Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 830 · 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.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 36 (c) 37 (d) 49
2. 2.A bag has 6 blue, 7 red and 3 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 3/8 (c) 11/16 (d) 5/8
3. 3.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
4. 4.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
5. 5.How many prime numbers are there between 50 and 70? (a) 3 (b) 6 (c) 5 (d) 4
6. 6.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
7. 7.A bag has 10 blue balls and 11 red 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) 11 (c) 21 (d) 12
8. 8.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) 36 (b) 24 (c) 37 (d) 25
9. 9.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
10. 10.What is the mean of 13, 19, 11 and 21? (a) 15 (b) 17 (c) 16 (d) 18
11. 11.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 80° (d) 50°
12. 12.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 70° (c) 110° (d) 150°
13. 13.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 2702 (c) 5402 (d) 2701
14. 14.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 40° (c) 50° (d) 130°
15. 15.What is the midpoint of the line joining (7, 21) and (17, 9)? (a) (15, 12) (b) (5, 6) (c) (12, 15) (d) (24, 30)
16. 16.What are the roots of x² − 15x + 56 = 0? (a) 1 and 56 (b) 2 and 28 (c) 7 and 8 (d) 1 and 14
17. 17.In a class of 26 children, 11 like mangoes, 12 like bananas and 6 like both. How many like at least one of the two? (a) 11 (b) 23 (c) 26 (d) 17
18. 18.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 40° (c) 140° (d) 50°
19. 19.What is the missing term in the AP 15, 22, ?, 36, 43? (a) 36 (b) 29 (c) 30 (d) 28
20. 20.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 20 (c) 100 (d) 90
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/12 (d) 1/9
22. 22.If a + b = 14 and ab = 33, what is (a − b)²? (a) 8 (b) 196 (c) 64 (d) 130
23. 23.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 36 (d) 12
24. 24.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 24 (c) 12 (d) 8
25. 25.What is the 18th term of the AP 10, 12, 14, 16, …? (a) 46 (b) 34 (c) 44 (d) 36
26. 26.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 110 (d) 55
27. 27.What is the mean of 6, 5, 20, 5, 18 and 12? (a) 10 (b) 11 (c) 13 (d) 12
28. 28.Which is the correct factorisation of x² + 6x + 8? (a) (x + 1)(x + 8) (b) (x + 1)(x + 5) (c) (x − 2)(x − 4) (d) (x + 2)(x + 4)
29. 29.What is the median of 19, 25, 36, 21, 22, 8 and 28? (a) 25 (b) 21 (c) 22 (d) 23
30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 9 (d) 19
31. 31.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 55° (d) 70°
32. 32.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 16 (d) 24
33. 33.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
34. 34.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 5/6 (b) 1/3 (c) 1/4 (d) 2/3
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/9 (c) 1/11 (d) 5/36
36. 36.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
37. 37.How many prime numbers are there between 50 and 80? (a) 8 (b) 7 (c) 9 (d) 6
38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 8 (d) 17
39. 39.If a + b = 9 and ab = 8, what is a² + b²? (a) 65 (b) 97 (c) 73 (d) 81
40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11

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