Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 877 · 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.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
2. 2.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 225 (b) 635 (c) 425 (d) 625
3. 3.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 80° (d) 105°
4. 4.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 453 (c) 444 (d) 374
5. 5.If a + b = 10 and ab = 24, what is (a − b)²? (a) 52 (b) 2 (c) 100 (d) 4
6. 6.What is the mode of 6, 15, 15, 15, 11, 8 and 6? (a) 11 (b) 8 (c) 6 (d) 15
7. 7.How many prime numbers are there between 60 and 80? (a) 4 (b) 6 (c) 5 (d) 7
8. 8.A bag has 6 blue balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 8 (c) 2 (d) 13
9. 9.What is the sum of the roots of x² − 13x + 40 = 0? (a) 12 (b) 13 (c) 14 (d) 40
10. 10.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 5 (d) 6
11. 11.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 40° (c) 41° (d) 80°
12. 12.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 30° (d) 150°
13. 13.What is the mean of 17, 13, 20, 9, 6 and 7? (a) 11 (b) 14 (c) 13 (d) 12
14. 14.What is the smallest prime factor of 209? (a) 19 (b) 2 (c) 11 (d) 1
15. 15.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) 8 (c) 14 (d) 7
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 16 (b) 15 (c) 4 (d) 14
17. 17.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/4
18. 18.What is the mean of 13, 16, 6 and 9? (a) 12 (b) 11 (c) 10 (d) 13
19. 19.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 42 (d) 14
20. 20.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 40° (b) 220° (c) 110° (d) 140°
21. 21.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 231 (d) 41
22. 22.A drawer has lots of red, yellow, 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) 5 (b) 2 (c) 8 (d) 4
23. 23.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 28 (c) 42 (d) 49
24. 24.What is the mean of 2, 8, 18, 16, 12 and 22? (a) 15 (b) 12 (c) 14 (d) 13
25. 25.What is the median of 13, 12, 15, 9 and 26? (a) 14 (b) 12 (c) 15 (d) 13
26. 26.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/4 (d) 1/3
27. 27.What is the 10th term of the AP 18, 21, 24, 27, …? (a) 48 (b) 30 (c) 45 (d) 27
28. 28.What is the midpoint of the line joining (0, 0) and (6, 12)? (a) (3, 6) (b) (6, 12) (c) (6, 3) (d) (4, 6)
29. 29.A bag has 7 yellow balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 19 (c) 8 (d) 2
30. 30.Which is the correct factorisation of x² + 12x + 35? (a) (x + 1)(x + 35) (b) (x + 1)(x + 11) (c) (x − 5)(x − 7) (d) (x + 5)(x + 7)
31. 31.What is the smallest prime factor of 121? (a) 3 (b) 2 (c) 1 (d) 11
32. 32.A cuboid is 6 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 288 sq cm (b) 72 sq cm (c) 144 sq cm (d) 108 sq cm
33. 33.If a + b = 15 and ab = 50, what is (a − b)²? (a) 125 (b) 5 (c) 225 (d) 25
34. 34.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7² (c) 2 × 3 × 7 (d) 2² × 3 × 7
35. 35.What is the mode of 8, 12, 6, 4, 6, 4 and 4? (a) 4 (b) 8 (c) 12 (d) 6
36. 36.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 48 (d) 16
37. 37.How many factors does 19 have? (a) 2 (b) 4 (c) 3 (d) 1
38. 38.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1711 (c) 1682 (d) 1653
39. 39.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
40. 40.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2

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