Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 249 · 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.In a class of 30 children, 22 like tea, 13 like coffee and 6 like both. How many like neither? (a) 7 (b) 6 (c) 2 (d) 1
2. 2.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 1128 (c) 2352 (d) 1176
3. 3.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
4. 4.What is the mean of 5, 20, 20 and 11? (a) 13 (b) 15 (c) 16 (d) 14
5. 5.In a class of 30 children, 12 like dance, 17 like music and 8 like neither. How many like both? (a) 6 (b) 22 (c) 8 (d) 7
6. 6.In a class of 22 children, 16 like mangoes, 9 like bananas and 5 like both. How many like only mangoes? (a) 11 (b) 4 (c) 16 (d) 13
7. 7.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 2 (d) 3
8. 8.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 25° (d) 155°
9. 9.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 50° (b) 105° (c) 125° (d) 130°
10. 10.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
11. 11.What is the midpoint of the line joining (3, 5) and (13, 11)? (a) (5, 3) (b) (16, 16) (c) (9, 8) (d) (8, 8)
12. 12.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
13. 13.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
14. 14.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 70° (d) 40°
15. 15.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 45 (b) 225 (c) 450 (d) 230
16. 16.A bag has 8 red balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 4 (d) 11
17. 17.In a class of 21 children, 16 like cricket, 16 like football and 12 like both. How many like only cricket? (a) 12 (b) 16 (c) 4 (d) 5
18. 18.Using (a − b)² = a² − 2ab + b², what is 36²? (a) 1936 (b) 1296 (c) 1306 (d) 1584
19. 19.In a class of 47 children, 17 like mangoes, 32 like bananas and 12 like both. How many like at least one of the two? (a) 47 (b) 25 (c) 37 (d) 49
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/12 (d) 1/11
21. 21.A bag has 3 green balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 10 (c) 4 (d) 2
22. 22.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 741 (c) 1482 (d) 722
23. 23.In a class of 24 children, 12 like mangoes, 11 like bananas and 2 like both. How many like neither? (a) 5 (b) 3 (c) 1 (d) 2
24. 24.A drawer has lots of green, yellow, blue, red 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) 6 (b) 10 (c) 5 (d) 2
25. 25.What is the midpoint of the line joining (8, 20) and (12, 10)? (a) (20, 30) (b) (2, 5) (c) (10, 15) (d) (15, 10)
26. 26.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
27. 27.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 4 (d) 2
29. 29.What is the mean of 5, 12, 3, 6, 10 and 18? (a) 8 (b) 10 (c) 11 (d) 9
30. 30.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 170° (c) 11° (d) 10°
31. 31.A bag has 7 yellow balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 2 (c) 8 (d) 13
32. 32.A bag has 4 green, 2 blue and 4 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 2/3 (b) 2/5 (c) 1/3 (d) 3/5
33. 33.What is the distance between the points (3, 21) and (11, 6)? (a) 23 (b) 17 (c) 289 (d) 18
34. 34.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
35. 35.What is the mode of 15, 20, 2, 20, 11, 20 and 15? (a) 15 (b) 11 (c) 2 (d) 20
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
37. 37.If a + b = 18 and ab = 80, what is (a − b)²? (a) 2 (b) 164 (c) 324 (d) 4
38. 38.If a + b = 10 and ab = 24, what is (a − b)²? (a) 52 (b) 4 (c) 2 (d) 100
39. 39.In a class of 42 children, 26 like mangoes, 24 like bananas and 12 like both. How many like only mangoes? (a) 12 (b) 18 (c) 26 (d) 14
40. 40.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 45 (c) 36 (d) 81

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