Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 127 · 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.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) 24 (b) 63 (c) 7 (d) 21
2. 2.Using (a + b)² = a² + 2ab + b², what is 63²? (a) 3249 (b) 3609 (c) 3979 (d) 3969
3. 3.What is the mode of 6, 4, 5, 4, 3, 3 and 4? (a) 6 (b) 3 (c) 5 (d) 4
4. 4.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 65° (d) 40°
5. 5.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
6. 6.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x + 7)(x + 8) (c) (x + 1)(x + 14) (d) (x − 7)(x − 8)
7. 7.What is the distance between the points (5, 3) and (9, 6)? (a) 5 (b) 25 (c) 6 (d) 7
8. 8.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 13 (b) 80 (c) 48 (d) 40
9. 9.What is the mean of 4, 5, 4, 18 and 14? (a) 10 (b) 8 (c) 9 (d) 11
10. 10.If a + b = 16 and ab = 55, what is (a − b)²? (a) 146 (b) 6 (c) 256 (d) 36
11. 11.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
12. 12.Using (a − b)² = a² − 2ab + b², what is 65²? (a) 5625 (b) 4235 (c) 4875 (d) 4225
13. 13.What is the mode of 16, 2, 16, 12, 2, 19 and 2? (a) 2 (b) 12 (c) 19 (d) 16
14. 14.What is the prime factorisation of 168? (a) 2³ × 3 × 7 (b) 2 × 3 × 7³ (c) 2⁴ × 3 × 7 (d) 2² × 3 × 7
15. 15.Which term of the AP 12, 20, 28, 36, … is 260? (a) 33rd (b) 31st (c) 34th (d) 32nd
16. 16.In a class of 30 children, 17 like tea, 12 like coffee and 9 like both. How many like neither? (a) 9 (b) 19 (c) 1 (d) 10
17. 17.What is the 18th term of the AP 8, 15, 22, 29, …? (a) 119 (b) 126 (c) 134 (d) 127
18. 18.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 24 (d) 132
19. 19.There are 3 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 36 (b) 9 (c) 21 (d) 18
20. 20.A bag has 6 yellow balls and 7 black 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) 8 (d) 7
21. 21.A bag has 8 red, 8 green and 5 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 16/21 (b) 17/21 (c) 1/3 (d) 5/21
22. 22.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 70° (c) 105° (d) 145°
23. 23.A drawer has lots of blue, green 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) 6 (b) 3 (c) 2 (d) 4
24. 24.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 279 (c) 289 (d) 288
25. 25.A bag has 12 yellow balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 13 (c) 2 (d) 22
26. 26.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) 25 (c) 37 (d) 24
27. 27.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
28. 28.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 2/3 (c) 5/6 (d) 1/3
29. 29.What is the mode of 4, 20, 20, 1, 4, 8 and 4? (a) 1 (b) 20 (c) 4 (d) 8
30. 30.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
31. 31.What is the median of 10, 24, 12, 20, 14, 26 and 6? (a) 16 (b) 20 (c) 14 (d) 12
32. 32.Which term of the AP 16, 19, 22, 25, … is 103? (a) 31st (b) 30th (c) 32nd (d) 29th
33. 33.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 189 (c) 63 (d) 21
34. 34.In a class of 35 children, 24 like dance, 15 like music and 12 like both. How many like only dance? (a) 3 (b) 12 (c) 20 (d) 24
35. 35.A bag has 6 yellow balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 8 (c) 10 (d) 7
36. 36.What is the 19th term of the AP 8, 17, 26, 35, …? (a) 162 (b) 170 (c) 171 (d) 179
37. 37.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 100° (b) 60° (c) 140° (d) 120°
38. 38.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
39. 39.In a class of 30 children, 14 like cricket, 15 like football and 3 like both. How many like only cricket? (a) 11 (b) 15 (c) 12 (d) 14
40. 40.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 120° (d) 105°

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