Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 794 · 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 26 children, 15 like dance, 15 like music and 11 like both. How many like only dance? (a) 15 (b) 11 (c) 4 (d) 5
2. 2.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 16 (d) 12
3. 3.What is the mode of 7, 2, 7, 3, 7, 13 and 2? (a) 3 (b) 2 (c) 7 (d) 13
4. 4.A drawer has lots of green, red, black 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) 8 (c) 4 (d) 2
5. 5.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
6. 6.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 16 (d) 48
7. 7.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) 36 (b) 33 (c) 99 (d) 11
8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 20 (d) 9
9. 9.A drawer has lots of blue and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 2 (d) 3
10. 10.Which term of the AP 19, 25, 31, 37, … is 145? (a) 23rd (b) 24th (c) 21st (d) 22nd
11. 11.What is the distance between the points (3, 12) and (11, 6)? (a) 11 (b) 14 (c) 100 (d) 10
12. 12.A bag has 7 blue balls and 8 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) 9 (c) 15 (d) 8
13. 13.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 231 (c) 242 (d) 253
14. 14.In a class of 34 children, 21 like tea, 7 like coffee and 2 like both. How many like at least one of the two? (a) 34 (b) 24 (c) 28 (d) 26
15. 15.A bag has 4 yellow balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 5 (c) 6 (d) 2
16. 16.What is the median of 32, 16, 21, 33 and 5? (a) 16 (b) 22 (c) 21 (d) 32
17. 17.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 85° (b) 110° (c) 155° (d) 95°
18. 18.What is the sum of the roots of x² − 9x + 14 = 0? (a) 9 (b) 14 (c) 8 (d) 10
19. 19.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 4160 (c) 2080 (d) 2016
20. 20.A bag has 11 black balls and 3 green 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) 12 (c) 14 (d) 2
21. 21.How many prime numbers are there between 80 and 110? (a) 8 (b) 9 (c) 6 (d) 7
22. 22.Which is the correct factorisation of x² + 5x + 6? (a) (x + 1)(x + 6) (b) (x + 1)(x + 4) (c) (x − 2)(x − 3) (d) (x + 2)(x + 3)
23. 23.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
24. 24.Which term of the AP 16, 20, 24, 28, … is 124? (a) 29th (b) 28th (c) 31st (d) 27th
25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 5 (b) 7 (c) 6 (d) 8
26. 26.In a class of 28 children, 6 like mangoes, 14 like bananas and 2 like both. How many like neither? (a) 10 (b) 12 (c) 2 (d) 8
27. 27.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 30 (c) 20 (d) 15
28. 28.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 55° (c) 110° (d) 35°
29. 29.What is the mode of 19, 2, 12, 2, 12, 10 and 2? (a) 19 (b) 10 (c) 2 (d) 12
30. 30.What is the 39th term of the AP 3, 7, 11, 15, …? (a) 159 (b) 152 (c) 155 (d) 156
31. 31.What is the distance between the points (4, 5) and (7, 1)? (a) 25 (b) 5 (c) 6 (d) 7
32. 32.What is the sum of the roots of x² − 14x + 48 = 0? (a) 48 (b) 13 (c) 14 (d) 15
33. 33.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4561 (c) 4560 (d) 4465
34. 34.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 63 (c) 7 (d) 21
35. 35.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 12 (d) 13
36. 36.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
37. 37.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 486 (c) 622 (d) 621
38. 38.What is the product of the roots of x² − 7x + 10 = 0? (a) 11 (b) 10 (c) 9 (d) 7
39. 39.In which quadrant does the point (9, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.In a class of 37 children, 17 like tea, 19 like coffee and 8 like neither. How many like both? (a) 6 (b) 29 (c) 7 (d) 8

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