Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 301 · 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 7, 9, 7, 7, 14, 14 and 10? (a) 14 (b) 9 (c) 7 (d) 10
2. 2.Which is the correct factorisation of x² + 15x + 54? (a) (x − 6)(x − 9) (b) (x + 1)(x + 14) (c) (x + 6)(x + 9) (d) (x + 1)(x + 54)
3. 3.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 9 (c) 24 (d) 18
4. 4.In a class of 37 children, 15 like cricket, 31 like football and 12 like both. How many like only cricket? (a) 3 (b) 6 (c) 19 (d) 15
5. 5.In which quadrant does the point (1, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
6. 6.What is the distance between the points (2, 0) and (8, 8)? (a) 11 (b) 14 (c) 10 (d) 100
7. 7.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 91 (c) 210 (d) 105
8. 8.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
9. 9.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 48 (c) 51 (d) 16
10. 10.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 48 (d) 12
11. 11.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 7 (c) 15 (d) 14
12. 12.A cuboid is 12 cm long, 7 cm wide and 5 cm high. What is its volume? (a) 84 cu cm (b) 24 cu cm (c) 358 cu cm (d) 420 cu cm
13. 13.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
14. 14.A bag has 2 green, 9 red and 7 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/8 (b) 8/9 (c) 1/9 (d) 1/3
15. 15.What is the mean of 2, 3, 12, 17 and 11? (a) 10 (b) 9 (c) 8 (d) 11
16. 16.What is the 27th term of the AP 20, 22, 24, 26, …? (a) 74 (b) 54 (c) 72 (d) 52
17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 17 (d) 19
18. 18.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 45° (d) 120°
19. 19.What is the distance between the points (3, 1) and (18, 9)? (a) 18 (b) 17 (c) 289 (d) 23
20. 20.Using (a + b)² = a² + 2ab + b², what is 52²? (a) 2704 (b) 2714 (c) 2504 (d) 2304
21. 21.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 40° (b) 135° (c) 140° (d) 85°
22. 22.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 28 (b) 280 (c) 140 (d) 152
23. 23.What is the distance between the points (0, 4) and (3, 8)? (a) 25 (b) 7 (c) 5 (d) 6
24. 24.What is the distance between the points (4, 6) and (10, 14)? (a) 14 (b) 11 (c) 10 (d) 100
25. 25.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
26. 26.A drawer has lots of 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) 2 (b) 5 (c) 4 (d) 3
27. 27.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) 24 (b) 7 (c) 16 (d) 12
28. 28.What is the mode of 16, 8, 2, 4, 2, 4 and 4? (a) 2 (b) 8 (c) 4 (d) 16
29. 29.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 60° (d) 100°
30. 30.What is the distance between the points (5, 13) and (11, 5)? (a) 14 (b) 11 (c) 100 (d) 10
31. 31.What is the 40th term of the AP 17, 22, 27, 32, …? (a) 217 (b) 195 (c) 200 (d) 212
32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 5 (b) 14 (c) 15 (d) 16
33. 33.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 35° (d) 110°
34. 34.A drawer has lots of blue and green 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.Using (a − b)² = a² − 2ab + b², what is 39²? (a) 1521 (b) 1531 (c) 1599 (d) 1681
36. 36.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 2/3 (d) 1/3
37. 37.A drawer has lots of red, yellow, white, green 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) 6 (b) 2 (c) 5 (d) 10
38. 38.What is the mode of 3, 3, 3, 11, 9, 9 and 13? (a) 3 (b) 11 (c) 13 (d) 9
39. 39.There are 5 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) 30 (b) 50 (c) 10 (d) 25
40. 40.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 30) (b) (x + 1)(x + 10) (c) (x − 5)(x − 6) (d) (x + 5)(x + 6)

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