Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 682 · 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.In a class of 53 children, 25 like mangoes, 27 like bananas and 9 like both. How many like at least one of the two? (a) 34 (b) 52 (c) 43 (d) 53
2. 2.In a class of 38 children, 18 like cricket, 26 like football and 9 like both. How many like at least one of the two? (a) 35 (b) 44 (c) 38 (d) 26
3. 3.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 94 (c) 84 (d) 93
4. 4.What is the median of 7, 40, 2, 35 and 26? (a) 2 (b) 26 (c) 35 (d) 22
5. 5.In a class of 22 children, 8 like maths, 15 like science and 3 like both. How many like at least one of the two? (a) 23 (b) 17 (c) 20 (d) 22
6. 6.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 81 (c) 72 (d) 18
7. 7.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
8. 8.Using (a − b)² = a² − 2ab + b², what is 18²? (a) 484 (b) 334 (c) 396 (d) 324
9. 9.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 50° (d) 40°
10. 10.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 20) (b) (x + 4)(x + 5) (c) (x + 1)(x + 8) (d) (x − 4)(x − 5)
11. 11.The mean of 8 numbers is 20. When the number 2 is added to them, what is the new mean? (a) 19 (b) 11 (c) 20 (d) 18
12. 12.In a class of 38 children, 29 like cricket, 15 like football and 11 like both. How many like at least one of the two? (a) 22 (b) 38 (c) 44 (d) 33
13. 13.What is the sum of the roots of x² − 7x + 12 = 0? (a) 7 (b) 6 (c) 8 (d) 12
14. 14.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 182 (c) 181 (d) 190
15. 15.The mean of 6 numbers is 22. When the number 29 is added to them, what is the new mean? (a) 25 (b) 24 (c) 22 (d) 23
16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 16 (d) 17
17. 17.In which quadrant does the point (1, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
18. 18.Which term of the AP 19, 26, 33, 40, … is 222? (a) 30th (b) 32nd (c) 31st (d) 29th
19. 19.A drawer has lots of white, green, black, yellow and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 6 (c) 2 (d) 10
20. 20.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/4 (c) 3/4 (d) 1/3
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 1/11 (c) 1/18 (d) 2/11
22. 22.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 35° (c) 55° (d) 125°
23. 23.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
24. 24.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 16 (d) 12
25. 25.A bag has 2 white, 3 yellow and 2 green balls. One ball is taken out without looking. What is the probability that it is white? (a) 2/5 (b) 2/7 (c) 1/3 (d) 5/7
26. 26.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 25 (d) 120
27. 27.What is the 22nd term of the AP 5, 9, 13, 17, …? (a) 88 (b) 93 (c) 84 (d) 89
28. 28.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 5 (b) 16 (c) 17 (d) 15
30. 30.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) 14 (b) 15 (c) 7 (d) 8
31. 31.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 27 (b) 26 (c) 35 (d) 28
32. 32.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 4 (d) 3
33. 33.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
34. 34.In which quadrant does the point (−2, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
35. 35.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 91° (d) 135°
36. 36.If a + b = 13 and ab = 42, what is a² + b²? (a) 253 (b) 85 (c) 169 (d) 127
37. 37.In a class of 20 children, 10 like cricket, 7 like football and 2 like both. How many like at least one of the two? (a) 15 (b) 13 (c) 20 (d) 17
38. 38.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7
39. 39.What is the mean of 11, 11, 17 and 5? (a) 10 (b) 11 (c) 13 (d) 12
40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 8 (b) 17 (c) 18 (d) 19

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