Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 281 · 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.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 1/11 (c) 7/36 (d) 6/11
3. 3.What is the midpoint of the line joining (2, 6) and (14, 2)? (a) (16, 8) (b) (6, 2) (c) (8, 4) (d) (4, 8)
4. 4.A bag has 5 green, 9 yellow and 9 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 5/23 (c) 5/18 (d) 18/23
5. 5.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁵ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2³ × 3 × 5
6. 6.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
7. 7.In a class of 28 children, 11 like cricket, 22 like football and 8 like both. How many like only cricket? (a) 11 (b) 3 (c) 6 (d) 14
8. 8.What is the median of 10, 39, 40, 12, 1, 9 and 15? (a) 10 (b) 15 (c) 18 (d) 12
9. 9.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 20° (c) 70° (d) 110°
10. 10.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
11. 11.What is the 36th term of the AP 6, 10, 14, 18, …? (a) 150 (b) 146 (c) 144 (d) 140
12. 12.What is the 20th term of the AP 11, 15, 19, 23, …? (a) 87 (b) 80 (c) 91 (d) 76
13. 13.Using (a − b)² = a² − 2ab + b², what is 97²? (a) 9419 (b) 9991 (c) 9409 (d) 10609
14. 14.What is the 40th term of the AP 19, 24, 29, 34, …? (a) 219 (b) 200 (c) 195 (d) 214
15. 15.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 580 (c) 579 (d) 570
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/36 (c) 1/11 (d) 1/12
17. 17.What are the roots of x² − 13x + 42 = 0? (a) 6 and 7 (b) 2 and 21 (c) 1 and 12 (d) 1 and 42
18. 18.What is the 40th term of the AP 9, 12, 15, 18, …? (a) 126 (b) 117 (c) 120 (d) 129
19. 19.In a class of 47 children, 23 like dance, 20 like music and 5 like both. How many like only dance? (a) 15 (b) 18 (c) 23 (d) 27
20. 20.What is the mode of 2, 2, 16, 16, 13, 1 and 16? (a) 13 (b) 16 (c) 2 (d) 1
21. 21.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 50° (d) 100°
22. 22.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 864 cu cm (c) 576 cu cm (d) 1728 cu cm
23. 23.A bag has 5 white balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 6 (c) 7 (d) 12
24. 24.What is the smallest prime factor of 49? (a) 1 (b) 7 (c) 3 (d) 2
25. 25.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
26. 26.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
27. 27.What is the product of the roots of x² − 13x + 42 = 0? (a) 41 (b) 42 (c) 43 (d) 13
28. 28.In a class of 42 children, 27 like maths, 15 like science and 9 like both. How many like only maths? (a) 18 (b) 27 (c) 9 (d) 6
29. 29.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
30. 30.What is the median of 7, 2, 30, 31, 35, 37 and 12? (a) 30 (b) 12 (c) 22 (d) 31
31. 31.A bag has 3 green balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 4 (c) 6 (d) 5
32. 32.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 273 (c) 254 (d) 264
33. 33.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 36° (d) 145°
34. 34.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 130° (b) 140° (c) 270° (d) 90°
35. 35.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 115° (b) 145° (c) 80° (d) 100°
36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 16 (b) 4 (c) 15 (d) 14
37. 37.A drawer has lots of white, red, black 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) 8 (b) 4 (c) 5 (d) 2
38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 17 (d) 18
39. 39.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
40. 40.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) 25 (b) 37 (c) 36 (d) 24

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