Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 346 · 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 39th term of the AP 12, 14, 16, 18, …? (a) 88 (b) 78 (c) 90 (d) 76
2. 2.What is the midpoint of the line joining (6, 19) and (14, 7)? (a) (4, 6) (b) (20, 26) (c) (13, 10) (d) (10, 13)
3. 3.A bag has 7 blue, 2 green and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 4/7 (b) 7/11 (c) 1/3 (d) 4/11
4. 4.A drawer has lots of red 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) 3 (b) 4 (c) 5 (d) 2
5. 5.What is the mean of 11, 6, 13, 20, 2 and 14? (a) 10 (b) 11 (c) 13 (d) 12
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
7. 7.What is the median of 30, 9, 8, 29 and 19? (a) 9 (b) 29 (c) 19 (d) 8
8. 8.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 30 (c) 27 (d) 9
9. 9.Using (a + b)² = a² + 2ab + b², what is 43²? (a) 1369 (b) 1609 (c) 1849 (d) 1859
10. 10.In a class of 31 children, 16 like mangoes, 16 like bananas and 1 like neither. How many like both? (a) 30 (b) 1 (c) 2 (d) 3
11. 11.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 70° (c) 145° (d) 110°
12. 12.A cuboid is 8 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 160 cu cm (b) 16 cu cm (c) 32 cu cm (d) 128 cu cm
13. 13.What is the product of the roots of x² − 12x + 27 = 0? (a) 27 (b) 26 (c) 12 (d) 28
14. 14.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 80° (d) 150°
15. 15.A bag has 9 black balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 14 (c) 11 (d) 10
16. 16.A bag has 5 green balls and 6 blue 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) 2 (c) 6 (d) 7
17. 17.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
18. 18.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 75° (c) 285° (d) 105°
19. 19.What is the 18th term of the AP 18, 24, 30, 36, …? (a) 120 (b) 108 (c) 126 (d) 102
20. 20.What is the product of the roots of x² − 9x + 14 = 0? (a) 14 (b) 13 (c) 15 (d) 9
21. 21.In a class of 29 children, 18 like dance, 18 like music and 10 like both. How many like at least one of the two? (a) 36 (b) 16 (c) 26 (d) 29
22. 22.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
23. 23.What is the sum of all the whole numbers from 1 to 77? (a) 3003 (b) 2926 (c) 6006 (d) 3004
24. 24.In a class of 21 children, 13 like maths, 11 like science and 2 like neither. How many like both? (a) 5 (b) 2 (c) 19 (d) 3
25. 25.What is the missing term in the AP 13, ?, 27, 34, 41? (a) 20 (b) 19 (c) 27 (d) 21
26. 26.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 8125 (b) 9025 (c) 9035 (d) 7225
27. 27.If a + b = 21 and ab = 108, what is (a − b)²? (a) 3 (b) 441 (c) 9 (d) 225
28. 28.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
29. 29.A bag has 9 white, 9 red and 2 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 3/5 (b) 9/20 (c) 11/20 (d) 1/3
30. 30.A drawer has lots of white, red, black and green 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) 4 (c) 8 (d) 5
31. 31.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 50° (c) 80° (d) 260°
32. 32.What is the median of 19, 38, 9, 1, 8, 4 and 18? (a) 1 (b) 8 (c) 18 (d) 9
33. 33.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 64 (d) 56
34. 34.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
35. 35.A drawer has lots of blue, white, yellow and green 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) 8 (d) 2
36. 36.If a + b = 16 and ab = 48, what is (a − b)²? (a) 160 (b) 8 (c) 256 (d) 64
37. 37.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 172 (c) 171 (d) 162
38. 38.A bag has 3 red balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 9 (b) 4 (c) 5 (d) 2
39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 16 (d) 17
40. 40.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 120 (d) 20

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