Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 419 · 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 two of them were born in the same day of the week? (a) 14 (b) 8 (c) 7 (d) 15
2. 2.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 36 (c) 81 (d) 72
3. 3.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
4. 4.4 T-shirts and 3 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) 12 (c) 24 (d) 7
5. 5.What is the mean of 16, 14, 15, 14 and 11? (a) 16 (b) 13 (c) 14 (d) 15
6. 6.How many prime numbers are there between 50 and 70? (a) 6 (b) 5 (c) 3 (d) 4
7. 7.Which term of the AP 6, 13, 20, 27, … is 279? (a) 41st (b) 42nd (c) 40th (d) 39th
8. 8.In a class of 31 children, 21 like dance, 13 like music and 4 like both. How many like neither? (a) 4 (b) 5 (c) 2 (d) 1
9. 9.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 45 (c) 20 (d) 100
10. 10.Which is the correct factorisation of x² + 10x + 21? (a) (x + 1)(x + 9) (b) (x + 1)(x + 21) (c) (x + 3)(x + 7) (d) (x − 3)(x − 7)
11. 11.A bag has 11 green balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 13 (b) 2 (c) 12 (d) 18
12. 12.A bag has 6 yellow balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 8 (c) 2 (d) 7
13. 13.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 250° (d) 71°
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/36 (c) 5/11 (d) 1/6
15. 15.What is the 15th term of the AP 3, 9, 15, 21, …? (a) 87 (b) 84 (c) 90 (d) 93
16. 16.What is the distance between the points (8, 17) and (20, 8)? (a) 225 (b) 15 (c) 21 (d) 16
17. 17.How many factors does 92 have? (a) 7 (b) 5 (c) 6 (d) 4
18. 18.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 3 (d) 12
19. 19.What is the midpoint of the line joining (10, 10) and (18, 22)? (a) (16, 14) (b) (14, 16) (c) (4, 6) (d) (28, 32)
20. 20.How many factors does 101 have? (a) 1 (b) 2 (c) 4 (d) 3
21. 21.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 399 (b) 441 (c) 371 (d) 361
22. 22.A bag has 3 red balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 2 (c) 13 (d) 11
23. 23.How many factors does 41 have? (a) 1 (b) 3 (c) 4 (d) 2
24. 24.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 150° (c) 30° (d) 25°
25. 25.What is the median of 15, 1, 39, 13, 32, 2 and 30? (a) 16 (b) 13 (c) 30 (d) 15
26. 26.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 40° (d) 30°
27. 27.What is the distance between the points (4, 8) and (11, 32)? (a) 31 (b) 26 (c) 25 (d) 625
28. 28.How many prime numbers are there between 40 and 60? (a) 5 (b) 6 (c) 4 (d) 7
29. 29.If a + b = 12 and ab = 35, what is (a − b)²? (a) 74 (b) 4 (c) 144 (d) 2
30. 30.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 49 (c) 42 (d) 14
31. 31.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 60° (b) 40° (c) 160° (d) 140°
32. 32.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
33. 33.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/8 (c) 1/8 (d) 7/8
34. 34.A bag has 7 white balls and 5 blue 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) 2 (c) 8 (d) 12
35. 35.Which is the correct factorisation of x² + 8x + 12? (a) (x − 2)(x − 6) (b) (x + 1)(x + 12) (c) (x + 2)(x + 6) (d) (x + 1)(x + 7)
36. 36.What is the mean of 10, 19, 19, 15, 12 and 9? (a) 13 (b) 15 (c) 12 (d) 14
37. 37.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
38. 38.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 80° (c) 135° (d) 100°
39. 39.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
40. 40.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8

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