Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 303 · 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 mode of 4, 12, 4, 18, 12, 2 and 12? (a) 18 (b) 2 (c) 12 (d) 4
2. 2.There are 7 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 21 (c) 28 (d) 9
3. 3.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 115° (b) 95° (c) 150° (d) 85°
4. 4.What is the sum of the roots of x² − 13x + 42 = 0? (a) 14 (b) 42 (c) 12 (d) 13
5. 5.Which is the correct factorisation of x² + 8x + 15? (a) (x − 3)(x − 5) (b) (x + 1)(x + 7) (c) (x + 1)(x + 15) (d) (x + 3)(x + 5)
6. 6.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
7. 7.In a class of 43 children, 23 like mangoes, 26 like bananas and 9 like both. How many like at least one of the two? (a) 49 (b) 43 (c) 31 (d) 40
8. 8.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 108 (c) 12 (d) 36
9. 9.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
10. 10.What is the midpoint of the line joining (4, 12) and (6, 2)? (a) (1, 5) (b) (5, 7) (c) (7, 5) (d) (10, 14)
11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 5 (b) 16 (c) 15 (d) 17
12. 12.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x + 7)(x + 9) (c) (x − 7)(x − 9) (d) (x + 1)(x + 63)
13. 13.A bag has 12 red balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 13 (c) 2 (d) 5
14. 14.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 120 (d) 25
15. 15.A drawer has lots of green, black, 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) 5 (b) 4 (c) 2 (d) 8
16. 16.A bag has 11 red balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 23 (c) 13 (d) 12
17. 17.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 117 (c) 13 (d) 42
18. 18.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
19. 19.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 8101 (b) 7921 (c) 8291 (d) 8281
20. 20.In a class of 39 children, 25 like mangoes, 18 like bananas and 6 like neither. How many like both? (a) 6 (b) 4 (c) 33 (d) 10
21. 21.A bag has 8 blue, 3 red and 8 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 8/19 (b) 8/11 (c) 1/3 (d) 11/19
22. 22.Which is the correct factorisation of x² + 14x + 48? (a) (x − 6)(x − 8) (b) (x + 1)(x + 48) (c) (x + 1)(x + 13) (d) (x + 6)(x + 8)
23. 23.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 916 (b) 676 (c) 1166 (d) 1156
24. 24.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 11 (b) 14 (c) 12 (d) 13
25. 25.What is the mean of 18, 15, 12, 3 and 7? (a) 11 (b) 12 (c) 10 (d) 13
26. 26.A bag has 7 green, 7 blue and 2 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 15/16 (c) 1/8 (d) 7/8
27. 27.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 80° (c) 50° (d) 130°
28. 28.A bag has 11 yellow balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 19 (c) 12 (d) 13
29. 29.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 21 (c) 14 (d) 15
30. 30.In which quadrant does the point (7, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
31. 31.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
32. 32.What is the median of 3, 33, 1, 15, 11, 14 and 28? (a) 15 (b) 14 (c) 13 (d) 11
33. 33.In a class of 32 children, 12 like mangoes, 21 like bananas and 3 like both. How many like at least one of the two? (a) 27 (b) 33 (c) 30 (d) 32
34. 34.In which quadrant does the point (4, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
35. 35.How many factors does 120 have? (a) 15 (b) 14 (c) 16 (d) 17
36. 36.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 8 (c) 7 (d) 15
37. 37.In a class of 26 children, 18 like maths, 18 like science and 1 like neither. How many like both? (a) 10 (b) 11 (c) 1 (d) 25
38. 38.What is the distance between the points (7, 12) and (19, 3)? (a) 21 (b) 15 (c) 225 (d) 16
39. 39.In a class of 27 children, 12 like tea, 17 like coffee and 1 like neither. How many like both? (a) 3 (b) 26 (c) 1 (d) 2
40. 40.What is the sum of the roots of x² − 11x + 28 = 0? (a) 28 (b) 12 (c) 11 (d) 10

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