Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 161 · 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 bag has 9 black balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 15 (b) 2 (c) 11 (d) 10
2. 2.What is the mean of 5, 15, 15, 20, 9 and 2? (a) 10 (b) 13 (c) 12 (d) 11
3. 3.A bag has 7 black balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 18 (b) 2 (c) 8 (d) 9
4. 4.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
6. 6.3 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) 18 (b) 9 (c) 6 (d) 12
7. 7.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 130° (b) 95° (c) 135° (d) 85°
8. 8.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
9. 9.In a class of 37 children, 22 like maths, 8 like science and 2 like both. How many like only maths? (a) 22 (b) 6 (c) 29 (d) 20
10. 10.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
11. 11.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 55 (b) 45 (c) 90 (d) 17
12. 12.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 18 (c) 54 (d) 6
13. 13.In a class of 36 children, 14 like dance, 25 like music and 8 like both. How many like at least one of the two? (a) 31 (b) 23 (c) 39 (d) 36
14. 14.In a class of 41 children, 15 like cricket, 27 like football and 9 like both. How many like only cricket? (a) 15 (b) 18 (c) 14 (d) 6
15. 15.What is the median of 5, 18, 13, 22, 4, 26 and 16? (a) 16 (b) 22 (c) 13 (d) 18
16. 16.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
17. 17.What is the distance between the points (3, 2) and (18, 10)? (a) 18 (b) 17 (c) 289 (d) 23
18. 18.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
19. 19.A drawer has lots of blue, white 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) 3 (b) 6 (c) 4 (d) 2
20. 20.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
21. 21.In a class of 43 children, 22 like mangoes, 23 like bananas and 6 like both. How many like neither? (a) 10 (b) 6 (c) 5 (d) 4
22. 22.A drawer has lots of white, red, yellow, black and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 10 (c) 5 (d) 6
23. 23.What is the 15th term of the AP 6, 10, 14, 18, …? (a) 56 (b) 60 (c) 62 (d) 66
24. 24.What is the mean of 15, 15, 18, 19 and 13? (a) 20 (b) 15 (c) 17 (d) 16
25. 25.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
26. 26.What are the roots of x² − 8x + 15 = 0? (a) 3 and 5 (b) 1 and 15 (c) 2 and 6 (d) 1 and 7
27. 27.A drawer has lots of yellow, green, white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 5 (c) 4 (d) 2
28. 28.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 90 (c) 33 (d) 10
29. 29.What is the mode of 11, 3, 19, 3, 3, 11 and 17? (a) 3 (b) 11 (c) 17 (d) 19
30. 30.A bag has 6 green balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 7 (c) 8 (d) 2
31. 31.What is the distance between the points (4, 5) and (11, 29)? (a) 31 (b) 625 (c) 25 (d) 26
32. 32.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 100° (d) 50°
33. 33.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 2/3
34. 34.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) 60 (d) 19
35. 35.Which is the correct factorisation of x² + 8x + 15? (a) (x + 1)(x + 15) (b) (x + 1)(x + 7) (c) (x + 3)(x + 5) (d) (x − 3)(x − 5)
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/11 (c) 3/11 (d) 1/12
37. 37.What is the midpoint of the line joining (10, 4) and (12, 14)? (a) (1, 5) (b) (11, 9) (c) (22, 18) (d) (9, 11)
38. 38.Which term of the AP 5, 14, 23, 32, … is 68? (a) 9th (b) 10th (c) 7th (d) 8th
39. 39.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 150° (c) 60° (d) 30°
40. 40.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 235° (b) 55° (c) 110° (d) 125°

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