Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 714 · 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 sum of the roots of x² − 15x + 56 = 0? (a) 56 (b) 15 (c) 16 (d) 14
2. 2.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2⁴ × 3² × 5 (c) 2² × 3² × 5 (d) 2³ × 3² × 5
3. 3.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 22 (c) 28 (d) 29
4. 4.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 155° (d) 105°
5. 5.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 15 (c) 36 (d) 12
6. 6.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
7. 7.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
8. 8.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
9. 9.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 5/36 (c) 1/9 (d) 4/11
11. 11.What is the smallest prime factor of 65? (a) 5 (b) 2 (c) 1 (d) 13
12. 12.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 5 (c) 6 (d) 12
13. 13.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4371 (c) 4465 (d) 4418
14. 14.What is the midpoint of the line joining (9, 1) and (11, 9)? (a) (20, 10) (b) (5, 10) (c) (10, 5) (d) (1, 4)
15. 15.A drawer has lots of blue, red 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) 6 (b) 2 (c) 4 (d) 3
16. 16.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 800 (c) 1640 (d) 780
17. 17.What is the median of 28, 25, 6, 17 and 16? (a) 6 (b) 25 (c) 16 (d) 17
18. 18.What is the smallest prime factor of 119? (a) 1 (b) 17 (c) 2 (d) 7
19. 19.How many factors does 26 have? (a) 4 (b) 5 (c) 3 (d) 2
20. 20.Using (a − b)² = a² − 2ab + b², what is 96²? (a) 9216 (b) 9226 (c) 9984 (d) 10816
21. 21.What is the distance between the points (9, 2) and (18, 14)? (a) 15 (b) 16 (c) 21 (d) 225
22. 22.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 30° (c) 15° (d) 16°
23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 4 (b) 1 (c) 2 (d) 3
24. 24.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 135° (d) 155°
25. 25.A bag has 8 red, 6 green and 4 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 7/9 (b) 2/9 (c) 2/7 (d) 1/3
26. 26.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 36 (d) 72
27. 27.Which is the correct factorisation of x² + 6x + 8? (a) (x + 2)(x + 4) (b) (x − 2)(x − 4) (c) (x + 1)(x + 8) (d) (x + 1)(x + 5)
28. 28.What is the mode of 5, 7, 10, 7, 14, 10 and 7? (a) 14 (b) 7 (c) 5 (d) 10
29. 29.The mean of 3 numbers is 33. When the number 37 is added to them, what is the new mean? (a) 35 (b) 34 (c) 36 (d) 33
30. 30.A bag has 2 green, 4 red and 2 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/4 (b) 3/4 (c) 1/3 (d) 3/8
31. 31.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 140° (c) 40° (d) 30°
32. 32.A drawer has lots of black, blue and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 2 (c) 6 (d) 4
33. 33.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) 12 (c) 25 (d) 13
34. 34.What is the smallest prime factor of 319? (a) 2 (b) 29 (c) 1 (d) 11
35. 35.In which quadrant does the point (−7, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
36. 36.How many factors does 49 have? (a) 4 (b) 2 (c) 3 (d) 1
37. 37.What is the median of 36, 5, 11, 30, 12, 22 and 10? (a) 22 (b) 12 (c) 30 (d) 18
38. 38.Which is the correct factorisation of x² + 15x + 54? (a) (x + 6)(x + 9) (b) (x + 1)(x + 14) (c) (x − 6)(x − 9) (d) (x + 1)(x + 54)
39. 39.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
40. 40.What is the mean of 19, 2, 9 and 10? (a) 9 (b) 8 (c) 11 (d) 10

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