Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 648 · 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 fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
2. 2.A bag has 5 yellow, 3 green and 3 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 5/11 (b) 1/3 (c) 7/11 (d) 6/11
3. 3.In which quadrant does the point (−5, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
4. 4.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 155° (b) 45° (c) 135° (d) 160°
5. 5.A bag has 11 green balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 12 (b) 13 (c) 2 (d) 20
6. 6.A drawer has lots of red, black and white 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) 2 (c) 4 (d) 6
7. 7.What is the mean of 15, 4, 17, 13 and 11? (a) 10 (b) 15 (c) 13 (d) 12
8. 8.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) 54 (b) 6 (c) 21 (d) 18
9. 9.What is the 30th term of the AP 1, 9, 17, 25, …? (a) 241 (b) 233 (c) 240 (d) 232
10. 10.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 8 (b) 13 (c) 16 (d) 15
12. 12.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
13. 13.8 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 96 (b) 56 (c) 48 (d) 14
14. 14.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 45 (d) 20
15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 36 (c) 11 (d) 21
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 3/11 (c) 1/12 (d) 1/9
17. 17.A bag has 6 blue balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 12 (b) 8 (c) 2 (d) 7
18. 18.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 81° (c) 80° (d) 160°
19. 19.In a class of 48 children, 27 like mangoes, 26 like bananas and 7 like both. How many like only mangoes? (a) 27 (b) 20 (c) 22 (d) 19
20. 20.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
21. 21.What is the median of 12, 21, 16, 17 and 25? (a) 16 (b) 18 (c) 21 (d) 17
22. 22.A bag has 9 yellow, 2 blue and 6 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 15/17 (c) 2/15 (d) 2/17
23. 23.In a class of 37 children, 21 like dance, 9 like music and 2 like both. How many like neither? (a) 2 (b) 9 (c) 11 (d) 7
24. 24.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 216 (b) 240 (c) 48 (d) 432
25. 25.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 76° (c) 75° (d) 150°
26. 26.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 169 (c) 78 (d) 156
27. 27.Which is the correct factorisation of x² + 15x + 56? (a) (x + 7)(x + 8) (b) (x + 1)(x + 14) (c) (x + 1)(x + 56) (d) (x − 7)(x − 8)
28. 28.A drawer has lots of red, white, green, 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) 10 (b) 5 (c) 2 (d) 6
29. 29.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 6/11 (c) 7/36 (d) 1/6
31. 31.What is the 17th term of the AP 16, 24, 32, 40, …? (a) 136 (b) 128 (c) 144 (d) 152
32. 32.In a class of 15 children, 7 like maths, 11 like science and 4 like both. How many like neither? (a) 5 (b) 1 (c) 4 (d) 2
33. 33.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
34. 34.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 110 (c) 66 (d) 121
35. 35.What is the 31st term of the AP 9, 13, 17, 21, …? (a) 120 (b) 124 (c) 133 (d) 129
36. 36.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 30 (b) 39 (c) 31 (d) 32
37. 37.In a class of 32 children, 6 like dance, 20 like music and 8 like neither. How many like both? (a) 2 (b) 24 (c) 8 (d) 3
38. 38.A cuboid is 8 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 92 cu cm (b) 13 cu cm (c) 16 cu cm (d) 48 cu cm
39. 39.What is the mode of 7, 14, 7, 3, 14, 14 and 13? (a) 13 (b) 3 (c) 14 (d) 7
40. 40.A bag has 10 black balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 12 (b) 21 (c) 2 (d) 11

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