Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 414 · 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 an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 60° (c) 120° (d) 61°
2. 2.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 60° (b) 105° (c) 135° (d) 120°
3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 7 (b) 8 (c) 9 (d) 10
4. 4.If a + b = 16 and ab = 60, what is a² + b²? (a) 136 (b) 376 (c) 196 (d) 256
5. 5.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 110° (b) 70° (c) 250° (d) 125°
6. 6.What is the smallest prime factor of 93? (a) 1 (b) 3 (c) 2 (d) 31
7. 7.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 130° (b) 120° (c) 110° (d) 70°
8. 8.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 10 (c) 15 (d) 20
9. 9.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 36 (d) 81
10. 10.What is the median of 22, 4, 13, 37, 18, 36 and 9? (a) 18 (b) 13 (c) 22 (d) 37
11. 11.What is the 28th term of the AP 11, 19, 27, 35, …? (a) 227 (b) 216 (c) 224 (d) 235
12. 12.In a class of 24 children, 14 like dance, 13 like music and 9 like both. How many like at least one of the two? (a) 27 (b) 9 (c) 18 (d) 24
13. 13.A bag has 12 green balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 23 (c) 2 (d) 13
14. 14.What is the median of 16, 33, 2, 12, 40, 36 and 4? (a) 33 (b) 16 (c) 12 (d) 17
15. 15.Using (a + b)² = a² + 2ab + b², what is 62²? (a) 3854 (b) 3604 (c) 3844 (d) 3364
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 14 (b) 15 (c) 4 (d) 13
17. 17.If a + b = 8 and ab = 15, what is (a − b)²? (a) 4 (b) 34 (c) 64 (d) 2
18. 18.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
19. 19.A bag has 2 red, 2 green and 5 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 2/3 (b) 1/3 (c) 5/9 (d) 4/9
20. 20.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) 7 (c) 15 (d) 8
21. 21.How many prime numbers are there between 80 and 90? (a) 4 (b) 3 (c) 2 (d) 1
22. 22.A drawer has lots of green, black, yellow, white 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) 10 (b) 5 (c) 6 (d) 2
23. 23.In a class of 37 children, 21 like maths, 19 like science and 1 like neither. How many like both? (a) 1 (b) 3 (c) 36 (d) 4
24. 24.What is the mean of 16, 16, 13, 9, 10 and 8? (a) 14 (b) 13 (c) 11 (d) 12
25. 25.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 54 (c) 57 (d) 162
26. 26.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 60° (d) 120°
27. 27.In a class of 44 children, 22 like mangoes, 20 like bananas and 5 like both. How many like at least one of the two? (a) 32 (b) 44 (c) 42 (d) 37
28. 28.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
29. 29.How many factors does 110 have? (a) 6 (b) 8 (c) 7 (d) 9
30. 30.In a class of 26 children, 20 like tea, 16 like coffee and 12 like both. How many like only tea? (a) 20 (b) 10 (c) 8 (d) 4
31. 31.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 152 (b) 80 (c) 76 (d) 13
32. 32.There are 8 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 32 (c) 64 (d) 40
33. 33.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
34. 34.Using (a + b)² = a² + 2ab + b², what is 75²? (a) 4225 (b) 4925 (c) 5635 (d) 5625
35. 35.If a + b = 17 and ab = 66, what is (a − b)²? (a) 5 (b) 25 (c) 289 (d) 157
36. 36.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/8 (c) 1/8 (d) 7/8
37. 37.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
38. 38.What is the mean of 9, 4, 19 and 20? (a) 15 (b) 12 (c) 13 (d) 14
39. 39.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
40. 40.In a class of 33 children, 22 like tea, 7 like coffee and 4 like both. How many like neither? (a) 4 (b) 12 (c) 9 (d) 8

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