Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 844 · 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 angles of a triangle are 20° and 40°. What is the third angle? (a) 60° (b) 140° (c) 160° (d) 120°
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/12 (c) 1/11 (d) 1/18
3. 3.What is the 38th term of the AP 3, 5, 7, 9, …? (a) 77 (b) 74 (c) 76 (d) 79
4. 4.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
5. 5.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 32 (c) 8 (d) 20
6. 6.What is the mean of 16, 13, 2, 19 and 5? (a) 12 (b) 10 (c) 13 (d) 11
7. 7.In a class of 29 children, 11 like cricket, 16 like football and 2 like both. How many like at least one of the two? (a) 23 (b) 29 (c) 27 (d) 25
8. 8.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
9. 9.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 156 (c) 78 (d) 72
10. 10.The mean of 7 numbers is 17. When the number 33 is added to them, what is the new mean? (a) 19 (b) 17 (c) 20 (d) 25
11. 11.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) 64 times (c) 8 times (d) 16 times
12. 12.How many factors does 60 have? (a) 11 (b) 13 (c) 10 (d) 12
13. 13.What is the mode of 7, 1, 7, 18, 1, 1 and 5? (a) 5 (b) 1 (c) 18 (d) 7
14. 14.What is the distance between the points (9, 2) and (15, 10)? (a) 11 (b) 100 (c) 10 (d) 14
15. 15.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 24 (c) 25 (d) 37
16. 16.There are 8 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 32 (c) 11 (d) 24
17. 17.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 42 (c) 41 (d) 32
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 1/6 (c) 5/36 (d) 5/11
19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 18 (b) 20 (c) 19 (d) 9
20. 20.What is the mean of 13, 10, 12 and 9? (a) 11 (b) 12 (c) 13 (d) 10
21. 21.What is the smallest prime factor of 51? (a) 2 (b) 3 (c) 17 (d) 1
22. 22.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 210° (c) 30° (d) 105°
23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
24. 24.In a class of 34 children, 22 like cricket, 11 like football and 9 like neither. How many like both? (a) 9 (b) 8 (c) 7 (d) 25
25. 25.In a class of 33 children, 22 like cricket, 17 like football and 10 like both. How many like neither? (a) 5 (b) 14 (c) 4 (d) 10
26. 26.What is the midpoint of the line joining (9, 14) and (21, 10)? (a) (12, 15) (b) (6, 2) (c) (30, 24) (d) (15, 12)
27. 27.There are 4 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 28 (c) 24 (d) 10
28. 28.In a class of 40 children, 20 like tea, 22 like coffee and 12 like both. How many like at least one of the two? (a) 42 (b) 18 (c) 40 (d) 30
29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 21 (b) 20 (c) 9 (d) 19
30. 30.What is the distance between the points (5, 1) and (11, 9)? (a) 10 (b) 14 (c) 100 (d) 11
31. 31.In which quadrant does the point (4, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 14 (d) 15
33. 33.How many prime numbers are there between 60 and 70? (a) 4 (b) 3 (c) 2 (d) 1
34. 34.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
35. 35.How many factors does 15 have? (a) 5 (b) 4 (c) 2 (d) 3
36. 36.What is the distance between the points (0, 9) and (12, 25)? (a) 21 (b) 28 (c) 400 (d) 20
37. 37.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
38. 38.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 16) (b) (x − 2)(x − 8) (c) (x + 1)(x + 9) (d) (x + 2)(x + 8)
39. 39.In a class of 32 children, 9 like tea, 21 like coffee and 3 like both. How many like only tea? (a) 18 (b) 11 (c) 9 (d) 6
40. 40.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2 × 3⁴ (d) 2⁴ × 3

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