Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 174 · 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 area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
2. 2.A drawer has lots of yellow, red, black 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) 5 (b) 8 (c) 2 (d) 4
3. 3.What is the midpoint of the line joining (5, 4) and (7, 10)? (a) (6, 7) (b) (12, 14) (c) (1, 3) (d) (7, 6)
4. 4.A drawer has lots of red 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) 4 (b) 3 (c) 2 (d) 5
5. 5.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 100° (c) 80° (d) 150°
6. 6.In a class of 38 children, 13 like tea, 23 like coffee and 3 like both. How many like neither? (a) 5 (b) 2 (c) 3 (d) 8
7. 7.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 100 cu cm (d) 125 cu cm
8. 8.A bag has 4 yellow balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 6 (b) 5 (c) 9 (d) 2
9. 9.A bag has 8 green, 7 red and 7 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 15/22 (b) 1/3 (c) 7/22 (d) 8/11
10. 10.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
11. 11.A bag has 5 black balls and 3 white 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) 4 (c) 8 (d) 2
12. 12.In a class of 22 children, 6 like maths, 10 like science and 2 like both. How many like at least one of the two? (a) 14 (b) 12 (c) 22 (d) 16
13. 13.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 22 (c) 28 (d) 21
14. 14.What is the mean of 17, 8, 5 and 14? (a) 13 (b) 11 (c) 10 (d) 12
15. 15.What is the smallest prime factor of 33? (a) 11 (b) 3 (c) 2 (d) 1
16. 16.What is the mode of 18, 12, 13, 12, 5, 12 and 5? (a) 5 (b) 13 (c) 12 (d) 18
17. 17.In which quadrant does the point (−3, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
18. 18.What is the distance between the points (7, 9) and (13, 1)? (a) 11 (b) 10 (c) 100 (d) 14
19. 19.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 25 (d) 120
20. 20.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 85° (c) 160° (d) 95°
21. 21.A bag has 4 red, 2 green and 3 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 2/3 (b) 1/3 (c) 1/2 (d) 4/9
22. 22.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 45 (c) 72 (d) 81
23. 23.What is the mode of 7, 12, 2, 12, 8, 8 and 8? (a) 7 (b) 8 (c) 2 (d) 12
24. 24.In a class of 32 children, 8 like dance, 23 like music and 3 like both. How many like only dance? (a) 9 (b) 5 (c) 20 (d) 8
25. 25.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
26. 26.In a class of 38 children, 22 like dance, 20 like music and 5 like both. How many like neither? (a) 5 (b) 2 (c) 6 (d) 1
27. 27.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 12 (c) 13 (d) 24
28. 28.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
29. 29.Using (a + b)² = a² + 2ab + b², what is 81²? (a) 6571 (b) 6241 (c) 6561 (d) 6401
30. 30.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) 8 (b) 14 (c) 15 (d) 7
31. 31.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
32. 32.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 85° (b) 10° (c) 170° (d) 105°
33. 33.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 50° (c) 130° (d) 25°
34. 34.In which quadrant does the point (9, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
35. 35.The numbers 14 to 22 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) 162 (c) 18 (d) 57
36. 36.What is the midpoint of the line joining (5, 12) and (15, 2)? (a) (20, 14) (b) (10, 7) (c) (7, 10) (d) (5, 5)
37. 37.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 160° (d) 140°
38. 38.How many prime numbers are there between 60 and 70? (a) 2 (b) 4 (c) 3 (d) 1
39. 39.Using (a − b)² = a² − 2ab + b², what is 36²? (a) 1584 (b) 1306 (c) 1296 (d) 1936
40. 40.How many prime numbers are there between 30 and 50? (a) 4 (b) 5 (c) 6 (d) 7

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