Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 543 · 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 55° each. What is the third angle? (a) 125° (b) 70° (c) 55° (d) 35°
2. 2.Using (a + b)² = a² + 2ab + b², what is 73²? (a) 5329 (b) 4909 (c) 5339 (d) 4489
3. 3.How many factors does 98 have? (a) 5 (b) 4 (c) 6 (d) 7
4. 4.In a class of 30 children, 12 like tea, 18 like coffee and 4 like both. How many like at least one of the two? (a) 26 (b) 22 (c) 30 (d) 27
5. 5.What is the midpoint of the line joining (3, 14) and (5, 10)? (a) (12, 4) (b) (1, 2) (c) (8, 24) (d) (4, 12)
6. 6.What is the mode of 8, 3, 3, 14, 7, 8 and 3? (a) 14 (b) 8 (c) 3 (d) 7
7. 7.What is the median of 40, 10, 22, 30 and 39? (a) 31 (b) 22 (c) 39 (d) 30
8. 8.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
9. 9.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
10. 10.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
11. 11.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2² × 5 × 7
12. 12.What is the prime factorisation of 336? (a) 2 × 3 × 7⁴ (b) 2⁴ × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁵ × 3 × 7
13. 13.What is the distance between the points (8, 8) and (17, 20)? (a) 225 (b) 16 (c) 21 (d) 15
14. 14.What is the midpoint of the line joining (4, 14) and (6, 10)? (a) (10, 24) (b) (1, 2) (c) (5, 12) (d) (12, 5)
15. 15.Using (a + b)² = a² + 2ab + b², what is 51²? (a) 2601 (b) 2401 (c) 2501 (d) 2611
16. 16.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
17. 17.A bag has 6 yellow balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 7 (c) 11 (d) 8
18. 18.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) 30° (d) 75°
19. 19.A bag has 7 yellow, 8 red and 6 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 2/7 (b) 16/21 (c) 5/7 (d) 1/3
20. 20.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 176 (c) 185 (d) 194
21. 21.What is the mode of 19, 4, 2, 16, 4, 4 and 16? (a) 4 (b) 19 (c) 16 (d) 2
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
23. 23.What is the sum of the roots of x² − 10x + 16 = 0? (a) 9 (b) 16 (c) 10 (d) 11
24. 24.What is the mean of 2, 15, 10 and 13? (a) 8 (b) 11 (c) 9 (d) 10
25. 25.A bag has 6 red balls and 4 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) 5 (c) 7 (d) 10
26. 26.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 48 (c) 58 (d) 57
27. 27.What is the prime factorisation of 35? (a) 5 × 7² (b) 5³ × 7 (c) 5 × 7 (d) 5² × 7
28. 28.The mean of 3 numbers is 34. When the number 30 is added to them, what is the new mean? (a) 32 (b) 33 (c) 35 (d) 34
29. 29.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 41° (c) 40° (d) 140°
30. 30.The mean of 9 numbers is 21. When the number 51 is added to them, what is the new mean? (a) 36 (b) 21 (c) 25 (d) 24
31. 31.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 2/3 (c) 5/6 (d) 1/3
32. 32.The mean of 3 numbers is 14. When the number 10 is added to them, what is the new mean? (a) 14 (b) 15 (c) 12 (d) 13
33. 33.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 22 (c) 198 (d) 69
34. 34.A drawer has lots of red, blue, green, black 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) 10 (b) 6 (c) 5 (d) 2
35. 35.The mean of 3 numbers is 21. When the number 5 is added to them, what is the new mean? (a) 13 (b) 17 (c) 21 (d) 18
36. 36.A drawer has lots of green, black, white, red 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) 6 (b) 10 (c) 2 (d) 5
37. 37.How many prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 8 (d) 6
38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 6 (b) 4 (c) 3 (d) 5
39. 39.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
40. 40.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 5/6 (b) 1/6 (c) 1/3 (d) 1/5

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