Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 561 · 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.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 50° (d) 130°
2. 2.What is the mean of 8, 2, 5, 20 and 10? (a) 11 (b) 9 (c) 8 (d) 10
3. 3.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 37 (c) 25 (d) 36
4. 4.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
5. 5.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 2/11 (d) 1/12
7. 7.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3656 (c) 3655 (d) 3570
8. 8.A bag has 2 red, 7 blue and 3 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/6 (b) 1/3 (c) 11/12 (d) 5/6
9. 9.A cuboid is 9 cm long, 7 cm wide and 6 cm high. What is its total surface area? (a) 636 sq cm (b) 378 sq cm (c) 318 sq cm (d) 159 sq cm
10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
11. 11.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
12. 12.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 75° (d) 30°
13. 13.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 5/6 (c) 1/5 (d) 1/3
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/18 (c) 1/36 (d) 1/11
15. 15.A drawer has lots of white and black 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) 4 (c) 3 (d) 5
16. 16.What is the median of 40, 26, 11, 35, 36, 22 and 32? (a) 32 (b) 35 (c) 33 (d) 26
17. 17.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 45° (b) 115° (c) 110° (d) 135°
18. 18.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 125° (d) 305°
19. 19.What is the distance between the points (4, 0) and (28, 7)? (a) 625 (b) 25 (c) 26 (d) 31
20. 20.A bag has 4 white, 7 green and 4 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 4/15 (b) 11/15 (c) 4/11 (d) 1/3
21. 21.In a class of 20 children, 14 like mangoes, 7 like bananas and 3 like both. How many like only mangoes? (a) 14 (b) 13 (c) 11 (d) 4
22. 22.A drawer has lots of red, white, black 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) 4 (c) 5 (d) 2
23. 23.In a class of 27 children, 23 like dance, 10 like music and 1 like neither. How many like both? (a) 6 (b) 1 (c) 26 (d) 7
24. 24.The mean of 4 numbers is 12. When the number 7 is added to them, what is the new mean? (a) 10 (b) 13 (c) 12 (d) 11
25. 25.What is the 20th term of the AP 17, 21, 25, 29, …? (a) 76 (b) 97 (c) 80 (d) 93
26. 26.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 120 (d) 25
27. 27.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 2/3 (c) 5/6 (d) 1/4
28. 28.What is the sum of the roots of x² − 13x + 36 = 0? (a) 14 (b) 12 (c) 36 (d) 13
29. 29.The mean of 5 numbers is 40. When the number 46 is added to them, what is the new mean? (a) 42 (b) 40 (c) 43 (d) 41
30. 30.What is the median of 20, 19, 40, 1, 37, 22 and 5? (a) 20 (b) 22 (c) 1 (d) 19
31. 31.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 595 (c) 594 (d) 585
32. 32.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) 2 (b) 5 (c) 4 (d) 3
33. 33.A bag has 5 black 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) 6 (b) 10 (c) 14 (d) 2
34. 34.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 14 (b) 15 (c) 16 (d) 5
36. 36.What are the roots of x² − 8x + 12 = 0? (a) 3 and 4 (b) 2 and 6 (c) 1 and 12 (d) 1 and 7
37. 37.A bag has 6 white balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 17 (b) 2 (c) 7 (d) 8
38. 38.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 2 (d) 1
39. 39.What is the distance between the points (8, 28) and (15, 4)? (a) 31 (b) 625 (c) 26 (d) 25
40. 40.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 132 (d) 66

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