Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 267 · 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 + 13x + 42? (a) (x + 1)(x + 12) (b) (x + 6)(x + 7) (c) (x − 6)(x − 7) (d) (x + 1)(x + 42)
2. 2.A bag has 7 yellow balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 10 (c) 8 (d) 2
3. 3.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 54 (c) 62 (d) 53
4. 4.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) 11 (b) 36 (c) 99 (d) 33
5. 5.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 24 (d) 7
6. 6.What is the mean of 6, 15, 19, 13 and 17? (a) 13 (b) 14 (c) 16 (d) 15
7. 7.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 156 (d) 169
8. 8.How many factors does 45 have? (a) 5 (b) 4 (c) 7 (d) 6
9. 9.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
10. 10.In a class of 28 children, 22 like mangoes, 11 like bananas and 6 like both. How many like only mangoes? (a) 17 (b) 16 (c) 5 (d) 22
11. 11.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 24) (b) (x − 4)(x − 6) (c) (x + 4)(x + 6) (d) (x + 1)(x + 9)
12. 12.Using (a − b)² = a² − 2ab + b², what is 28²? (a) 794 (b) 784 (c) 1024 (d) 896
13. 13.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 30 (c) 15 (d) 36
14. 14.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 75° (c) 155° (d) 105°
15. 15.If a + b = 17 and ab = 70, what is a² + b²? (a) 289 (b) 149 (c) 429 (d) 219
16. 16.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 12 (d) 30
17. 17.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 10 (c) 42 (d) 21
18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 5 (c) 6 (d) 9
19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 14 (b) 11 (c) 13 (d) 8
20. 20.In a class of 36 children, 18 like tea, 25 like coffee and 8 like both. How many like at least one of the two? (a) 43 (b) 36 (c) 27 (d) 35
21. 21.A drawer has lots of white, blue, red, yellow and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 2 (c) 6 (d) 5
22. 22.A bag has 8 red balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 9 (c) 2 (d) 12
23. 23.What is the sum of the roots of x² − 11x + 30 = 0? (a) 11 (b) 12 (c) 30 (d) 10
24. 24.What is the mode of 15, 16, 2, 15, 10, 15 and 10? (a) 16 (b) 10 (c) 2 (d) 15
25. 25.Using (a − b)² = a² − 2ab + b², what is 69²? (a) 4771 (b) 5041 (c) 4761 (d) 4899
26. 26.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 256 sq cm (c) 64 sq cm (d) 512 sq cm
27. 27.The mean of 5 numbers is 32. When the number 26 is added to them, what is the new mean? (a) 30 (b) 31 (c) 32 (d) 29
28. 28.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
29. 29.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 24 (d) 16
30. 30.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 240 (d) 20
31. 31.How many factors does 114 have? (a) 8 (b) 9 (c) 6 (d) 7
32. 32.The mean of 3 numbers is 17. When the number 1 is added to them, what is the new mean? (a) 14 (b) 9 (c) 13 (d) 17
33. 33.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
34. 34.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 115° (b) 140° (c) 65° (d) 105°
35. 35.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 28 (c) 56 (d) 36
36. 36.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 85° (c) 95° (d) 160°
37. 37.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
38. 38.A drawer has lots of green, red, black 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) 2 (b) 4 (c) 5 (d) 8
39. 39.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 21 (c) 28 (d) 14
40. 40.If a + b = 13 and ab = 22, what is (a − b)²? (a) 125 (b) 9 (c) 169 (d) 81

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