Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 646 · 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 mean of 15, 10, 7 and 8? (a) 11 (b) 10 (c) 9 (d) 8
2. 2.What is the 16th term of the AP 15, 20, 25, 30, …? (a) 80 (b) 90 (c) 95 (d) 75
3. 3.What is the sum of all the whole numbers from 1 to 15? (a) 120 (b) 121 (c) 105 (d) 240
4. 4.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 137 (b) 146 (c) 138 (d) 128
5. 5.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 50° (d) 70°
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
7. 7.A bag has 8 red balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 10 (c) 16 (d) 2
8. 8.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 8)(x + 9) (c) (x + 1)(x + 16) (d) (x + 1)(x + 72)
9. 9.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
10. 10.Using (a + b)² = a² + 2ab + b², what is 52²? (a) 2304 (b) 2504 (c) 2714 (d) 2704
11. 11.What is the distance between the points (4, 5) and (20, 17)? (a) 28 (b) 400 (c) 21 (d) 20
12. 12.What is the mode of 16, 15, 19, 1, 16, 19 and 16? (a) 15 (b) 1 (c) 19 (d) 16
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 2/11 (c) 1/11 (d) 1/12
14. 14.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 1089 (b) 1099 (c) 909 (d) 729
15. 15.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 48) (b) (x − 6)(x − 8) (c) (x + 6)(x + 8) (d) (x + 1)(x + 13)
16. 16.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 130° (b) 75° (c) 155° (d) 105°
17. 17.What is the mode of 11, 1, 11, 8, 11, 6 and 6? (a) 6 (b) 11 (c) 1 (d) 8
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 5/36 (c) 1/11 (d) 1/6
19. 19.In which quadrant does the point (8, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
20. 20.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 165° (c) 30° (d) 15°
21. 21.What is the 14th term of the AP 14, 18, 22, 26, …? (a) 70 (b) 56 (c) 66 (d) 52
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
23. 23.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 49 (c) 37 (d) 36
24. 24.In a class of 42 children, 19 like cricket, 26 like football and 8 like neither. How many like both? (a) 8 (b) 34 (c) 11 (d) 3
25. 25.In a class of 51 children, 23 like maths, 26 like science and 6 like both. How many like at least one of the two? (a) 49 (b) 37 (c) 43 (d) 51
26. 26.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 66 (c) 24 (d) 144
27. 27.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 90 (c) 30 (d) 10
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/11 (b) 1/11 (c) 1/6 (d) 5/36
29. 29.In a class of 34 children, 12 like dance, 23 like music and 3 like both. How many like at least one of the two? (a) 34 (b) 35 (c) 32 (d) 29
30. 30.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
31. 31.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 81 (c) 36 (d) 45
32. 32.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 123 (b) 33 (c) 138 (d) 246
33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 15 (b) 5 (c) 16 (d) 17
34. 34.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15
35. 35.The mean of 8 numbers is 24. When the number 51 is added to them, what is the new mean? (a) 26 (b) 28 (c) 27 (d) 24
36. 36.In a class of 21 children, 15 like maths, 14 like science and 2 like neither. How many like both? (a) 8 (b) 10 (c) 19 (d) 2
37. 37.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
38. 38.In a class of 35 children, 13 like maths, 24 like science and 7 like both. How many like neither? (a) 5 (b) 12 (c) 7 (d) 6
39. 39.How many factors does 54 have? (a) 7 (b) 8 (c) 9 (d) 6
40. 40.In a class of 24 children, 10 like dance, 18 like music and 6 like both. How many like only dance? (a) 10 (b) 4 (c) 6 (d) 12

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