Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 270 · 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.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 490 (c) 627 (d) 628
2. 2.How many factors does 30 have? (a) 7 (b) 9 (c) 6 (d) 8
3. 3.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) 63 (b) 20 (c) 60 (d) 180
4. 4.What is the median of 34, 12, 27, 19 and 35? (a) 27 (b) 28 (c) 19 (d) 34
5. 5.The mean of 6 numbers is 23. When the number 37 is added to them, what is the new mean? (a) 26 (b) 25 (c) 30 (d) 23
6. 6.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2² × 3⁴ (c) 2⁴ × 3² (d) 2³ × 3²
7. 7.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
8. 8.A bag has 8 yellow balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 10 (c) 2 (d) 14
9. 9.What is the mean of 16, 17, 4, 9, 8 and 18? (a) 11 (b) 14 (c) 12 (d) 13
10. 10.What is the mode of 17, 19, 9, 9, 19, 1 and 19? (a) 9 (b) 17 (c) 19 (d) 1
11. 11.How many factors does 56 have? (a) 7 (b) 6 (c) 8 (d) 9
12. 12.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 336 (c) 302 (d) 345
13. 13.In a class of 23 children, 10 like cricket, 6 like football and 2 like both. How many like neither? (a) 9 (b) 2 (c) 7 (d) 11
14. 14.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
15. 15.What is the midpoint of the line joining (10, 6) and (22, 14)? (a) (10, 16) (b) (32, 20) (c) (16, 10) (d) (6, 4)
16. 16.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
17. 17.How many factors does 17 have? (a) 1 (b) 2 (c) 4 (d) 3
18. 18.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 21 (c) 15 (d) 36
19. 19.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 220 (c) 213 (d) 223
20. 20.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 3 (d) 1
21. 21.Which is the correct factorisation of x² + 12x + 35? (a) (x + 1)(x + 35) (b) (x + 5)(x + 7) (c) (x + 1)(x + 11) (d) (x − 5)(x − 7)
22. 22.What are the roots of x² − 11x + 30 = 0? (a) 1 and 30 (b) 1 and 10 (c) 2 and 15 (d) 5 and 6
23. 23.What is the mode of 5, 5, 18, 9, 18, 16 and 18? (a) 9 (b) 5 (c) 16 (d) 18
24. 24.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 288 (b) 144 (c) 23 (d) 156
25. 25.In a class of 36 children, 15 like cricket, 24 like football and 7 like neither. How many like both? (a) 7 (b) 3 (c) 10 (d) 29
26. 26.What is the mean of 4, 12, 5, 6, 2 and 19? (a) 10 (b) 8 (c) 9 (d) 7
27. 27.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
28. 28.In a class of 47 children, 26 like cricket, 20 like football and 6 like both. How many like at least one of the two? (a) 40 (b) 46 (c) 34 (d) 47
29. 29.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 140° (c) 30° (d) 150°
30. 30.The mean of 9 numbers is 34. When the number 24 is added to them, what is the new mean? (a) 32 (b) 33 (c) 29 (d) 34
31. 31.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 51 (b) 486 (c) 243 (d) 270
32. 32.A cuboid is 8 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 128 sq cm (b) 80 sq cm (c) 320 sq cm (d) 160 sq cm
33. 33.In a class of 45 children, 22 like cricket, 30 like football and 10 like both. How many like only cricket? (a) 12 (b) 20 (c) 15 (d) 22
34. 34.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 25 sq cm (c) 125 sq cm (d) 150 sq cm
35. 35.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
36. 36.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 946 (c) 1980 (d) 968
37. 37.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 539 (b) 409 (c) 529 (d) 289
38. 38.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 5/8 (c) 1/4 (d) 3/5
39. 39.What is the midpoint of the line joining (1, 3) and (5, 5)? (a) (3, 4) (b) (4, 3) (c) (2, 1) (d) (6, 8)
40. 40.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 8 times (d) 4 times

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