Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 392 · 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 how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 120 (c) 240 (d) 20
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
3. 3.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 28 (c) 64 (d) 56
4. 4.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 11 (b) 57 (c) 56 (d) 112
5. 5.What is the sum of the roots of x² − 16x + 63 = 0? (a) 63 (b) 15 (c) 16 (d) 17
6. 6.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 24 (d) 16
7. 7.In a class of 29 children, 17 like cricket, 14 like football and 3 like neither. How many like both? (a) 26 (b) 2 (c) 3 (d) 5
8. 8.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 132 (d) 66
9. 9.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 3/5 (d) 1/4
10. 10.A bag has 7 blue balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 15 (c) 9 (d) 2
11. 11.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
12. 12.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 66 (c) 78 (d) 144
13. 13.A bag has 3 white, 3 blue and 7 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 3/13 (b) 11/13 (c) 10/13 (d) 1/3
14. 14.What is the mode of 17, 8, 4, 17, 8, 16 and 17? (a) 4 (b) 16 (c) 8 (d) 17
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
16. 16.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 400 sq cm
17. 17.The mean of 3 numbers is 11. When the number 23 is added to them, what is the new mean? (a) 17 (b) 14 (c) 15 (d) 11
18. 18.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
19. 19.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 6 (c) 9 (d) 5
20. 20.What is the mode of 8, 8, 5, 8, 9, 17 and 9? (a) 5 (b) 8 (c) 17 (d) 9
21. 21.In a class of 36 children, 16 like maths, 14 like science and 3 like both. How many like only maths? (a) 13 (b) 11 (c) 16 (d) 22
22. 22.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 169 (c) 156 (d) 78
23. 23.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/8 (c) 3/4 (d) 1/8
24. 24.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 11 (b) 65 (c) 130 (d) 70
25. 25.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 270° (b) 160° (c) 110° (d) 90°
26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 19 (b) 7 (c) 17 (d) 18
27. 27.A bag has 9 black balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 10 (c) 17 (d) 11
28. 28.A bag has 6 yellow balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 7 (b) 8 (c) 10 (d) 2
29. 29.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 252 (c) 243 (d) 240
30. 30.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 105 (b) 21 (c) 210 (d) 112
31. 31.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/4
32. 32.What is the distance between the points (6, 0) and (18, 9)? (a) 16 (b) 225 (c) 15 (d) 21
33. 33.The mean of 3 numbers is 24. When the number 32 is added to them, what is the new mean? (a) 26 (b) 24 (c) 28 (d) 27
34. 34.A bag has 9 yellow balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 19 (c) 2 (d) 11
35. 35.In which quadrant does the point (−9, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
36. 36.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
37. 37.What is the mean of 16, 11, 11 and 10? (a) 16 (b) 13 (c) 12 (d) 11
38. 38.What is the median of 16, 13, 2, 31 and 29? (a) 29 (b) 2 (c) 16 (d) 13
39. 39.In which quadrant does the point (9, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
40. 40.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/3 (c) 1/2 (d) 3/4

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