Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 544 · 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 angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 70° (d) 140°
2. 2.What is the smallest prime factor of 209? (a) 2 (b) 11 (c) 1 (d) 19
3. 3.What is the distance between the points (5, 14) and (21, 2)? (a) 21 (b) 28 (c) 400 (d) 20
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
5. 5.What is the median of 33, 24, 38, 29, 9, 12 and 26? (a) 27 (b) 24 (c) 29 (d) 26
6. 6.A bag has 3 yellow balls and 4 red 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) 4 (c) 5 (d) 7
7. 7.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 85° (c) 170° (d) 86°
8. 8.A bag has 3 red balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 4 (b) 2 (c) 5 (d) 12
9. 9.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 9 (c) 20 (d) 24
10. 10.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 36 (c) 25 (d) 37
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 1/11 (c) 3/11 (d) 1/9
12. 12.What is the mode of 11, 14, 11, 18, 18, 11 and 17? (a) 17 (b) 14 (c) 18 (d) 11
13. 13.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 65° (d) 50°
14. 14.In a class of 25 children, 12 like mangoes, 15 like bananas and 5 like both. How many like at least one of the two? (a) 27 (b) 17 (c) 22 (d) 25
15. 15.If a + b = 13 and ab = 36, what is a² + b²? (a) 97 (b) 241 (c) 133 (d) 169
16. 16.How many prime numbers are there between 50 and 70? (a) 5 (b) 3 (c) 6 (d) 4
17. 17.How many prime numbers are there between 30 and 40? (a) 2 (b) 1 (c) 4 (d) 3
18. 18.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
19. 19.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 22 (d) 15
20. 20.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 841 (b) 901 (c) 961 (d) 971
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 1/11 (c) 2/11 (d) 1/18
22. 22.What is the mean of 2, 20, 6 and 12? (a) 10 (b) 9 (c) 8 (d) 11
23. 23.In a class of 41 children, 11 like tea, 24 like coffee and 4 like both. How many like at least one of the two? (a) 27 (b) 35 (c) 31 (d) 41
24. 24.In a class of 40 children, 27 like cricket, 15 like football and 7 like both. How many like neither? (a) 6 (b) 5 (c) 12 (d) 7
25. 25.Which term of the AP 13, 22, 31, 40, … is 193? (a) 20th (b) 21st (c) 22nd (d) 23rd
26. 26.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
27. 27.What is the midpoint of the line joining (7, 15) and (9, 3)? (a) (1, 6) (b) (16, 18) (c) (8, 9) (d) (9, 8)
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 day of the week? (a) 7 (b) 15 (c) 14 (d) 8
29. 29.A drawer has lots of red and yellow 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) 3 (c) 2 (d) 4
30. 30.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 11035 (b) 9025 (c) 10025 (d) 11025
31. 31.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 224 (c) 219 (d) 229
32. 32.In a class of 37 children, 24 like tea, 9 like coffee and 6 like both. How many like neither? (a) 10 (b) 4 (c) 6 (d) 16
33. 33.A bag has 2 green, 2 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 5/6 (c) 2/3 (d) 1/6
34. 34.A bag has 12 blue balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 14 (b) 20 (c) 13 (d) 2
35. 35.A bag has 7 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) 6 (b) 2 (c) 12 (d) 8
36. 36.In a class of 41 children, 25 like mangoes, 24 like bananas and 1 like neither. How many like both? (a) 9 (b) 8 (c) 1 (d) 40
37. 37.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 49 (d) 42
38. 38.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
39. 39.How many prime numbers are there between 10 and 30? (a) 6 (b) 7 (c) 5 (d) 8
40. 40.If a + b = 13 and ab = 42, what is (a − b)²? (a) 127 (b) 169 (c) 85 (d) 1

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