Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 515 · 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.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 155° (b) 65° (c) 40° (d) 140°
2. 2.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 4802 (c) 4851 (d) 9702
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
4. 4.What is the distance between the points (3, 5) and (15, 10)? (a) 14 (b) 169 (c) 13 (d) 17
5. 5.What is the 31st term of the AP 1, 8, 15, 22, …? (a) 217 (b) 211 (c) 218 (d) 210
6. 6.A drawer has lots of blue, black and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 2 (c) 4 (d) 6
7. 7.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 9 (d) 30
8. 8.A bag has 9 black balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 11 (c) 16 (d) 10
9. 9.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
10. 10.What is the 23rd term of the AP 12, 15, 18, 21, …? (a) 78 (b) 81 (c) 66 (d) 69
11. 11.What is the median of 17, 33, 5, 7 and 31? (a) 7 (b) 31 (c) 5 (d) 17
12. 12.The mean of 3 numbers is 28. When the number 24 is added to them, what is the new mean? (a) 28 (b) 29 (c) 27 (d) 26
13. 13.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 140° (c) 115° (d) 105°
14. 14.How many factors does 99 have? (a) 4 (b) 5 (c) 6 (d) 7
15. 15.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 3025 (b) 3035 (c) 2525 (d) 2025
16. 16.A bag has 4 blue balls and 5 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) 5 (c) 6 (d) 9
17. 17.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 240 (c) 25 (d) 120
18. 18.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 55 (d) 110
19. 19.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 48 (d) 12
20. 20.In a class of 30 children, 17 like tea, 16 like coffee and 9 like both. How many like at least one of the two? (a) 33 (b) 15 (c) 30 (d) 24
21. 21.In a class of 32 children, 23 like maths, 13 like science and 1 like neither. How many like both? (a) 31 (b) 4 (c) 5 (d) 1
22. 22.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 150° (b) 50° (c) 130° (d) 160°
23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 4 (d) 2
24. 24.If a + b = 16 and ab = 63, what is (a − b)²? (a) 256 (b) 130 (c) 2 (d) 4
25. 25.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 310° (c) 40° (d) 50°
26. 26.What is the median of 37, 38, 13, 33, 36, 10 and 1? (a) 24 (b) 36 (c) 13 (d) 33
27. 27.What is the product of the roots of x² − 9x + 18 = 0? (a) 9 (b) 17 (c) 19 (d) 18
28. 28.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 228 (c) 219 (d) 224
29. 29.If a + b = 9 and ab = 8, what is (a − b)²? (a) 49 (b) 81 (c) 7 (d) 65
30. 30.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
31. 31.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2850 (c) 2926 (d) 2888
32. 32.What is the mean of 4, 14, 15 and 11? (a) 11 (b) 13 (c) 12 (d) 10
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/9 (d) 1/11
34. 34.If a + b = 20 and ab = 99, what is (a − b)²? (a) 2 (b) 400 (c) 202 (d) 4
35. 35.The mean of 4 numbers is 25. When the number 30 is added to them, what is the new mean? (a) 26 (b) 25 (c) 27 (d) 28
36. 36.A drawer has lots of green, 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) 4 (b) 6 (c) 2 (d) 3
37. 37.What is the mean of 8, 5, 19 and 16? (a) 16 (b) 11 (c) 12 (d) 13
38. 38.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
39. 39.What is the median of 40, 18, 8, 28, 2, 10 and 15? (a) 18 (b) 10 (c) 28 (d) 15
40. 40.How many prime numbers are there between 10 and 40? (a) 9 (b) 8 (c) 10 (d) 7

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