Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 668 · 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 smallest prime factor of 403? (a) 31 (b) 2 (c) 13 (d) 1
2. 2.What is the mode of 4, 16, 16, 16, 15, 4 and 11? (a) 11 (b) 16 (c) 15 (d) 4
3. 3.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 49 (c) 14 (d) 98
4. 4.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 21 (d) 9
6. 6.In a class of 34 children, 18 like mangoes, 26 like bananas and 2 like neither. How many like both? (a) 32 (b) 2 (c) 10 (d) 12
7. 7.The mean of 5 numbers is 19. When the number 25 is added to them, what is the new mean? (a) 20 (b) 19 (c) 21 (d) 22
8. 8.In a class of 42 children, 23 like maths, 21 like science and 3 like neither. How many like both? (a) 5 (b) 2 (c) 3 (d) 39
9. 9.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 60° (b) 90° (c) 150° (d) 120°
10. 10.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 2/3 (c) 1/4 (d) 5/6
11. 11.A bag has 8 white, 2 green and 6 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 7/8 (b) 1/8 (c) 1/3 (d) 15/16
12. 12.A bag has 6 white balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 16 (b) 2 (c) 7 (d) 8
13. 13.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
14. 14.What is the mean of 19, 3, 17 and 21? (a) 12 (b) 16 (c) 20 (d) 15
15. 15.What is the distance between the points (8, 9) and (14, 17)? (a) 100 (b) 14 (c) 11 (d) 10
16. 16.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
17. 17.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 29 (c) 28 (d) 21
18. 18.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 6 (c) 12 (d) 5
19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 20 (d) 18
20. 20.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 126 (c) 116 (d) 125
21. 21.What is the smallest prime factor of 65? (a) 1 (b) 5 (c) 2 (d) 13
22. 22.A bag has 11 red balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 12 (c) 2 (d) 16
23. 23.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
24. 24.In a class of 15 children, 9 like dance, 9 like music and 6 like both. How many like neither? (a) 4 (b) 3 (c) 6 (d) 9
25. 25.If a + b = 10 and ab = 9, what is (a − b)²? (a) 64 (b) 100 (c) 8 (d) 82
26. 26.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 54 (c) 18 (d) 162
27. 27.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
28. 28.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 250° (b) 110° (c) 70° (d) 125°
29. 29.A bag has 5 yellow, 8 green and 3 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 3/16 (c) 7/8 (d) 13/16
30. 30.The mean of 9 numbers is 26. When the number 6 is added to them, what is the new mean? (a) 24 (b) 25 (c) 16 (d) 26
31. 31.A bag has 8 yellow, 7 green and 2 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 8/17 (b) 9/17 (c) 1/3 (d) 8/9
32. 32.How many factors does 14 have? (a) 3 (b) 4 (c) 5 (d) 2
33. 33.Using (a + b)² = a² + 2ab + b², what is 104²? (a) 10016 (b) 10826 (c) 9216 (d) 10816
34. 34.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 24 (d) 16
35. 35.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 72 (c) 8 (d) 24
36. 36.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 12 (d) 16
37. 37.A bag has 11 black balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 12 (c) 19 (d) 13
38. 38.What is the distance between the points (0, 0) and (12, 5)? (a) 14 (b) 169 (c) 13 (d) 17
39. 39.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 150 cu cm (d) 125 cu cm
40. 40.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 120° (d) 30°

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