Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 623 · 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.What is the mode of 5, 18, 4, 3, 3, 18 and 3? (a) 5 (b) 3 (c) 4 (d) 18
2. 2.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/12 (c) 3/11 (d) 1/9
4. 4.A bag has 5 red, 3 green and 7 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 8/15 (b) 1/3 (c) 7/8 (d) 7/15
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
6. 6.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 15 (d) 36
7. 7.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 64 (c) 15 (d) 112
8. 8.A bag has 3 black balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 4 (b) 2 (c) 9 (d) 5
9. 9.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/2 (c) 3/4 (d) 1/3
10. 10.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 1770 (c) 3660 (d) 1830
11. 11.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
12. 12.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/5 (c) 1/4 (d) 3/8
13. 13.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
14. 14.What is the smallest prime factor of 51? (a) 3 (b) 17 (c) 1 (d) 2
15. 15.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 75° (b) 105° (c) 150° (d) 255°
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/18 (c) 1/11 (d) 1/12
17. 17.In which quadrant does the point (−8, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
18. 18.The mean of 9 numbers is 38. When the number 48 is added to them, what is the new mean? (a) 40 (b) 38 (c) 39 (d) 43
19. 19.In a class of 38 children, 19 like cricket, 18 like football and 8 like both. How many like neither? (a) 9 (b) 17 (c) 8 (d) 1
20. 20.How many prime numbers are there between 70 and 100? (a) 6 (b) 5 (c) 7 (d) 8
21. 21.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 121 (b) 16 (c) 242 (d) 122
22. 22.How many prime numbers are there between 40 and 60? (a) 5 (b) 7 (c) 4 (d) 6
23. 23.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 5 (d) 7
24. 24.What is the midpoint of the line joining (3, 18) and (7, 10)? (a) (14, 5) (b) (2, 4) (c) (5, 14) (d) (10, 28)
25. 25.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 150° (c) 110° (d) 70°
26. 26.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 207 (c) 69 (d) 72
27. 27.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 16 (c) 56 (d) 28
28. 28.The mean of 3 numbers is 30. When the number 46 is added to them, what is the new mean? (a) 38 (b) 34 (c) 30 (d) 35
29. 29.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 80° (d) 135°
30. 30.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 21 (c) 14 (d) 49
31. 31.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 14 (b) 22 (c) 13 (d) 12
32. 32.In a class of 48 children, 29 like dance, 21 like music and 9 like both. How many like neither? (a) 16 (b) 9 (c) 7 (d) 8
33. 33.In a class of 34 children, 18 like tea, 20 like coffee and 12 like both. How many like at least one of the two? (a) 34 (b) 14 (c) 38 (d) 26
34. 34.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 75° (b) 100° (c) 155° (d) 105°
35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19
36. 36.How many factors does 44 have? (a) 7 (b) 6 (c) 4 (d) 5
37. 37.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 4032 (c) 1953 (d) 2017
38. 38.If a + b = 13 and ab = 42, what is (a − b)²? (a) 85 (b) 169 (c) 1 (d) 127
39. 39.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 105° (d) 40°
40. 40.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 600 sq cm (c) 1000 sq cm (d) 100 sq cm

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