Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 152 · 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 8, 14, 15, 11, 15 and 3? (a) 12 (b) 10 (c) 13 (d) 11
2. 2.What is the distance between the points (6, 0) and (12, 8)? (a) 11 (b) 100 (c) 14 (d) 10
3. 3.Using (a − b)² = a² − 2ab + b², what is 87²? (a) 7579 (b) 8091 (c) 7569 (d) 8649
4. 4.The mean of 3 numbers is 29. When the number 25 is added to them, what is the new mean? (a) 29 (b) 27 (c) 28 (d) 30
5. 5.A bag has 8 white balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 2 (c) 16 (d) 10
6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 14 (b) 4 (c) 15 (d) 16
7. 7.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 35° (c) 145° (d) 110°
8. 8.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
9. 9.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 153 (c) 17 (d) 54
10. 10.A bag has 4 blue balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 9 (b) 6 (c) 2 (d) 5
11. 11.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 196 (c) 182 (d) 105
12. 12.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 15 (d) 12
13. 13.What is the distance between the points (0, 2) and (7, 26)? (a) 31 (b) 625 (c) 26 (d) 25
14. 14.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 15 (c) 14 (d) 22
15. 15.What is the mean of 12, 13, 15 and 20? (a) 16 (b) 15 (c) 20 (d) 12
16. 16.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 2556 (c) 2485 (d) 5112
17. 17.In a class of 48 children, 21 like cricket, 22 like football and 9 like neither. How many like both? (a) 5 (b) 4 (c) 9 (d) 39
18. 18.In a class of 26 children, 19 like maths, 9 like science and 4 like both. How many like at least one of the two? (a) 26 (b) 24 (c) 28 (d) 20
19. 19.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 576 sq cm
20. 20.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
21. 21.What is the mean of 18, 6, 20 and 4? (a) 11 (b) 13 (c) 12 (d) 16
22. 22.What is the 33rd term of the AP 3, 10, 17, 24, …? (a) 231 (b) 234 (c) 227 (d) 224
23. 23.What is the sum of the roots of x² − 17x + 72 = 0? (a) 17 (b) 72 (c) 18 (d) 16
24. 24.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
25. 25.What is the distance between the points (3, 5) and (15, 10)? (a) 17 (b) 169 (c) 14 (d) 13
26. 26.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 42 (d) 49
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 3/11 (c) 1/9 (d) 1/11
28. 28.Using (a − b)² = a² − 2ab + b², what is 17²? (a) 391 (b) 529 (c) 299 (d) 289
29. 29.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
30. 30.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 552 (c) 553 (d) 543
31. 31.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
32. 32.How many prime numbers are there between 20 and 30? (a) 1 (b) 4 (c) 3 (d) 2
33. 33.What are the roots of x² − 15x + 56 = 0? (a) 7 and 8 (b) 1 and 14 (c) 1 and 56 (d) 2 and 28
34. 34.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 16 (d) 24
35. 35.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
36. 36.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/4 (c) 1/3 (d) 2/3
37. 37.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) 21 (b) 28 (c) 29 (d) 22
38. 38.A bag has 9 black balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 10 (c) 7 (d) 15
39. 39.A cuboid is 8 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 144 sq cm (b) 72 sq cm (c) 36 sq cm (d) 32 sq cm
40. 40.Which is the correct factorisation of x² + 14x + 48? (a) (x + 6)(x + 8) (b) (x + 1)(x + 13) (c) (x + 1)(x + 48) (d) (x − 6)(x − 8)

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