Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 749 · 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 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) 22 (b) 14 (c) 21 (d) 15
2. 2.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 64 sq cm (c) 512 sq cm (d) 384 sq cm
3. 3.What is the 38th term of the AP 18, 26, 34, 42, …? (a) 314 (b) 296 (c) 322 (d) 304
4. 4.A drawer has lots of black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 3 (c) 5 (d) 2
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/11 (c) 5/36 (d) 1/9
6. 6.In a class of 39 children, 14 like tea, 18 like coffee and 3 like both. How many like at least one of the two? (a) 39 (b) 26 (c) 29 (d) 32
7. 7.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 702 (d) 351
8. 8.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 270° (b) 115° (c) 90° (d) 155°
9. 9.What is the midpoint of the line joining (9, 9) and (11, 15)? (a) (12, 10) (b) (20, 24) (c) (1, 3) (d) (10, 12)
10. 10.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 55° (b) 10° (c) 135° (d) 170°
11. 11.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 228 (b) 132 (c) 114 (d) 34
12. 12.A bag has 4 blue balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 15 (c) 5 (d) 6
13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 16 (b) 6 (c) 17 (d) 15
14. 14.Which is the correct factorisation of x² + 12x + 35? (a) (x + 1)(x + 35) (b) (x + 1)(x + 11) (c) (x + 5)(x + 7) (d) (x − 5)(x − 7)
15. 15.What is the median of 21, 3, 16, 39, 15, 6 and 36? (a) 16 (b) 21 (c) 15 (d) 39
16. 16.How many factors does 15 have? (a) 5 (b) 4 (c) 3 (d) 2
17. 17.What is the distance between the points (0, 9) and (12, 4)? (a) 169 (b) 14 (c) 13 (d) 17
18. 18.How many factors does 41 have? (a) 1 (b) 3 (c) 4 (d) 2
19. 19.In a class of 44 children, 24 like tea, 25 like coffee and 6 like both. How many like neither? (a) 7 (b) 6 (c) 2 (d) 1
20. 20.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 91 (d) 105
21. 21.If a + b = 9 and ab = 18, what is (a − b)²? (a) 3 (b) 9 (c) 81 (d) 45
22. 22.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 14 (d) 21
23. 23.What is the smallest prime factor of 55? (a) 5 (b) 2 (c) 11 (d) 1
24. 24.What is the distance between the points (4, 0) and (28, 7)? (a) 31 (b) 625 (c) 25 (d) 26
25. 25.If a + b = 13 and ab = 22, what is a² + b²? (a) 213 (b) 169 (c) 125 (d) 147
26. 26.A bag has 4 yellow, 2 white and 2 blue balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 1/2 (c) 5/8 (d) 1/8
27. 27.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 56 (c) 16 (d) 28
28. 28.What is the distance between the points (2, 6) and (14, 22)? (a) 21 (b) 400 (c) 28 (d) 20
29. 29.In which quadrant does the point (−3, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
30. 30.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 81 sq cm (d) 486 sq cm
31. 31.What is the sum of the roots of x² − 9x + 20 = 0? (a) 20 (b) 9 (c) 8 (d) 10
32. 32.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 28 (d) 64
33. 33.In a class of 30 children, 21 like tea, 15 like coffee and 7 like both. How many like at least one of the two? (a) 36 (b) 22 (c) 29 (d) 30
34. 34.Which term of the AP 4, 6, 8, 10, … is 74? (a) 37th (b) 38th (c) 35th (d) 36th
35. 35.If a + b = 19 and ab = 90, what is (a − b)²? (a) 1 (b) 181 (c) 271 (d) 361
36. 36.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 150° (d) 255°
37. 37.What is the 26th term of the AP 15, 23, 31, 39, …? (a) 215 (b) 223 (c) 208 (d) 200
38. 38.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°
39. 39.A bag has 9 black balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 13 (c) 10 (d) 21
40. 40.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 36 (d) 81

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