Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 563 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/18 (d) 1/12
2. 2.What is the 35th term of the AP 8, 13, 18, 23, …? (a) 175 (b) 178 (c) 183 (d) 170
3. 3.A bag has 4 blue, 7 yellow and 7 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 2/3 (b) 11/18 (c) 7/18 (d) 1/3
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 1/11 (c) 1/6 (d) 5/36
5. 5.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 238 (c) 240 (d) 250
6. 6.In which quadrant does the point (−9, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
7. 7.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 1/2 (d) 2/3
8. 8.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 49 (d) 42
9. 9.What is the smallest prime factor of 33? (a) 2 (b) 11 (c) 3 (d) 1
10. 10.In a class of 28 children, 17 like dance, 11 like music and 6 like both. How many like at least one of the two? (a) 23 (b) 28 (c) 16 (d) 22
11. 11.If a + b = 15 and ab = 54, what is a² + b²? (a) 171 (b) 225 (c) 117 (d) 333
12. 12.In a class of 43 children, 25 like cricket, 21 like football and 5 like both. How many like at least one of the two? (a) 36 (b) 46 (c) 43 (d) 41
13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 3 (b) 12 (c) 13 (d) 14
14. 14.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 65° (d) 150°
15. 15.A bag has 8 green, 4 white and 6 yellow balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 7/9 (c) 5/6 (d) 2/9
16. 16.Using (a − b)² = a² − 2ab + b², what is 36²? (a) 1936 (b) 1584 (c) 1306 (d) 1296
17. 17.What is the smallest prime factor of 121? (a) 2 (b) 11 (c) 3 (d) 1
18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 7 (b) 5 (c) 6 (d) 4
19. 19.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 397 (c) 387 (d) 336
20. 20.What is the missing term in the AP 11, ?, 27, 35, 43? (a) 18 (b) 19 (c) 20 (d) 27
21. 21.What is the median of 25, 8, 1, 26 and 12? (a) 1 (b) 25 (c) 12 (d) 8
22. 22.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 110° (c) 55° (d) 70°
23. 23.What is the mode of 2, 8, 2, 8, 17, 2 and 18? (a) 18 (b) 8 (c) 17 (d) 2
24. 24.A bag has 8 white balls and 11 yellow 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) 9 (c) 2 (d) 12
25. 25.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
26. 26.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 125° (b) 160° (c) 75° (d) 105°
27. 27.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 108 (b) 28 (c) 120 (d) 216
28. 28.In which quadrant does the point (−1, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
29. 29.How many factors does 95 have? (a) 5 (b) 3 (c) 2 (d) 4
30. 30.How many prime numbers are there between 50 and 80? (a) 9 (b) 7 (c) 6 (d) 8
31. 31.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
32. 32.In a class of 27 children, 18 like dance, 11 like music and 8 like both. How many like neither? (a) 6 (b) 8 (c) 14 (d) 7
33. 33.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 91 (d) 196
34. 34.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 4 times (d) 8 times
35. 35.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 7/8 (c) 1/8 (d) 3/8
36. 36.A bag has 8 green, 7 red and 6 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 2/7 (c) 16/21 (d) 5/7
37. 37.In a class of 36 children, 16 like cricket, 22 like football and 4 like both. How many like only cricket? (a) 16 (b) 12 (c) 14 (d) 18
38. 38.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 15 (c) 30 (d) 21
39. 39.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 2/3 (d) 1/3
40. 40.What is the mode of 1, 1, 1, 7, 11, 18 and 18? (a) 7 (b) 11 (c) 18 (d) 1

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