Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 553 · 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 35° and 90°. What is the third angle? (a) 125° (b) 55° (c) 145° (d) 90°
2. 2.In a class of 20 children, 11 like maths, 11 like science and 7 like both. How many like at least one of the two? (a) 15 (b) 8 (c) 22 (d) 20
3. 3.A drawer has lots of yellow, green 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) 2 (b) 6 (c) 3 (d) 4
4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 17 (b) 19 (c) 8 (d) 18
5. 5.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 3403 (c) 3321 (d) 6806
6. 6.If a + b = 20 and ab = 99, what is a² + b²? (a) 400 (b) 301 (c) 202 (d) 598
7. 7.What is the mean of 18, 18, 15 and 17? (a) 17 (b) 19 (c) 18 (d) 16
8. 8.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 820 (c) 780 (d) 800
9. 9.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 40) (b) (x + 1)(x + 12) (c) (x + 5)(x + 8) (d) (x − 5)(x − 8)
10. 10.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 20° (c) 70° (d) 340°
11. 11.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
12. 12.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) 36 (b) 25 (c) 37 (d) 24
13. 13.What is the missing term in the AP 9, 15, 21, ?, 33? (a) 27 (b) 33 (c) 28 (d) 26
14. 14.What is the midpoint of the line joining (0, 8) and (8, 12)? (a) (10, 4) (b) (4, 2) (c) (8, 20) (d) (4, 10)
15. 15.What is the median of 1, 21, 33, 18 and 30? (a) 30 (b) 21 (c) 18 (d) 33
16. 16.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) 8 (d) 14
17. 17.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
18. 18.The mean of 3 numbers is 33. When the number 37 is added to them, what is the new mean? (a) 33 (b) 34 (c) 35 (d) 36
19. 19.A drawer has lots of black, red, 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) 8 (b) 4 (c) 2 (d) 5
20. 20.In which quadrant does the point (−3, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
21. 21.A drawer has lots of black, green 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) 2 (b) 6 (c) 3 (d) 4
22. 22.A bag has 3 black balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 4 (b) 5 (c) 2 (d) 10
23. 23.A drawer has lots of red, yellow, blue, green 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) 10 (b) 2 (c) 5 (d) 6
24. 24.In a class of 27 children, 16 like mangoes, 10 like bananas and 6 like both. How many like neither? (a) 13 (b) 7 (c) 1 (d) 6
25. 25.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
26. 26.If a + b = 7 and ab = 12, what is a² + b²? (a) 37 (b) 73 (c) 25 (d) 49
27. 27.How many prime numbers are there between 10 and 20? (a) 4 (b) 6 (c) 3 (d) 5
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) 25 (b) 13 (c) 12 (d) 24
29. 29.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 70° (d) 130°
30. 30.5 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
31. 31.A bag has 5 green balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 4 (d) 6
32. 32.In which quadrant does the point (1, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
33. 33.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 49 (c) 14 (d) 21
34. 34.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 45 (d) 81
35. 35.What is the 40th term of the AP 1, 4, 7, 10, …? (a) 121 (b) 118 (c) 120 (d) 117
36. 36.How many factors does 91 have? (a) 3 (b) 5 (c) 4 (d) 2
37. 37.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 135° (b) 100° (c) 80° (d) 125°
38. 38.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
39. 39.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 130° (c) 51° (d) 50°
40. 40.In a class of 26 children, 15 like cricket, 12 like football and 9 like both. How many like at least one of the two? (a) 18 (b) 26 (c) 9 (d) 27

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