Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 304 · 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 median of 33, 9, 10, 32, 11, 3 and 4? (a) 9 (b) 11 (c) 32 (d) 10
2. 2.What are the roots of x² − 17x + 72 = 0? (a) 1 and 16 (b) 8 and 9 (c) 1 and 72 (d) 2 and 36
3. 3.In a class of 35 children, 18 like mangoes, 23 like bananas and 7 like both. How many like at least one of the two? (a) 41 (b) 34 (c) 27 (d) 35
4. 4.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x − 8)(x − 9) (c) (x + 8)(x + 9) (d) (x + 1)(x + 72)
5. 5.In a class of 51 children, 25 like mangoes, 24 like bananas and 6 like both. How many like neither? (a) 6 (b) 2 (c) 8 (d) 14
6. 6.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 4 (d) 5
7. 7.If a + b = 11 and ab = 10, what is (a − b)²? (a) 81 (b) 101 (c) 121 (d) 9
8. 8.A bag has 3 white balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 9 (c) 2 (d) 7
9. 9.What is the mean of 16, 9, 17, 15, 10 and 11? (a) 15 (b) 13 (c) 12 (d) 14
10. 10.If a + b = 17 and ab = 72, what is a² + b²? (a) 217 (b) 433 (c) 289 (d) 145
11. 11.What is the mean of 8, 10, 16, 20 and 21? (a) 15 (b) 14 (c) 17 (d) 16
12. 12.What is the 11th term of the AP 9, 13, 17, 21, …? (a) 44 (b) 53 (c) 49 (d) 40
13. 13.In a class of 51 children, 23 like mangoes, 24 like bananas and 9 like neither. How many like both? (a) 9 (b) 6 (c) 5 (d) 42
14. 14.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 13 (b) 11 (c) 10 (d) 12
15. 15.In a class of 36 children, 12 like cricket, 26 like football and 9 like both. How many like at least one of the two? (a) 38 (b) 20 (c) 29 (d) 36
16. 16.What is the prime factorisation of 72? (a) 2² × 3² (b) 2³ × 3² (c) 2² × 3³ (d) 2⁴ × 3²
17. 17.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 1/4 (d) 3/4
18. 18.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 572 (b) 286 (c) 46 (d) 308
19. 19.How many factors does 19 have? (a) 2 (b) 4 (c) 3 (d) 1
20. 20.In a class of 35 children, 23 like cricket, 10 like football and 7 like both. How many like at least one of the two? (a) 35 (b) 19 (c) 26 (d) 33
21. 21.What is the mean of 11, 17, 18, 6, 20 and 12? (a) 13 (b) 15 (c) 14 (d) 12
22. 22.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
23. 23.Which is the correct factorisation of x² + 16x + 63? (a) (x − 7)(x − 9) (b) (x + 1)(x + 15) (c) (x + 1)(x + 63) (d) (x + 7)(x + 9)
24. 24.The mean of 7 numbers is 22. When the number 14 is added to them, what is the new mean? (a) 20 (b) 22 (c) 18 (d) 21
25. 25.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 33 (c) 36 (d) 11
26. 26.If a + b = 8 and ab = 12, what is (a − b)²? (a) 64 (b) 40 (c) 4 (d) 16
27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 17 (b) 19 (c) 8 (d) 18
28. 28.A bag has 2 white, 4 yellow and 8 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/7 (b) 6/7 (c) 1/3 (d) 13/14
29. 29.What is the mean of 4, 12, 4 and 4? (a) 5 (b) 8 (c) 6 (d) 7
30. 30.If a + b = 13 and ab = 22, what is a² + b²? (a) 169 (b) 125 (c) 147 (d) 213
31. 31.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 120 (c) 119 (d) 110
32. 32.A bag has 5 white balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 6 (b) 7 (c) 2 (d) 8
33. 33.How many factors does 115 have? (a) 5 (b) 4 (c) 3 (d) 2
34. 34.In a class of 26 children, 18 like cricket, 16 like football and 9 like both. How many like neither? (a) 2 (b) 9 (c) 10 (d) 1
35. 35.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 91 (d) 182
36. 36.Using (a + b)² = a² + 2ab + b², what is 102²? (a) 9604 (b) 10004 (c) 10404 (d) 10414
37. 37.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
38. 38.How many prime numbers are there between 30 and 60? (a) 9 (b) 8 (c) 6 (d) 7
39. 39.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 150° (c) 65° (d) 115°
40. 40.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 5/6 (c) 1/3 (d) 2/3

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