Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 277 · 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.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/18 (c) 1/12 (d) 1/36
3. 3.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
4. 4.How many prime numbers are there between 10 and 40? (a) 9 (b) 8 (c) 10 (d) 7
5. 5.In a class of 54 children, 30 like cricket, 25 like football and 11 like both. How many like only cricket? (a) 29 (b) 19 (c) 30 (d) 14
6. 6.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 24 (d) 16
7. 7.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 564 (b) 40 (c) 282 (d) 300
8. 8.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 252 (c) 246 (d) 261
9. 9.In a class of 42 children, 19 like cricket, 23 like football and 9 like both. How many like neither? (a) 0 (b) 18 (c) 10 (d) 9
10. 10.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 56 cu cm (b) 172 cu cm (c) 112 cu cm (d) 17 cu cm
11. 11.A bag has 9 blue, 4 green and 7 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 13/20 (b) 7/20 (c) 7/13 (d) 1/3
12. 12.In a class of 21 children, 15 like mangoes, 8 like bananas and 4 like both. How many like at least one of the two? (a) 19 (b) 21 (c) 15 (d) 23
13. 13.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 22 (c) 21 (d) 15
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 2/11 (c) 1/18 (d) 1/11
15. 15.A drawer has lots of blue, yellow, black, white 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) 2 (b) 5 (c) 10 (d) 6
16. 16.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
17. 17.What is the smallest prime factor of 253? (a) 2 (b) 23 (c) 11 (d) 1
18. 18.A drawer has lots of white 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) 2 (b) 5 (c) 4 (d) 3
19. 19.What is the mode of 6, 19, 3, 6, 2, 19 and 6? (a) 6 (b) 2 (c) 3 (d) 19
20. 20.What is the distance between the points (2, 17) and (14, 8)? (a) 225 (b) 15 (c) 16 (d) 21
21. 21.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 23 (b) 17 (c) 18 (d) 19
22. 22.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
23. 23.If a + b = 18 and ab = 77, what is (a − b)²? (a) 16 (b) 170 (c) 4 (d) 324
24. 24.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 450 (c) 435 (d) 465
25. 25.What is the 19th term of the AP 20, 25, 30, 35, …? (a) 90 (b) 95 (c) 115 (d) 110
26. 26.How many factors does 95 have? (a) 4 (b) 5 (c) 2 (d) 3
27. 27.In which quadrant does the point (−1, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
28. 28.A bag has 11 blue balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 12 (b) 2 (c) 16 (d) 13
29. 29.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
30. 30.What is the distance between the points (5, 32) and (12, 8)? (a) 26 (b) 25 (c) 625 (d) 31
31. 31.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 45° (c) 155° (d) 135°
32. 32.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 37 (b) 266 (c) 133 (d) 154
33. 33.A drawer has lots of white, blue, 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) 2 (b) 5 (c) 10 (d) 6
34. 34.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 150° (b) 75° (c) 255° (d) 105°
35. 35.What is the missing term in the AP 9, ?, 21, 27, 33? (a) 15 (b) 16 (c) 21 (d) 14
36. 36.How many factors does 47 have? (a) 3 (b) 2 (c) 4 (d) 1
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/9 (c) 1/12 (d) 3/11
38. 38.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
39. 39.A bag has 10 black balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 11 (c) 5 (d) 2
40. 40.In which quadrant does the point (8, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant

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