Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 551 · 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 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 25° (d) 50°
2. 2.What is the midpoint of the line joining (3, 4) and (5, 12)? (a) (4, 8) (b) (1, 4) (c) (8, 4) (d) (8, 16)
3. 3.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 6)(x + 7) (c) (x + 1)(x + 12) (d) (x − 6)(x − 7)
4. 4.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 468 (b) 234 (c) 42 (d) 252
5. 5.How many prime numbers are there between 20 and 40? (a) 3 (b) 5 (c) 6 (d) 4
6. 6.What is the mean of 17, 14, 10, 17, 3 and 11? (a) 11 (b) 12 (c) 14 (d) 13
7. 7.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 55 (c) 110 (d) 121
8. 8.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 704 (b) 385 (c) 62 (d) 352
9. 9.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 25 (c) 20 (d) 10
10. 10.3 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 15 (b) 24 (c) 12 (d) 7
11. 11.The mean of 6 numbers is 31. When the number 17 is added to them, what is the new mean? (a) 29 (b) 31 (c) 30 (d) 24
12. 12.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 1/4 (d) 3/4
13. 13.What is the median of 18, 3, 31, 34 and 22? (a) 31 (b) 18 (c) 23 (d) 22
14. 14.Which term of the AP 14, 20, 26, 32, … is 140? (a) 21st (b) 23rd (c) 24th (d) 22nd
15. 15.A drawer has lots of white 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) 4 (b) 5 (c) 3 (d) 2
16. 16.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 95° (b) 150° (c) 85° (d) 125°
17. 17.How many prime numbers are there between 80 and 110? (a) 7 (b) 8 (c) 9 (d) 6
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/9 (c) 3/11 (d) 1/11
19. 19.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 91 (d) 78
20. 20.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
21. 21.What is the mean of 13, 20, 12 and 3? (a) 13 (b) 11 (c) 12 (d) 16
22. 22.A drawer has lots of red, white, green 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) 8 (c) 2 (d) 4
23. 23.What is the midpoint of the line joining (4, 10) and (8, 0)? (a) (2, 5) (b) (5, 6) (c) (12, 10) (d) (6, 5)
24. 24.Which is the correct factorisation of x² + 5x + 6? (a) (x + 1)(x + 6) (b) (x + 2)(x + 3) (c) (x − 2)(x − 3) (d) (x + 1)(x + 4)
25. 25.In a class of 24 children, 9 like mangoes, 10 like bananas and 5 like both. How many like neither? (a) 5 (b) 15 (c) 10 (d) 11
26. 26.In a class of 47 children, 23 like maths, 26 like science and 7 like both. How many like only maths? (a) 19 (b) 16 (c) 23 (d) 21
27. 27.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
28. 28.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 100 (c) 109 (d) 110
29. 29.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 24 (c) 8 (d) 72
30. 30.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 147 (b) 294 (c) 168 (d) 39
31. 31.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 140° (c) 80° (d) 40°
32. 32.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/8 (c) 3/8 (d) 1/4
33. 33.In a class of 25 children, 17 like dance, 10 like music and 6 like both. How many like neither? (a) 5 (b) 4 (c) 6 (d) 10
34. 34.What is the midpoint of the line joining (7, 7) and (19, 17)? (a) (12, 13) (b) (13, 12) (c) (6, 5) (d) (26, 24)
35. 35.A drawer has lots of red, 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) 2 (b) 6 (c) 4 (d) 3
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
37. 37.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
38. 38.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 30° (c) 95° (d) 150°
39. 39.What is the mean of 4, 11, 18 and 3? (a) 8 (b) 12 (c) 9 (d) 10
40. 40.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 128 sq cm (b) 64 sq cm (c) 65 sq cm (d) 32 sq cm

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