Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 336 · 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 mean of 5, 3, 10 and 6? (a) 8 (b) 7 (c) 5 (d) 6
2. 2.In a class of 44 children, 17 like mangoes, 31 like bananas and 8 like neither. How many like both? (a) 36 (b) 8 (c) 4 (d) 12
3. 3.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 60° (d) 75°
4. 4.What is the product of the roots of x² − 5x + 6 = 0? (a) 7 (b) 5 (c) 8 (d) 6
5. 5.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 100° (b) 80° (c) 130° (d) 150°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 135° (c) 45° (d) 270°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 20° (b) 100° (c) 200° (d) 80°
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
9. 9.What is the mode of 3, 2, 17, 2, 19, 3 and 2? (a) 19 (b) 3 (c) 17 (d) 2
10. 10.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
11. 11.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) 12 (b) 25 (c) 13 (d) 24
12. 12.The mean of 5 numbers is 18. When the number 24 is added to them, what is the new mean? (a) 20 (b) 19 (c) 18 (d) 21
13. 13.If a + b = 8 and ab = 7, what is (a − b)²? (a) 6 (b) 50 (c) 64 (d) 36
14. 14.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 23 (b) 196 (c) 101 (d) 98
15. 15.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
16. 16.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 272 (c) 120 (d) 128
17. 17.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 120 (d) 20
18. 18.A bag has 8 green, 6 white and 7 yellow balls. One ball is taken out without looking. What is the probability that it is white? (a) 2/5 (b) 5/7 (c) 2/7 (d) 1/3
19. 19.A cuboid is 12 cm long, 10 cm wide and 2 cm high. What is its volume? (a) 120 cu cm (b) 240 cu cm (c) 328 cu cm (d) 24 cu cm
20. 20.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 15 (d) 30
21. 21.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 24 (d) 48
22. 22.What is the distance between the points (1, 14) and (6, 2)? (a) 169 (b) 14 (c) 13 (d) 17
23. 23.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
24. 24.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 100° (d) 40°
25. 25.What is the sum of the roots of x² − 13x + 42 = 0? (a) 13 (b) 14 (c) 12 (d) 42
26. 26.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 20° (c) 70° (d) 290°
27. 27.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 37 (b) 245 (c) 484 (d) 242
28. 28.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3 (d) 2 × 3²
29. 29.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 216 (b) 17 (c) 112 (d) 108
30. 30.In which quadrant does the point (3, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
31. 31.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) 8 times (c) 2 times (d) 4 times
32. 32.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 75° (d) 145°
33. 33.If a + b = 17 and ab = 72, what is a² + b²? (a) 145 (b) 289 (c) 217 (d) 433
34. 34.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 8) (b) (x + 1)(x + 20) (c) (x + 4)(x + 5) (d) (x − 4)(x − 5)
35. 35.What is the distance between the points (3, 15) and (18, 7)? (a) 289 (b) 18 (c) 23 (d) 17
36. 36.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 66 (d) 144
37. 37.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) 4 times (c) 8 times (d) 6 times
38. 38.The mean of 7 numbers is 20. When the number 36 is added to them, what is the new mean? (a) 22 (b) 28 (c) 20 (d) 23
39. 39.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) 24 (d) 37
40. 40.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5

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