Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 526 · 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 prime factor of 35? (a) 1 (b) 7 (c) 5 (d) 2
2. 2.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 145° (b) 90° (c) 125° (d) 55°
3. 3.A bag has 2 green, 3 red and 5 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 3/10 (b) 1/3 (c) 4/5 (d) 7/10
4. 4.What is the mode of 20, 19, 20, 20, 14, 19 and 3? (a) 3 (b) 19 (c) 14 (d) 20
5. 5.A bag has 10 black balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 15 (d) 6
6. 6.In which quadrant does the point (−1, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
7. 7.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/4 (c) 2/3 (d) 1/2
8. 8.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 50° (c) 100° (d) 80°
9. 9.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 153 (c) 51 (d) 54
10. 10.In a class of 28 children, 11 like mangoes, 22 like bananas and 7 like both. How many like neither? (a) 2 (b) 9 (c) 7 (d) 3
11. 11.In a class of 30 children, 17 like tea, 18 like coffee and 8 like both. How many like at least one of the two? (a) 19 (b) 30 (c) 27 (d) 35
12. 12.A bag has 3 blue balls and 4 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) 4 (c) 7 (d) 5
13. 13.In a class of 37 children, 17 like dance, 23 like music and 5 like neither. How many like both? (a) 3 (b) 5 (c) 32 (d) 8
14. 14.In a class of 35 children, 24 like mangoes, 19 like bananas and 10 like both. How many like only mangoes? (a) 14 (b) 16 (c) 24 (d) 9
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
16. 16.What is the median of 2, 25, 10, 26 and 15? (a) 10 (b) 15 (c) 25 (d) 16
17. 17.A drawer has lots of blue and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 3 (c) 5 (d) 2
18. 18.In a class of 31 children, 19 like mangoes, 6 like bananas and 3 like both. How many like at least one of the two? (a) 19 (b) 31 (c) 25 (d) 22
19. 19.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) 15 (b) 8 (c) 14 (d) 7
20. 20.What is the median of 13, 37, 33, 1 and 38? (a) 34 (b) 33 (c) 13 (d) 37
21. 21.What is the mode of 11, 11, 20, 2, 20, 11 and 16? (a) 16 (b) 2 (c) 11 (d) 20
22. 22.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/2 (c) 3/4 (d) 1/4
23. 23.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/9 (c) 1/11 (d) 1/12
25. 25.What is the distance between the points (2, 20) and (10, 5)? (a) 18 (b) 23 (c) 289 (d) 17
26. 26.A drawer has lots of blue and green 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) 5 (c) 2 (d) 4
27. 27.What is the missing term in the AP 7, 12, ?, 22, 27? (a) 22 (b) 18 (c) 16 (d) 17
28. 28.What is the 32nd term of the AP 2, 6, 10, 14, …? (a) 130 (b) 126 (c) 124 (d) 128
29. 29.What is the mean of 13, 11, 10, 13, 16 and 21? (a) 15 (b) 13 (c) 14 (d) 12
30. 30.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 144 (d) 66
31. 31.In a class of 29 children, 14 like tea, 20 like coffee and 8 like both. How many like neither? (a) 3 (b) 4 (c) 8 (d) 11
32. 32.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 150° (b) 155° (c) 125° (d) 55°
33. 33.What is the mode of 19, 12, 9, 9, 19, 7 and 9? (a) 9 (b) 7 (c) 19 (d) 12
34. 34.What is the smallest prime factor of 91? (a) 2 (b) 1 (c) 7 (d) 13
35. 35.What is the 15th term of the AP 14, 16, 18, 20, …? (a) 44 (b) 42 (c) 28 (d) 30
36. 36.A bag has 3 green balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 10 (c) 4 (d) 5
37. 37.What is the 13th term of the AP 12, 17, 22, 27, …? (a) 72 (b) 65 (c) 77 (d) 60
38. 38.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
39. 39.A bag has 8 blue, 7 red and 7 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 15/22 (b) 7/15 (c) 7/22 (d) 1/3
40. 40.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm

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