Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 461 · 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 first 12 terms of the AP 10, 14, 18, …? (a) 54 (b) 408 (c) 384 (d) 768
2. 2.If a + b = 19 and ab = 90, what is (a − b)²? (a) 1 (b) 361 (c) 271 (d) 181
3. 3.In which quadrant does the point (6, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
4. 4.What is the median of 40, 10, 38, 25 and 18? (a) 18 (b) 26 (c) 38 (d) 25
5. 5.What is the 21st term of the AP 4, 11, 18, 25, …? (a) 151 (b) 147 (c) 144 (d) 140
6. 6.What is the midpoint of the line joining (2, 14) and (10, 2)? (a) (6, 8) (b) (8, 6) (c) (4, 6) (d) (12, 16)
7. 7.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 2/3 (c) 1/3 (d) 1/4
8. 8.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
9. 9.How many factors does 52 have? (a) 5 (b) 4 (c) 6 (d) 7
10. 10.In a class of 43 children, 22 like mangoes, 25 like bananas and 8 like both. How many like neither? (a) 12 (b) 8 (c) 4 (d) 5
11. 11.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
12. 12.How many prime numbers are there between 50 and 80? (a) 7 (b) 9 (c) 6 (d) 8
13. 13.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 10°
14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
15. 15.How many prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 3 (d) 5
16. 16.What is the distance between the points (6, 13) and (22, 1)? (a) 400 (b) 20 (c) 28 (d) 21
17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
18. 18.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
19. 19.What is the median of 10, 28, 24, 30 and 36? (a) 30 (b) 29 (c) 24 (d) 28
20. 20.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 80° (b) 60° (c) 160° (d) 120°
21. 21.A drawer has lots of black, red, green, white 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) 2 (b) 5 (c) 6 (d) 10
22. 22.How many factors does 99 have? (a) 4 (b) 7 (c) 5 (d) 6
23. 23.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 24 sq cm (d) 16 sq cm
24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
25. 25.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) 7 (b) 14 (c) 15 (d) 8
26. 26.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
27. 27.A bag has 8 green, 5 red and 6 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 6/19 (c) 6/13 (d) 13/19
28. 28.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 48 (c) 10 (d) 30
29. 29.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
30. 30.What is the smallest prime factor of 91? (a) 7 (b) 1 (c) 13 (d) 2
31. 31.A drawer has lots of green, red 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
32. 32.A bag has 3 blue balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 5 (c) 2 (d) 4
33. 33.A bag has 8 white balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 9 (c) 2 (d) 10
34. 34.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 105° (b) 75° (c) 155° (d) 100°
35. 35.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 115° (c) 65° (d) 25°
36. 36.What is the midpoint of the line joining (0, 9) and (2, 17)? (a) (1, 13) (b) (13, 1) (c) (2, 26) (d) (1, 4)
37. 37.If a + b = 18 and ab = 77, what is (a − b)²? (a) 170 (b) 16 (c) 4 (d) 324
38. 38.What is the mean of 4, 8, 3, 14 and 16? (a) 11 (b) 8 (c) 9 (d) 10
39. 39.What is the smallest prime factor of 65? (a) 5 (b) 2 (c) 13 (d) 1
40. 40.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 60° (c) 160° (d) 120°

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