Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 12 · 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 fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
2. 2.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 72 (c) 90 (d) 81
3. 3.4 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 6 (c) 8 (d) 12
4. 4.What is the distance between the points (6, 5) and (9, 9)? (a) 25 (b) 6 (c) 5 (d) 7
5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 5 (b) 14 (c) 16 (d) 15
6. 6.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 6 (d) 5
7. 7.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 150° (d) 155°
8. 8.A bag has 7 red balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 9 (b) 18 (c) 8 (d) 2
9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 4 (d) 16
10. 10.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
11. 11.A bag has 7 red balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 8 (b) 2 (c) 10 (d) 9
12. 12.A drawer has lots of red, yellow, 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) 5 (b) 8 (c) 4 (d) 2
13. 13.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
14. 14.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 2/11 (c) 1/18 (d) 1/12
16. 16.What is the distance between the points (4, 5) and (10, 13)? (a) 100 (b) 14 (c) 10 (d) 11
17. 17.What is the sum of the roots of x² − 17x + 72 = 0? (a) 72 (b) 18 (c) 17 (d) 16
18. 18.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) 15 (b) 7 (c) 8 (d) 14
19. 19.A bag has 12 green balls and 9 black 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) 10 (c) 13 (d) 21
20. 20.6 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 60 (b) 11 (c) 36 (d) 30
21. 21.What is the 40th term of the AP 9, 17, 25, 33, …? (a) 329 (b) 312 (c) 320 (d) 321
22. 22.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 16 (c) 72 (d) 80
23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
24. 24.What is the mode of 2, 10, 16, 5, 10, 2 and 2? (a) 2 (b) 10 (c) 5 (d) 16
25. 25.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
26. 26.A bag has 3 red, 8 blue and 3 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 11/14 (b) 3/14 (c) 1/3 (d) 6/7
27. 27.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 15 (c) 48 (d) 135
28. 28.A bag has 9 red, 6 white and 2 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 16/17 (b) 1/3 (c) 2/17 (d) 15/17
29. 29.The mean of 8 numbers is 10. When the number 37 is added to them, what is the new mean? (a) 14 (b) 13 (c) 12 (d) 10
30. 30.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 45° (b) 135° (c) 100° (d) 125°
31. 31.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 460 (c) 378 (d) 459
32. 32.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
33. 33.A bag has 3 red, 4 yellow and 4 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 4/11 (b) 1/3 (c) 7/11 (d) 4/7
34. 34.In a class of 42 children, 22 like dance, 15 like music and 2 like both. How many like only dance? (a) 13 (b) 27 (c) 22 (d) 20
35. 35.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
36. 36.How many prime numbers are there between 60 and 70? (a) 1 (b) 3 (c) 4 (d) 2
37. 37.What is the midpoint of the line joining (6, 11) and (12, 7)? (a) (3, 2) (b) (10, 9) (c) (18, 18) (d) (9, 9)
38. 38.A bag has 3 red balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 13 (c) 2 (d) 4
39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 14 (d) 15
40. 40.A drawer has lots of yellow, black, white, green 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) 5 (c) 6 (d) 10

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