Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 114 · 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.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 6 (b) 5 (c) 4 (d) 3
2. 2.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 142 (c) 152 (d) 160
3. 3.In which quadrant does the point (−9, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
4. 4.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
5. 5.Which is the correct factorisation of x² + 11x + 18? (a) (x + 1)(x + 10) (b) (x + 1)(x + 18) (c) (x + 2)(x + 9) (d) (x − 2)(x − 9)
6. 6.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 3/4 (c) 1/2 (d) 1/4
7. 7.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
8. 8.A bag has 9 yellow balls and 12 green 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) 2 (c) 10 (d) 21
9. 9.A bag has 10 white balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 12 (b) 16 (c) 11 (d) 2
10. 10.In a class of 47 children, 29 like mangoes, 26 like bananas and 9 like both. How many like only mangoes? (a) 29 (b) 20 (c) 17 (d) 21
11. 11.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
13. 13.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 25 (c) 37 (d) 24
14. 14.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 168 (b) 304 (c) 152 (d) 33
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 1/9 (c) 5/36 (d) 4/11
16. 16.What are the roots of x² − 8x + 15 = 0? (a) 1 and 15 (b) 1 and 7 (c) 2 and 6 (d) 3 and 5
17. 17.What is the midpoint of the line joining (1, 0) and (5, 4)? (a) (2, 2) (b) (3, 2) (c) (2, 3) (d) (6, 4)
18. 18.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 7 cu cm (b) 32 cu cm (c) 6 cu cm (d) 12 cu cm
19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 6 (b) 5 (c) 4 (d) 3
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 1/11 (c) 1/12 (d) 2/11
21. 21.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 90° (d) 45°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 95° (c) 86° (d) 170°
23. 23.In a class of 41 children, 14 like tea, 29 like coffee and 8 like neither. How many like both? (a) 10 (b) 2 (c) 8 (d) 33
24. 24.In which quadrant does the point (1, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
25. 25.In a class of 43 children, 24 like cricket, 16 like football and 7 like neither. How many like both? (a) 5 (b) 4 (c) 36 (d) 7
26. 26.What is the mean of 4, 19, 18 and 11? (a) 15 (b) 14 (c) 12 (d) 13
27. 27.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 196 (c) 105 (d) 182
28. 28.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
29. 29.4 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) 20 (b) 9 (c) 24 (d) 40
30. 30.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
31. 31.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
32. 32.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
33. 33.In a class of 41 children, 28 like maths, 15 like science and 11 like both. How many like neither? (a) 11 (b) 20 (c) 10 (d) 9
34. 34.What is the product of the roots of x² − 8x + 12 = 0? (a) 8 (b) 12 (c) 13 (d) 11
35. 35.What is the smallest prime factor of 91? (a) 7 (b) 1 (c) 2 (d) 13
36. 36.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 98 (b) 196 (c) 20 (d) 105
37. 37.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) 24 (b) 25 (c) 12 (d) 13
38. 38.Which is the correct factorisation of x² + 8x + 15? (a) (x + 1)(x + 15) (b) (x + 3)(x + 5) (c) (x + 1)(x + 7) (d) (x − 3)(x − 5)
39. 39.What is the median of 17, 28, 7, 1, 37, 13 and 21? (a) 17 (b) 13 (c) 21 (d) 1
40. 40.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 18 (c) 36 (d) 72

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