Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 937 · 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 14, 12, 12, 5, 20, 5 and 5? (a) 12 (b) 5 (c) 14 (d) 20
2. 2.What is the sum of the roots of x² − 14x + 48 = 0? (a) 15 (b) 14 (c) 13 (d) 48
3. 3.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 23 (c) 207 (d) 72
4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
5. 5.How many factors does 74 have? (a) 3 (b) 5 (c) 2 (d) 4
6. 6.The mean of 3 numbers is 30. When the number 34 is added to them, what is the new mean? (a) 33 (b) 30 (c) 32 (d) 31
7. 7.What is the median of 20, 19, 29, 39, 5, 14 and 22? (a) 39 (b) 20 (c) 19 (d) 22
8. 8.What is the midpoint of the line joining (1, 11) and (9, 9)? (a) (5, 10) (b) (4, 1) (c) (10, 20) (d) (10, 5)
9. 9.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 130° (b) 260° (c) 80° (d) 100°
10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 5 (b) 8 (c) 6 (d) 7
11. 11.What is the sum of the roots of x² − 13x + 42 = 0? (a) 12 (b) 42 (c) 14 (d) 13
12. 12.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
13. 13.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 6 (d) 5
14. 14.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 36 sq cm (c) 27 sq cm (d) 54 sq cm
15. 15.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 294 sq cm (c) 49 sq cm (d) 343 sq cm
16. 16.What is the smallest prime factor of 49? (a) 2 (b) 3 (c) 1 (d) 7
17. 17.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 576 sq cm (c) 864 sq cm (d) 1728 sq cm
18. 18.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 28 (b) 26 (c) 35 (d) 27
19. 19.What is the 16th term of the AP 3, 9, 15, 21, …? (a) 96 (b) 93 (c) 90 (d) 99
20. 20.How many factors does 48 have? (a) 10 (b) 11 (c) 9 (d) 8
21. 21.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 216 (b) 24 (c) 120 (d) 108
22. 22.What is the 12th term of the AP 2, 8, 14, 20, …? (a) 66 (b) 74 (c) 72 (d) 68
23. 23.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 12 (c) 15 (d) 36
24. 24.What is the smallest prime factor of 121? (a) 3 (b) 11 (c) 1 (d) 2
25. 25.A bag has 7 red balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 9 (c) 16 (d) 8
26. 26.A drawer has lots of green, red, yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 5 (c) 4 (d) 2
27. 27.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 6 (c) 18 (d) 54
28. 28.In a class of 22 children, 12 like mangoes, 15 like bananas and 8 like both. How many like only mangoes? (a) 7 (b) 8 (c) 4 (d) 12
29. 29.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
30. 30.What is the smallest prime factor of 253? (a) 2 (b) 11 (c) 1 (d) 23
31. 31.In a class of 29 children, 16 like mangoes, 19 like bananas and 9 like both. How many like only mangoes? (a) 7 (b) 16 (c) 9 (d) 10
32. 32.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 22 (c) 110 (d) 55
33. 33.Using (a − b)² = a² − 2ab + b², what is 28²? (a) 794 (b) 784 (c) 1024 (d) 896
34. 34.A drawer has lots of white 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) 4 (c) 3 (d) 5
35. 35.What is the midpoint of the line joining (3, 9) and (5, 11)? (a) (10, 4) (b) (8, 20) (c) (4, 10) (d) (1, 1)
36. 36.In which quadrant does the point (−8, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
37. 37.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 153 (d) 289
39. 39.What is the midpoint of the line joining (6, 4) and (8, 2)? (a) (14, 6) (b) (1, 1) (c) (3, 7) (d) (7, 3)
40. 40.How many factors does 55 have? (a) 3 (b) 5 (c) 4 (d) 2

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