 6 (b) 14 (c) 10 (d) 5
17. 17.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
18. 18.What is the mean of 6, 14, 7 and 17? (a) 12 (b) 10 (c) 13 (d) 11
19. 19.A bag has 3 white balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 4 (c) 5 (d) 12
20. 20.In which quadrant does the point (−1, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
21. 21.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 160° (d) 80°
22. 22.The mean of 8 numbers is 12. When the number 48 is added to them, what is the new mean? (a) 17 (b) 30 (c) 12 (d) 16
23. 23.What is the distance between the points (8, 4) and (12, 7)? (a) 7 (b) 6 (c) 5 (d) 25
24. 24.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 100 (d) 90
25. 25.What is the mean of 13, 14, 18 and 11? (a) 16 (b) 13 (c) 14 (d) 15
26. 26.A bag has 6 black balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 8 (c) 11 (d) 7
27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 16 (b) 14 (c) 15 (d) 4
28. 28.What is the smallest prime factor of 95? (a) 1 (b) 2 (c) 19 (d) 5
29. 29.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 48 (d) 12
30. 30.What is the distance between the points (5, 4) and (11, 12)? (a) 11 (b) 10 (c) 14 (d) 100
31. 31.If a + b = 20 and ab = 96, what is a² + b²? (a) 400 (b) 208 (c) 304 (d) 592
32. 32.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
33. 33.A bag has 5 red balls and 6 white 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) 6 (d) 11
34. 34.The mean of 8 numbers is 19. When the number 1 is added to them, what is the new mean? (a) 18 (b) 17 (c) 19 (d) 10
35. 35.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
36. 36.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 16 (d) 15
38. 38.What is the median of 15, 30, 8, 31, 34, 17 and 39? (a) 31 (b) 29 (c) 30 (d) 17
39. 39.A bag has 2 white, 4 green and 4 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 2/3 (b) 2/5 (c) 3/5 (d) 1/3
40. 40.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 351 (c) 342 (d) 306

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