Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 602 · 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.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 42 (c) 14 (d) 21
2. 2.Two angles of a triangle are 25° and 130°. What is the third angle? (a) 155° (b) 25° (c) 50° (d) 205°
3. 3.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) 8 (b) 15 (c) 7 (d) 14
4. 4.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 60° (c) 120° (d) 30°
5. 5.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 120° (b) 90° (c) 150° (d) 30°
6. 6.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 50° (d) 40°
7. 7.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 108 (c) 100 (d) 99
8. 8.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
10. 10.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
11. 11.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
12. 12.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 37 (b) 48 (c) 49 (d) 36
13. 13.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/18 (c) 1/36 (d) 1/12
15. 15.What is the sum of the roots of x² − 17x + 72 = 0? (a) 17 (b) 16 (c) 72 (d) 18
16. 16.There are 4 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 8 (b) 32 (c) 16 (d) 20
17. 17.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 5° (c) 95° (d) 85°
18. 18.Using (a − b)² = a² − 2ab + b², what is 38²? (a) 1454 (b) 1444 (c) 1596 (d) 1764
19. 19.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) 9 (b) 81 (c) 30 (d) 27
20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 17 (b) 16 (c) 18 (d) 6
21. 21.If a + b = 17 and ab = 72, what is (a − b)²? (a) 145 (b) 289 (c) 217 (d) 1
22. 22.If a + b = 13 and ab = 30, what is (a − b)²? (a) 109 (b) 49 (c) 7 (d) 169
23. 23.What is the midpoint of the line joining (3, 1) and (11, 11)? (a) (6, 7) (b) (7, 6) (c) (4, 5) (d) (14, 12)
24. 24.The mean of 7 numbers is 27. When the number 19 is added to them, what is the new mean? (a) 23 (b) 26 (c) 27 (d) 25
25. 25.What is the mode of 13, 13, 14, 13, 19, 14 and 8? (a) 19 (b) 14 (c) 8 (d) 13
26. 26.Which is the correct factorisation of x² + 14x + 45? (a) (x + 1)(x + 13) (b) (x + 5)(x + 9) (c) (x − 5)(x − 9) (d) (x + 1)(x + 45)
27. 27.In a class of 23 children, 12 like cricket, 14 like football and 4 like both. How many like at least one of the two? (a) 18 (b) 23 (c) 22 (d) 26
28. 28.If a + b = 18 and ab = 72, what is a² + b²? (a) 180 (b) 252 (c) 468 (d) 324
29. 29.In which quadrant does the point (−3, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
30. 30.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 45 (d) 20
31. 31.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 45 (c) 15 (d) 48
32. 32.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 60° (c) 30° (d) 150°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 130° (c) 50° (d) 100°
34. 34.What is the median of 8, 29, 11, 30, 3, 35 and 36? (a) 11 (b) 29 (c) 30 (d) 28
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/18 (c) 1/12 (d) 1/36
36. 36.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 4 times (d) 8 times
37. 37.What is the prime factorisation of 21? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7 (d) 3 × 7²
38. 38.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
39. 39.6 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) 8 (b) 24 (c) 18 (d) 12
40. 40.If a + b = 11 and ab = 18, what is (a − b)²? (a) 85 (b) 7 (c) 49 (d) 121

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