Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 627 · 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.The mean of 7 numbers is 21. When the number 29 is added to them, what is the new mean? (a) 21 (b) 23 (c) 22 (d) 25
2. 2.5 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) 8 (b) 30 (c) 20 (d) 15
3. 3.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
4. 4.In which quadrant does the point (4, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
5. 5.A drawer has lots of red 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) 2 (b) 4 (c) 5 (d) 3
6. 6.What is the midpoint of the line joining (4, 2) and (6, 6)? (a) (10, 8) (b) (1, 2) (c) (5, 4) (d) (4, 5)
7. 7.What is the 18th term of the AP 6, 11, 16, 21, …? (a) 91 (b) 96 (c) 85 (d) 90
8. 8.If the side of a square 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
9. 9.In a class of 23 children, 8 like dance, 9 like music and 9 like neither. How many like both? (a) 4 (b) 3 (c) 9 (d) 14
10. 10.A bag has 11 yellow 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) 16 (d) 12
11. 11.A drawer has lots of green, white and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 4 (d) 3
12. 12.What is the product of the roots of x² − 10x + 24 = 0? (a) 25 (b) 10 (c) 23 (d) 24
13. 13.What is the median of 20, 2, 36, 5, 27, 13 and 29? (a) 5 (b) 27 (c) 13 (d) 20
14. 14.How many factors does 24 have? (a) 7 (b) 6 (c) 9 (d) 8
15. 15.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/7 (c) 7/8 (d) 1/8
16. 16.A bag has 5 yellow balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 6 (c) 2 (d) 12
17. 17.In which quadrant does the point (−3, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
18. 18.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 150° (c) 15° (d) 25°
19. 19.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 14 (c) 48 (d) 96
20. 20.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 348 (b) 174 (c) 20 (d) 180
21. 21.In a class of 29 children, 20 like mangoes, 17 like bananas and 1 like neither. How many like both? (a) 9 (b) 8 (c) 1 (d) 28
22. 22.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 135° (b) 125° (c) 100° (d) 45°
23. 23.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 150° (d) 110°
24. 24.Using (a + b)² = a² + 2ab + b², what is 75²? (a) 5625 (b) 4925 (c) 4225 (d) 5635
25. 25.What is the midpoint of the line joining (7, 5) and (9, 15)? (a) (16, 20) (b) (10, 8) (c) (1, 5) (d) (8, 10)
26. 26.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 45 (d) 36
27. 27.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 40° (c) 120° (d) 30°
28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 16 (b) 5 (c) 14 (d) 15
29. 29.What is the mode of 3, 5, 13, 12, 5, 13 and 13? (a) 13 (b) 12 (c) 3 (d) 5
30. 30.A drawer has lots of blue, green, yellow, black and red 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) 5 (c) 10 (d) 6
31. 31.What is the mode of 19, 19, 2, 8, 17, 2 and 19? (a) 2 (b) 8 (c) 17 (d) 19
32. 32.In a class of 34 children, 19 like maths, 20 like science and 5 like neither. How many like both? (a) 11 (b) 10 (c) 29 (d) 5
33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 18 (d) 9
34. 34.In a class of 36 children, 21 like dance, 21 like music and 10 like both. How many like at least one of the two? (a) 42 (b) 32 (c) 36 (d) 22
35. 35.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 80° (d) 50°
36. 36.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 71° (c) 70° (d) 110°
37. 37.A cuboid is 8 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 376 cu cm (b) 48 cu cm (c) 480 cu cm (d) 24 cu cm
38. 38.In which quadrant does the point (7, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
39. 39.A bag has 3 blue balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 4 (b) 5 (c) 2 (d) 14
40. 40.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm

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