Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 810 · 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 a class of 26 children, 10 like cricket, 14 like football and 2 like both. How many like only cricket? (a) 12 (b) 8 (c) 2 (d) 10
2. 2.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 132 (b) 120 (c) 240 (d) 30
3. 3.What is the midpoint of the line joining (9, 19) and (21, 7)? (a) (15, 13) (b) (30, 26) (c) (13, 15) (d) (6, 6)
4. 4.A bag has 12 white balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 20 (d) 9
5. 5.What is the mean of 16, 7, 8, 3 and 6? (a) 8 (b) 9 (c) 10 (d) 7
6. 6.What is the mode of 6, 11, 6, 15, 11, 6 and 2? (a) 6 (b) 2 (c) 11 (d) 15
7. 7.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 99 (c) 33 (d) 11
8. 8.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/4
9. 9.The mean of 4 numbers is 40. When the number 25 is added to them, what is the new mean? (a) 40 (b) 36 (c) 38 (d) 37
10. 10.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 36 (c) 44 (d) 35
11. 11.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
12. 12.In a class of 36 children, 20 like cricket, 19 like football and 6 like neither. How many like both? (a) 30 (b) 6 (c) 3 (d) 9
13. 13.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
14. 14.What is the mean of 13, 15, 19 and 5? (a) 13 (b) 15 (c) 14 (d) 12
15. 15.How many prime numbers are there between 10 and 20? (a) 3 (b) 6 (c) 4 (d) 5
16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 11 (b) 12 (c) 10 (d) 4
17. 17.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 115° (d) 65°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 300° (c) 120° (d) 150°
19. 19.In a class of 34 children, 19 like cricket, 14 like football and 10 like neither. How many like both? (a) 9 (b) 8 (c) 24 (d) 10
20. 20.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 40° (b) 170° (c) 150° (d) 10°
21. 21.A bag has 6 green, 2 white and 5 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 2/11 (b) 1/3 (c) 2/13 (d) 11/13
22. 22.What is the smallest prime factor of 169? (a) 2 (b) 13 (c) 3 (d) 1
23. 23.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 55° (c) 45° (d) 90°
24. 24.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 20° (b) 290° (c) 110° (d) 70°
25. 25.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 6 (d) 5
26. 26.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 160° (d) 70°
27. 27.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 23 (b) 19 (c) 17 (d) 18
28. 28.A bag has 3 blue, 6 white and 9 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 5/9 (c) 1/2 (d) 1/18
29. 29.If a + b = 15 and ab = 50, what is (a − b)²? (a) 225 (b) 5 (c) 25 (d) 125
30. 30.What is the missing term in the AP 14, 21, ?, 35, 42? (a) 27 (b) 29 (c) 35 (d) 28
31. 31.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4656 (c) 9506 (d) 4753
32. 32.A bag has 4 yellow, 6 red and 9 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 11/19 (b) 9/19 (c) 10/19 (d) 1/3
33. 33.How many prime numbers are there between 30 and 50? (a) 6 (b) 7 (c) 5 (d) 4
34. 34.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
35. 35.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 60 (c) 20 (d) 63
36. 36.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 35° (b) 215° (c) 70° (d) 145°
37. 37.In which quadrant does the point (9, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
38. 38.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 105° (d) 30°
39. 39.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 14 (d) 42
40. 40.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 60° (c) 30° (d) 120°

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