Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 771 · 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.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 27) (b) (x − 3)(x − 9) (c) (x + 3)(x + 9) (d) (x + 1)(x + 11)
2. 2.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
3. 3.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
4. 4.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
5. 5.There are 4 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 7 (b) 16 (c) 12 (d) 24
6. 6.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 320° (c) 20° (d) 140°
7. 7.What is the mean of 14, 18, 15, 13, 9 and 9? (a) 15 (b) 14 (c) 13 (d) 12
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/11 (c) 7/36 (d) 1/6
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
10. 10.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 50 (b) 300 (c) 550 (d) 275
11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
12. 12.A drawer has lots of blue, white, yellow, red 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) 2 (c) 6 (d) 10
13. 13.What is the missing term in the AP 17, 21, 25, ?, 33? (a) 30 (b) 33 (c) 28 (d) 29
14. 14.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) 9 times (c) 3 times (d) 6 times
15. 15.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
17. 17.A bag has 3 green, 2 red and 6 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 2/9 (b) 9/11 (c) 2/11 (d) 1/3
18. 18.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 144 (d) 66
19. 19.How many factors does 73 have? (a) 4 (b) 1 (c) 2 (d) 3
20. 20.What is the 40th term of the AP 7, 14, 21, 28, …? (a) 273 (b) 281 (c) 280 (d) 287
21. 21.What is the midpoint of the line joining (9, 14) and (13, 6)? (a) (2, 4) (b) (10, 11) (c) (11, 10) (d) (22, 20)
22. 22.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
23. 23.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 15 (d) 10
24. 24.In a class of 28 children, 19 like mangoes, 12 like bananas and 9 like both. How many like at least one of the two? (a) 28 (b) 31 (c) 22 (d) 13
25. 25.In a class of 38 children, 16 like dance, 22 like music and 5 like neither. How many like both? (a) 4 (b) 33 (c) 6 (d) 5
26. 26.What is the mode of 4, 12, 4, 12, 7, 9 and 4? (a) 9 (b) 4 (c) 12 (d) 7
27. 27.What is the mode of 19, 12, 18, 12, 10, 10 and 10? (a) 12 (b) 10 (c) 18 (d) 19
28. 28.What is the 35th term of the AP 5, 13, 21, 29, …? (a) 277 (b) 280 (c) 272 (d) 285
29. 29.A drawer has lots of green 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) 4 (b) 5 (c) 3 (d) 2
30. 30.In a class of 24 children, 15 like mangoes, 14 like bananas and 11 like both. How many like at least one of the two? (a) 29 (b) 24 (c) 18 (d) 7
31. 31.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 280° (c) 40° (d) 140°
32. 32.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 7056 (b) 5776 (c) 7066 (d) 6416
33. 33.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
34. 34.What is the mean of 4, 15, 2 and 19? (a) 10 (b) 9 (c) 11 (d) 8
35. 35.What is the mode of 19, 5, 9, 19, 8, 5 and 5? (a) 9 (b) 8 (c) 5 (d) 19
36. 36.The mean of 5 numbers is 16. When the number 4 is added to them, what is the new mean? (a) 15 (b) 10 (c) 14 (d) 16
37. 37.A drawer has lots of blue, 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) 2 (b) 6 (c) 5 (d) 10
38. 38.A bag has 12 blue balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 20 (c) 9 (d) 13
39. 39.A bag has 5 white balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 17 (c) 2 (d) 6
40. 40.Using (a − b)² = a² − 2ab + b², what is 57²? (a) 3591 (b) 3969 (c) 3259 (d) 3249

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