Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 828 · 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 drawer has lots of black, blue, green, yellow 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) 10 (b) 6 (c) 5 (d) 2
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 1/9 (c) 4/11 (d) 5/36
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
4. 4.What is the median of 19, 30, 26, 13 and 6? (a) 20 (b) 26 (c) 19 (d) 13
5. 5.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 20 (d) 120
6. 6.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 11035 (b) 11025 (c) 9025 (d) 10025
7. 7.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 96 (b) 48 (c) 14 (d) 56
8. 8.What is the midpoint of the line joining (7, 10) and (11, 20)? (a) (18, 30) (b) (9, 15) (c) (2, 5) (d) (15, 9)
9. 9.6 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 30 (b) 24 (c) 48 (d) 10
10. 10.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 121 (d) 55
11. 11.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 585 (c) 595 (d) 468
12. 12.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 120 (d) 240
13. 13.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
14. 14.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 50° (c) 130° (d) 230°
15. 15.A bag has 4 black balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 15 (c) 2 (d) 12
16. 16.A drawer has lots of 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) 5 (c) 2 (d) 4
17. 17.What is the smallest prime factor of 77? (a) 11 (b) 2 (c) 7 (d) 1
18. 18.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 66 (c) 69 (d) 198
19. 19.What is the median of 24, 21, 12, 36 and 9? (a) 21 (b) 22 (c) 12 (d) 24
20. 20.A bag has 7 yellow, 9 blue and 9 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 18/25 (b) 1/3 (c) 7/25 (d) 7/18
21. 21.Using (a + b)² = a² + 2ab + b², what is 42²? (a) 1774 (b) 1764 (c) 1444 (d) 1604
22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 15 (d) 4
23. 23.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
24. 24.What is the mode of 4, 6, 6, 7, 6, 14 and 14? (a) 4 (b) 7 (c) 6 (d) 14
25. 25.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 50° (d) 40°
26. 26.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 36 (c) 64 (d) 28
27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
28. 28.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
29. 29.What is the median of 22, 13, 12, 38, 5, 3 and 11? (a) 38 (b) 13 (c) 12 (d) 11
30. 30.In a class of 40 children, 22 like cricket, 18 like football and 4 like both. How many like at least one of the two? (a) 40 (b) 37 (c) 32 (d) 36
31. 31.What is the mean of 7, 3, 3, 5, 7 and 17? (a) 8 (b) 9 (c) 7 (d) 6
32. 32.What is the midpoint of the line joining (0, 18) and (4, 10)? (a) (2, 14) (b) (14, 2) (c) (2, 4) (d) (4, 28)
33. 33.What is the median of 30, 15, 5, 31 and 22? (a) 15 (b) 30 (c) 5 (d) 22
34. 34.A bag has 6 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) 11 (b) 6 (c) 2 (d) 7
35. 35.In a class of 27 children, 16 like tea, 18 like coffee and 4 like neither. How many like both? (a) 23 (b) 4 (c) 11 (d) 7
36. 36.Which term of the AP 1, 5, 9, 13, … is 73? (a) 21st (b) 18th (c) 20th (d) 19th
37. 37.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 2/3 (d) 1/4
38. 38.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/4 (c) 7/8 (d) 1/8
39. 39.In a class of 38 children, 16 like mangoes, 25 like bananas and 12 like both. How many like only mangoes? (a) 12 (b) 16 (c) 13 (d) 4
40. 40.In which quadrant does the point (−1, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

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