Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 390 · 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.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 25 (d) 21
2. 2.What is the mean of 18, 4, 6 and 12? (a) 11 (b) 9 (c) 10 (d) 8
3. 3.If a + b = 18 and ab = 77, what is a² + b²? (a) 478 (b) 170 (c) 324 (d) 247
4. 4.A bag has 4 green balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 2 (c) 16 (d) 6
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 5/11 (c) 1/11 (d) 1/6
6. 6.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
7. 7.How many prime numbers are there between 50 and 70? (a) 5 (b) 4 (c) 6 (d) 3
8. 8.What is the sum of the roots of x² − 17x + 72 = 0? (a) 72 (b) 16 (c) 18 (d) 17
9. 9.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
10. 10.A bag has 4 black balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 16 (c) 5 (d) 6
11. 11.A bag has 3 yellow, 3 red and 6 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 1/4 (c) 1/12 (d) 3/4
12. 12.Which is the correct factorisation of x² + 9x + 14? (a) (x + 1)(x + 8) (b) (x + 2)(x + 7) (c) (x − 2)(x − 7) (d) (x + 1)(x + 14)
13. 13.In a class of 43 children, 16 like dance, 20 like music and 2 like both. How many like at least one of the two? (a) 34 (b) 36 (c) 43 (d) 32
14. 14.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 81 (d) 72
15. 15.What is the midpoint of the line joining (8, 13) and (20, 1)? (a) (6, 6) (b) (28, 14) (c) (7, 14) (d) (14, 7)
16. 16.What is the 16th term of the AP 3, 7, 11, 15, …? (a) 60 (b) 63 (c) 67 (d) 64
17. 17.In a class of 42 children, 26 like dance, 17 like music and 9 like both. How many like neither? (a) 8 (b) 17 (c) 9 (d) 7
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 18 (d) 8
20. 20.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
21. 21.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) 7 (c) 8 (d) 15
22. 22.A bag has 10 yellow 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) 14 (d) 11
23. 23.What is the mean of 15, 3, 19, 18 and 5? (a) 15 (b) 13 (c) 10 (d) 12
24. 24.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
25. 25.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 21 (c) 15 (d) 36
26. 26.A bag has 7 blue, 4 green and 3 yellow balls. One ball is taken out without looking. What is the probability that it is not green? (a) 11/14 (b) 5/7 (c) 1/3 (d) 2/7
27. 27.What are the roots of x² − 17x + 72 = 0? (a) 1 and 16 (b) 2 and 36 (c) 1 and 72 (d) 8 and 9
28. 28.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 57 (c) 19 (d) 60
29. 29.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 65 cu cm (d) 64 cu cm
30. 30.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 150° (c) 330° (d) 60°
31. 31.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 110° (b) 30° (c) 100° (d) 150°
32. 32.5 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) 15 (b) 30 (c) 20 (d) 8
33. 33.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 3 (d) 9
34. 34.In which quadrant does the point (5, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
35. 35.The mean of 4 numbers is 26. When the number 46 is added to them, what is the new mean? (a) 36 (b) 31 (c) 30 (d) 26
36. 36.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 75° (c) 30° (d) 210°
37. 37.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 144 (c) 66 (d) 132
38. 38.What is the mode of 7, 6, 2, 4, 4, 2 and 2? (a) 7 (b) 4 (c) 6 (d) 2
39. 39.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
40. 40.How many factors does 84 have? (a) 10 (b) 13 (c) 11 (d) 12

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