Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 6 · 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.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 13) (b) (x + 1)(x + 48) (c) (x − 6)(x − 8) (d) (x + 6)(x + 8)
2. 2.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 8 times (d) 2 times
3. 3.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 45° (c) 315° (d) 135°
4. 4.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 100 sq cm (c) 25 sq cm (d) 125 sq cm
5. 5.In a class of 47 children, 29 like mangoes, 23 like bananas and 12 like both. How many like at least one of the two? (a) 47 (b) 52 (c) 28 (d) 40
6. 6.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 66 (c) 78 (d) 132
7. 7.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
8. 8.If a + b = 19 and ab = 88, what is a² + b²? (a) 273 (b) 361 (c) 537 (d) 185
9. 9.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
10. 10.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)
11. 11.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
12. 12.What is the median of 9, 35, 19, 30, 13, 14 and 18? (a) 14 (b) 19 (c) 18 (d) 30
13. 13.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
14. 14.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
15. 15.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
16. 16.What is the 27th term of the AP 3, 5, 7, 9, …? (a) 55 (b) 52 (c) 54 (d) 57
17. 17.A bag has 5 yellow balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 7 (d) 11
18. 18.A drawer has lots of red 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) 5 (b) 3 (c) 4 (d) 2
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
20. 20.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
21. 21.What is the sum of the roots of x² − 14x + 45 = 0? (a) 14 (b) 45 (c) 13 (d) 15
22. 22.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) 11 (c) 36 (d) 33
23. 23.What is the mean of 15, 5, 13, 7 and 10? (a) 9 (b) 12 (c) 10 (d) 11
24. 24.Two angles of a triangle are 70° and 45°. What is the third angle? (a) 65° (b) 115° (c) 135° (d) 110°
25. 25.A drawer has lots of blue, black, 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) 4 (b) 5 (c) 8 (d) 2
26. 26.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
27. 27.A bag has 10 red balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 2 (c) 11 (d) 21
28. 28.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 97 sq cm (c) 16 sq cm (d) 64 sq cm
29. 29.A bag has 7 yellow balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 9 (c) 17 (d) 8
30. 30.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 60° (c) 120° (d) 30°
31. 31.A bag has 9 yellow, 7 green and 6 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 7/22 (b) 1/3 (c) 8/11 (d) 15/22
32. 32.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 2070 (d) 1035
33. 33.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 60 (c) 35 (d) 11
34. 34.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 45 (c) 15 (d) 135
35. 35.What is the midpoint of the line joining (0, 8) and (6, 4)? (a) (3, 2) (b) (6, 3) (c) (3, 6) (d) (6, 12)
36. 36.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 120 (b) 61 (c) 60 (d) 14
37. 37.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 12 (c) 30 (d) 36
38. 38.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 182 (d) 91
39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 7 (b) 17 (c) 19 (d) 18
40. 40.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 115° (b) 160° (c) 20° (d) 85°

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