Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 138 · 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 mode of 2, 18, 18, 14, 16, 2 and 18? (a) 2 (b) 14 (c) 18 (d) 16
2. 2.A cuboid is 10 cm long, 8 cm wide and 5 cm high. What is its volume? (a) 340 cu cm (b) 80 cu cm (c) 400 cu cm (d) 23 cu cm
3. 3.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 55 (d) 110
4. 4.A drawer has lots of blue, white 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) 6 (b) 2 (c) 4 (d) 3
5. 5.What is the smallest prime factor of 187? (a) 17 (b) 2 (c) 1 (d) 11
6. 6.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 33 (c) 36 (d) 11
7. 7.How many factors does 36 have? (a) 7 (b) 8 (c) 10 (d) 9
8. 8.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 24 (d) 16
9. 9.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 180 (c) 20 (d) 63
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 1/6 (c) 5/36 (d) 5/11
11. 11.A bag has 3 red balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 4 (c) 5 (d) 10
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) 48 (b) 37 (c) 49 (d) 36
13. 13.If a + b = 7 and ab = 12, what is (a − b)²? (a) 37 (b) 25 (c) 1 (d) 49
14. 14.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 25 (d) 15
15. 15.A bag has 2 yellow, 5 green and 9 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 1/8 (c) 1/7 (d) 7/8
16. 16.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)
17. 17.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 155° (b) 105° (c) 25° (d) 100°
18. 18.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 1/4 (d) 3/5
19. 19.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 36 (d) 30
20. 20.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 135° (b) 140° (c) 95° (d) 85°
21. 21.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2⁵ × 3² (c) 2³ × 3² (d) 2⁴ × 3²
22. 22.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
23. 23.In which quadrant does the point (−5, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
24. 24.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 70° (d) 125°
25. 25.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 80° (b) 150° (c) 130° (d) 50°
26. 26.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 21° (c) 200° (d) 160°
27. 27.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 553 (b) 440 (c) 543 (d) 552
28. 28.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 14 (c) 15 (d) 22
29. 29.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 6642 (c) 3322 (d) 3240
30. 30.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
31. 31.What are the roots of x² − 13x + 40 = 0? (a) 2 and 20 (b) 1 and 12 (c) 5 and 8 (d) 1 and 40
32. 32.What is the distance between the points (6, 13) and (30, 6)? (a) 625 (b) 25 (c) 26 (d) 31
33. 33.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) 10 times (c) 5 times (d) 25 times
34. 34.What is the smallest prime factor of 115? (a) 5 (b) 23 (c) 2 (d) 1
35. 35.A bag has 8 white, 8 blue and 9 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 18/25 (b) 8/25 (c) 1/3 (d) 17/25
36. 36.How many factors does 61 have? (a) 2 (b) 1 (c) 3 (d) 4
37. 37.In which quadrant does the point (−1, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
38. 38.In a class of 30 children, 14 like mangoes, 18 like bananas and 3 like both. How many like neither? (a) 3 (b) 4 (c) 1 (d) 2
39. 39.What is the mode of 10, 16, 9, 10, 11, 10 and 9? (a) 16 (b) 10 (c) 9 (d) 11
40. 40.What is the median of 2, 36, 8, 18, 23, 7 and 22? (a) 22 (b) 19 (c) 8 (d) 18

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