Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 178 · 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 17, 4, 9, 13 and 7? (a) 11 (b) 12 (c) 10 (d) 9
2. 2.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 399 (c) 390 (d) 400
3. 3.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
4. 4.In a class of 38 children, 13 like cricket, 20 like football and 9 like neither. How many like both? (a) 5 (b) 29 (c) 9 (d) 4
5. 5.What is the 14th term of the AP 11, 17, 23, 29, …? (a) 78 (b) 89 (c) 84 (d) 95
6. 6.How many prime numbers are there between 70 and 90? (a) 7 (b) 4 (c) 6 (d) 5
7. 7.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 61° (c) 240° (d) 60°
8. 8.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
10. 10.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1891 (c) 1892 (d) 3782
11. 11.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 15 (d) 10
12. 12.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 20 (d) 90
13. 13.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
15. 15.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 327 (c) 328 (d) 318
16. 16.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7² (b) 2³ × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
17. 17.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 12 (d) 3
18. 18.A bag has 8 yellow balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 10 (c) 20 (d) 9
19. 19.What is the midpoint of the line joining (1, 9) and (11, 21)? (a) (6, 15) (b) (12, 30) (c) (15, 6) (d) (5, 6)
20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 7 (b) 3 (c) 4 (d) 6
21. 21.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 24 (d) 12
22. 22.If a + b = 7 and ab = 10, what is a² + b²? (a) 29 (b) 39 (c) 69 (d) 49
23. 23.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
24. 24.A bag has 8 yellow, 3 red and 3 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 9/14 (b) 1/3 (c) 3/7 (d) 4/7
25. 25.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 14 (c) 15 (d) 8
26. 26.Which is the correct factorisation of x² + 10x + 21? (a) (x + 1)(x + 21) (b) (x − 3)(x − 7) (c) (x + 1)(x + 9) (d) (x + 3)(x + 7)
27. 27.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 1/4 (c) 3/8 (d) 3/5
28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
29. 29.A bag has 5 white balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 2 (c) 6 (d) 12
30. 30.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 37 (b) 264 (c) 132 (d) 150
31. 31.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 11° (c) 170° (d) 20°
32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 3/11 (c) 1/11 (d) 1/9
33. 33.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
34. 34.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 98 (c) 91 (d) 105
35. 35.How many factors does 61 have? (a) 1 (b) 2 (c) 3 (d) 4
36. 36.What is the median of 1, 3, 37, 35 and 32? (a) 37 (b) 32 (c) 35 (d) 3
37. 37.What is the distance between the points (6, 5) and (9, 9)? (a) 7 (b) 6 (c) 25 (d) 5
38. 38.A bag has 4 white balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 8 (c) 6 (d) 5
39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 20 (b) 9 (c) 21 (d) 19
40. 40.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 371 (b) 441 (c) 399 (d) 361

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