Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 202 · 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 team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 66 (d) 24
2. 2.In which quadrant does the point (2, 3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
3. 3.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) 15 (c) 21 (d) 22
4. 4.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) 24 (c) 37 (d) 25
5. 5.What is the median of 16, 14, 40, 37, 22, 32 and 8? (a) 32 (b) 16 (c) 37 (d) 22
6. 6.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 150 (b) 23 (c) 280 (d) 140
7. 7.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 126 sq cm (b) 162 sq cm (c) 324 sq cm (d) 81 sq cm
8. 8.In a class of 31 children, 12 like maths, 25 like science and 8 like both. How many like at least one of the two? (a) 21 (b) 29 (c) 37 (d) 31
9. 9.In a class of 30 children, 15 like cricket, 11 like football and 6 like both. How many like neither? (a) 16 (b) 4 (c) 10 (d) 6
10. 10.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
11. 11.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7 (b) 2³ × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
12. 12.A drawer has lots of black, blue, red, white 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) 6 (c) 2 (d) 10
13. 13.What is the sum of the roots of x² − 7x + 10 = 0? (a) 10 (b) 6 (c) 7 (d) 8
14. 14.The mean of 3 numbers is 33. When the number 25 is added to them, what is the new mean? (a) 32 (b) 33 (c) 29 (d) 31
15. 15.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
16. 16.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 45 (c) 100 (d) 55
17. 17.The mean of 6 numbers is 37. When the number 16 is added to them, what is the new mean? (a) 33 (b) 35 (c) 37 (d) 34
18. 18.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
19. 19.The mean of 5 numbers is 21. When the number 9 is added to them, what is the new mean? (a) 19 (b) 20 (c) 21 (d) 15
20. 20.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 57 (c) 60 (d) 171
21. 21.What is the 35th term of the AP 3, 7, 11, 15, …? (a) 140 (b) 136 (c) 143 (d) 139
22. 22.How many factors does 75 have? (a) 7 (b) 4 (c) 5 (d) 6
23. 23.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 144 (b) 34 (c) 129 (d) 258
24. 24.What is the missing term in the AP 1, ?, 17, 25, 33? (a) 10 (b) 8 (c) 17 (d) 9
25. 25.A bag has 8 green, 6 white and 2 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/2 (b) 1/16 (c) 9/16 (d) 1/3
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 3/11 (c) 1/12 (d) 1/11
28. 28.A bag has 10 green balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 8 (c) 11 (d) 2
29. 29.What is the prime factorisation of 35? (a) 5² × 7 (b) 5³ × 7 (c) 5 × 7 (d) 5 × 7²
30. 30.What is the smallest prime factor of 187? (a) 2 (b) 1 (c) 17 (d) 11
31. 31.A bag has 12 black balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 4 (c) 2 (d) 13
32. 32.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 6 cu cm (b) 11 cu cm (c) 36 cu cm (d) 72 cu cm
33. 33.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
34. 34.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 90 (d) 45
35. 35.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 140° (c) 30° (d) 40°
36. 36.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 11 (b) 132 (c) 67 (d) 66
37. 37.In a class of 37 children, 17 like maths, 20 like science and 4 like both. How many like at least one of the two? (a) 29 (b) 37 (c) 34 (d) 33
38. 38.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
39. 39.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
40. 40.A bag has 11 green balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 12 (c) 13 (d) 17

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