Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 695 · 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 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
2. 2.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 330° (d) 150°
3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 5/36 (c) 5/11 (d) 1/11
4. 4.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 65° (b) 115° (c) 150° (d) 95°
5. 5.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 55° (b) 235° (c) 110° (d) 125°
6. 6.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 73 (b) 960 (c) 480 (d) 516
7. 7.In a class of 29 children, 12 like tea, 19 like coffee and 1 like neither. How many like both? (a) 28 (b) 3 (c) 2 (d) 1
8. 8.What is the distance between the points (6, 19) and (18, 3)? (a) 20 (b) 28 (c) 21 (d) 400
9. 9.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁵ × 3 × 5 (d) 2⁴ × 3 × 5
10. 10.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 24 (c) 75 (d) 216
11. 11.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 63 (c) 21 (d) 24
12. 12.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 15 (c) 135 (d) 45
13. 13.A drawer has lots of red, green, yellow and black 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) 4 (c) 2 (d) 8
14. 14.What is the distance between the points (7, 7) and (19, 23)? (a) 28 (b) 21 (c) 20 (d) 400
15. 15.What is the mean of 7, 6, 17, 4, 8 and 18? (a) 12 (b) 11 (c) 10 (d) 9
16. 16.How many prime numbers are there between 20 and 40? (a) 5 (b) 3 (c) 6 (d) 4
17. 17.A bag has 3 blue, 2 white and 9 green balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 6/7 (c) 1/7 (d) 1/6
18. 18.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 9 (b) 5 (c) 6 (d) 7
19. 19.In a class of 30 children, 24 like tea, 16 like coffee and 11 like both. How many like at least one of the two? (a) 30 (b) 40 (c) 18 (d) 29
20. 20.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 72 (c) 45 (d) 81
21. 21.What is the median of 35, 2, 25, 14 and 39? (a) 35 (b) 25 (c) 14 (d) 23
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
23. 23.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
24. 24.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 15 (d) 30
25. 25.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 20 (c) 100 (d) 90
26. 26.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 5 (b) 2 (c) 4 (d) 3
28. 28.In which quadrant does the point (−7, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
29. 29.What is the 24th term of the AP 13, 16, 19, 22, …? (a) 69 (b) 85 (c) 72 (d) 82
30. 30.What is the prime factorisation of 140? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7 (d) 2 × 5 × 7²
31. 31.In which quadrant does the point (−3, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
32. 32.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 217 (b) 46 (c) 196 (d) 392
33. 33.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 24 (c) 12 (d) 16
34. 34.In a class of 54 children, 29 like mangoes, 30 like bananas and 11 like both. How many like only mangoes? (a) 19 (b) 18 (c) 29 (d) 24
35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 15 (d) 6
36. 36.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 90 (c) 100 (d) 55
37. 37.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 160° (c) 80° (d) 100°
38. 38.6 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 36 (b) 72 (c) 42 (d) 12
39. 39.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
40. 40.Which is the correct factorisation of x² + 9x + 20? (a) (x + 4)(x + 5) (b) (x − 4)(x − 5) (c) (x + 1)(x + 20) (d) (x + 1)(x + 8)

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