Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 812 · 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.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
2. 2.What is the sum of all the whole numbers from 1 to 41? (a) 862 (b) 820 (c) 861 (d) 1722
3. 3.There are 3 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 36 (c) 18 (d) 21
4. 4.Which term of the AP 19, 23, 27, 31, … is 163? (a) 36th (b) 38th (c) 37th (d) 39th
5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
6. 6.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 95° (c) 5° (d) 85°
7. 7.A bag has 5 red balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 6 (b) 2 (c) 8 (d) 7
8. 8.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 5 (b) 6 (c) 4 (d) 7
10. 10.A bag has 3 green balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 6 (c) 5 (d) 4
11. 11.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 16 sq cm (c) 8 sq cm (d) 4 sq cm
12. 12.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 75° (c) 105° (d) 76°
13. 13.What is the midpoint of the line joining (0, 4) and (6, 8)? (a) (3, 2) (b) (6, 3) (c) (3, 6) (d) (6, 12)
14. 14.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 42 (c) 117 (d) 39
15. 15.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
16. 16.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 15 (d) 30
17. 17.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 20 (b) 19 (c) 21 (d) 18
18. 18.What is the mean of 10, 6, 6, 8 and 5? (a) 7 (b) 6 (c) 9 (d) 8
19. 19.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 210 (d) 225
20. 20.What is the sum of the roots of x² − 16x + 63 = 0? (a) 15 (b) 17 (c) 16 (d) 63
21. 21.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 30° (c) 61° (d) 60°
22. 22.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 140° (b) 65° (c) 155° (d) 25°
23. 23.If a + b = 15 and ab = 56, what is (a − b)²? (a) 1 (b) 169 (c) 113 (d) 225
24. 24.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 55 (c) 66 (d) 67
25. 25.A drawer has lots of yellow, white, black 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) 5 (b) 8 (c) 4 (d) 2
26. 26.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 54 cu cm (c) 9 cu cm (d) 36 cu cm
27. 27.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 18 (d) 9
29. 29.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2 × 5 × 7 (c) 2² × 5 × 7 (d) 2³ × 5 × 7
30. 30.What is the distance between the points (9, 9) and (17, 3)? (a) 100 (b) 11 (c) 10 (d) 14
31. 31.A drawer has lots of blue, yellow, white, 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) 10 (b) 5 (c) 2 (d) 6
32. 32.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 4278 (c) 8742 (d) 4372
33. 33.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
34. 34.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
35. 35.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 250° (c) 70° (d) 71°
36. 36.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 100 (c) 20 (d) 45
37. 37.In a class of 29 children, 15 like cricket, 21 like football and 12 like both. How many like at least one of the two? (a) 12 (b) 29 (c) 36 (d) 24
38. 38.In a class of 45 children, 19 like dance, 21 like music and 4 like both. How many like at least one of the two? (a) 45 (b) 32 (c) 40 (d) 36
39. 39.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 40 (c) 70 (d) 35
40. 40.A bag has 9 red, 4 white and 4 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 4/13 (b) 13/17 (c) 1/3 (d) 4/17

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