Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 806 · 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 63? (a) 17 (b) 16 (c) 18 (d) 6
2. 2.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
3. 3.In a class of 42 children, 22 like maths, 14 like science and 3 like both. How many like at least one of the two? (a) 33 (b) 42 (c) 30 (d) 36
4. 4.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
5. 5.What is the distance between the points (1, 2) and (9, 17)? (a) 23 (b) 289 (c) 18 (d) 17
6. 6.A bag has 8 white, 5 yellow and 7 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 13/20 (b) 7/13 (c) 1/3 (d) 7/20
7. 7.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 522 (c) 532 (d) 531
8. 8.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 14 (c) 21 (d) 9
9. 9.A drawer has lots of black, red, yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 4 (c) 2 (d) 5
10. 10.In a class of 27 children, 7 like maths, 19 like science and 4 like both. How many like at least one of the two? (a) 18 (b) 27 (c) 26 (d) 22
11. 11.In a class of 20 children, 9 like mangoes, 12 like bananas and 4 like both. How many like at least one of the two? (a) 21 (b) 17 (c) 20 (d) 13
12. 12.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 321 (c) 292 (d) 330
13. 13.What is the distance between the points (2, 2) and (5, 6)? (a) 6 (b) 25 (c) 7 (d) 5
14. 14.If a + b = 21 and ab = 108, what is (a − b)²? (a) 9 (b) 225 (c) 3 (d) 441
15. 15.A bag has 11 blue balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 2 (c) 13 (d) 15
16. 16.What is the mode of 3, 1, 3, 2, 7, 1 and 1? (a) 1 (b) 2 (c) 7 (d) 3
17. 17.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 36) (b) (x + 4)(x + 9) (c) (x + 1)(x + 12) (d) (x − 4)(x − 9)
18. 18.In which quadrant does the point (−4, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
19. 19.A bag has 4 blue, 8 yellow and 9 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 13/21 (b) 1/3 (c) 4/7 (d) 3/7
20. 20.Using (a + b)² = a² + 2ab + b², what is 53²? (a) 2209 (b) 2809 (c) 2819 (d) 2509
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
22. 22.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
23. 23.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 160° (b) 75° (c) 95° (d) 105°
24. 24.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) 15 (b) 14 (c) 21 (d) 22
25. 25.What is the median of 23, 40, 27, 3, 4, 28 and 25? (a) 25 (b) 23 (c) 3 (d) 27
26. 26.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 80° (b) 15° (c) 165° (d) 115°
27. 27.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 2 (d) 7
28. 28.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 450 (c) 465 (d) 435
29. 29.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 80° (c) 150° (d) 100°
30. 30.A bag has 10 blue balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 13 (b) 12 (c) 2 (d) 11
31. 31.What is the distance between the points (4, 16) and (12, 1)? (a) 18 (b) 23 (c) 289 (d) 17
32. 32.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 45° (c) 70° (d) 35°
33. 33.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 85° (b) 135° (c) 95° (d) 130°
34. 34.A bag has 6 yellow balls and 5 white 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) 2 (d) 7
35. 35.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 86° (c) 85° (d) 95°
36. 36.How many factors does 69 have? (a) 5 (b) 3 (c) 4 (d) 2
37. 37.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 158 (c) 140 (d) 150
38. 38.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
39. 39.What is the smallest prime factor of 209? (a) 1 (b) 19 (c) 11 (d) 2
40. 40.What is the distance between the points (4, 5) and (12, 20)? (a) 289 (b) 23 (c) 17 (d) 18

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