Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 578 · 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 drawer has lots of black, yellow, white, red 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) 6 (b) 5 (c) 2 (d) 10
2. 2.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 165 (b) 154 (c) 24 (d) 308
3. 3.A bag has 5 red balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 6 (c) 15 (d) 2
4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
5. 5.What is the midpoint of the line joining (10, 10) and (18, 18)? (a) (4, 4) (b) (15, 14) (c) (14, 14) (d) (28, 28)
6. 6.In a class of 31 children, 16 like maths, 22 like science and 12 like both. How many like at least one of the two? (a) 26 (b) 38 (c) 14 (d) 31
7. 7.What is the distance between the points (7, 3) and (31, 10)? (a) 625 (b) 26 (c) 25 (d) 31
8. 8.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 335° (c) 65° (d) 155°
9. 9.What is the midpoint of the line joining (9, 6) and (17, 2)? (a) (26, 8) (b) (4, 13) (c) (4, 2) (d) (13, 4)
10. 10.Which is the correct factorisation of x² + 10x + 21? (a) (x + 1)(x + 9) (b) (x + 3)(x + 7) (c) (x − 3)(x − 7) (d) (x + 1)(x + 21)
11. 11.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/3 (c) 1/4 (d) 2/3
12. 12.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 10° (c) 100° (d) 80°
13. 13.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
14. 14.How many prime numbers are there between 60 and 80? (a) 4 (b) 7 (c) 5 (d) 6
15. 15.What is the median of 3, 16, 2, 40, 34, 25 and 27? (a) 27 (b) 25 (c) 21 (d) 40
16. 16.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 35° (c) 70° (d) 145°
17. 17.In a class of 18 children, 10 like tea, 7 like coffee and 4 like both. How many like neither? (a) 5 (b) 4 (c) 1 (d) 9
18. 18.If a + b = 17 and ab = 66, what is (a − b)²? (a) 289 (b) 25 (c) 157 (d) 5
19. 19.How many prime numbers are there between 20 and 30? (a) 1 (b) 2 (c) 3 (d) 4
20. 20.What is the 40th term of the AP 9, 12, 15, 18, …? (a) 129 (b) 117 (c) 120 (d) 126
21. 21.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 78 (d) 91
22. 22.A cuboid is 7 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 20 cu cm (b) 252 cu cm (c) 28 cu cm (d) 254 cu cm
23. 23.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 135° (b) 40° (c) 140° (d) 85°
24. 24.Which term of the AP 7, 11, 15, 19, … is 147? (a) 36th (b) 38th (c) 37th (d) 35th
25. 25.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 33 (b) 25 (c) 24 (d) 23
26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 20 (d) 21
27. 27.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
28. 28.What is the 17th term of the AP 16, 20, 24, 28, …? (a) 80 (b) 64 (c) 68 (d) 84
29. 29.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 42 (c) 70 (d) 35
30. 30.A drawer has lots of green, 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) 4 (b) 3 (c) 2 (d) 6
31. 31.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) 24 (c) 13 (d) 12
32. 32.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x − 7)(x − 8) (c) (x + 1)(x + 14) (d) (x + 7)(x + 8)
33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 6 (b) 4 (c) 5 (d) 3
34. 34.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 579 (c) 570 (d) 580
35. 35.The mean of 5 numbers is 11. When the number 5 is added to them, what is the new mean? (a) 10 (b) 8 (c) 11 (d) 9
36. 36.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 225 (d) 105
37. 37.What is the midpoint of the line joining (9, 9) and (13, 7)? (a) (8, 11) (b) (22, 16) (c) (2, 1) (d) (11, 8)
38. 38.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 36 (c) 49 (d) 37
39. 39.What is the mean of 5, 19, 3, 10 and 18? (a) 10 (b) 12 (c) 13 (d) 11
40. 40.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 15 cu cm (d) 125 cu cm

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