Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 821 · 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.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 81 (c) 36 (d) 45
2. 2.How many factors does 64 have? (a) 7 (b) 8 (c) 6 (d) 5
3. 3.In which quadrant does the point (5, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
4. 4.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
5. 5.3 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 7 (c) 15 (d) 12
6. 6.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 50° (d) 160°
7. 7.A drawer has lots of blue, white, yellow, black and red 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
8. 8.Which is the correct factorisation of x² + 10x + 24? (a) (x + 4)(x + 6) (b) (x + 1)(x + 24) (c) (x + 1)(x + 9) (d) (x − 4)(x − 6)
9. 9.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 290 (b) 265 (c) 530 (d) 49
10. 10.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 132 (d) 144
11. 11.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 81° (d) 260°
12. 12.The numbers 15 to 23 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) 171 (c) 57 (d) 19
13. 13.What are the roots of x² − 11x + 18 = 0? (a) 2 and 9 (b) 1 and 18 (c) 1 and 10 (d) 3 and 6
14. 14.If a + b = 18 and ab = 72, what is a² + b²? (a) 324 (b) 252 (c) 468 (d) 180
15. 15.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
16. 16.A drawer has lots of blue, black, yellow and red 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) 8 (c) 2 (d) 5
17. 17.There are 4 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 24 (c) 7 (d) 16
18. 18.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
19. 19.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) 24 (c) 37 (d) 25
20. 20.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/8 (c) 3/5 (d) 5/8
21. 21.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
22. 22.A bag has 2 red, 4 yellow and 9 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 2/5 (b) 1/3 (c) 3/5 (d) 2/3
23. 23.What is the missing term in the AP 9, ?, 27, 36, 45? (a) 17 (b) 18 (c) 27 (d) 19
24. 24.What is the distance between the points (3, 15) and (9, 7)? (a) 14 (b) 100 (c) 11 (d) 10
25. 25.What is the midpoint of the line joining (1, 3) and (13, 5)? (a) (6, 1) (b) (7, 4) (c) (14, 8) (d) (4, 7)
26. 26.In a class of 39 children, 29 like maths, 17 like science and 11 like both. How many like neither? (a) 5 (b) 4 (c) 11 (d) 15
27. 27.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 95° (b) 130° (c) 85° (d) 135°
28. 28.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 114 (c) 124 (d) 132
29. 29.What is the distance between the points (8, 16) and (20, 7)? (a) 225 (b) 21 (c) 16 (d) 15
30. 30.If a + b = 19 and ab = 90, what is a² + b²? (a) 361 (b) 181 (c) 271 (d) 541
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 4/11 (c) 5/36 (d) 1/11
32. 32.If a + b = 12 and ab = 32, what is a² + b²? (a) 80 (b) 144 (c) 112 (d) 208
33. 33.What is the mode of 7, 5, 8, 13, 13, 7 and 7? (a) 7 (b) 5 (c) 13 (d) 8
34. 34.Two angles of a triangle are 25° and 85°. What is the exterior angle at the third corner? (a) 155° (b) 95° (c) 70° (d) 110°
35. 35.A bag has 5 red balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 7 (b) 6 (c) 2 (d) 17
36. 36.The mean of 3 numbers is 35. When the number 19 is added to them, what is the new mean? (a) 32 (b) 31 (c) 35 (d) 27
37. 37.What is the 27th term of the AP 5, 13, 21, 29, …? (a) 221 (b) 213 (c) 216 (d) 208
38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 18 (d) 19
39. 39.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 57 (c) 18 (d) 54
40. 40.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times

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