Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 586 · 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 bag has 3 red balls and 11 blue 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) 14 (c) 12 (d) 4
2. 2.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 54 cu cm (c) 36 cu cm (d) 9 cu cm
3. 3.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 258 (c) 249 (d) 259
4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 18 (d) 20
5. 5.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 324 sq cm (d) 729 sq cm
6. 6.A bag has 3 red, 7 green and 2 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 5/6 (c) 1/4 (d) 3/4
7. 7.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 270° (c) 135° (d) 45°
8. 8.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 4 (b) 3 (c) 2 (d) 5
10. 10.What is the smallest prime factor of 65? (a) 2 (b) 13 (c) 1 (d) 5
11. 11.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
12. 12.What is the 12th term of the AP 13, 15, 17, 19, …? (a) 37 (b) 35 (c) 24 (d) 22
13. 13.What is the mode of 15, 13, 13, 12, 15, 13 and 11? (a) 11 (b) 12 (c) 15 (d) 13
14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 3 (b) 5 (c) 4 (d) 6
15. 15.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 49 (c) 14 (d) 98
16. 16.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 20 (d) 15
17. 17.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 12 (d) 16
18. 18.What is the product of the roots of x² − 7x + 10 = 0? (a) 11 (b) 7 (c) 10 (d) 9
19. 19.In a class of 51 children, 28 like cricket, 23 like football and 8 like both. How many like at least one of the two? (a) 51 (b) 35 (c) 43 (d) 44
20. 20.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2 × 3 × 5³ (d) 2³ × 3 × 5
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 16 (b) 15 (c) 5 (d) 17
22. 22.In a class of 34 children, 13 like tea, 22 like coffee and 6 like both. How many like at least one of the two? (a) 34 (b) 29 (c) 35 (d) 23
23. 23.What is the distance between the points (1, 4) and (4, 8)? (a) 7 (b) 6 (c) 5 (d) 25
24. 24.A bag has 5 white balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 10 (c) 6 (d) 7
25. 25.What is the mean of 10, 5, 12, 18, 3 and 18? (a) 10 (b) 13 (c) 11 (d) 12
26. 26.In a class of 30 children, 16 like tea, 15 like coffee and 1 like neither. How many like both? (a) 3 (b) 2 (c) 1 (d) 29
27. 27.What is the distance between the points (8, 20) and (13, 8)? (a) 17 (b) 169 (c) 13 (d) 14
28. 28.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) 13 (b) 24 (c) 25 (d) 12
29. 29.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 70° (d) 160°
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 5/36 (c) 1/6 (d) 1/11
31. 31.Using (a + b)² = a² + 2ab + b², what is 53²? (a) 2819 (b) 2209 (c) 2809 (d) 2509
32. 32.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 120 (d) 240
33. 33.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 135° (b) 145° (c) 80° (d) 100°
34. 34.Using (a − b)² = a² − 2ab + b², what is 38²? (a) 1764 (b) 1444 (c) 1454 (d) 1596
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 day of the week? (a) 15 (b) 8 (c) 14 (d) 7
36. 36.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 110° (d) 105°
37. 37.How many prime numbers are there between 60 and 90? (a) 7 (b) 9 (c) 6 (d) 8
38. 38.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 20° (b) 290° (c) 70° (d) 110°
39. 39.A drawer has lots of red and green 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) 2 (c) 5 (d) 3
40. 40.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5

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