Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 803 · 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.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
2. 2.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
3. 3.If a + b = 21 and ab = 108, what is (a − b)²? (a) 3 (b) 225 (c) 441 (d) 9
4. 4.What is the mean of 9, 8, 11 and 8? (a) 12 (b) 9 (c) 10 (d) 8
5. 5.In a class of 41 children, 23 like dance, 25 like music and 11 like both. How many like neither? (a) 5 (b) 15 (c) 11 (d) 4
6. 6.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 264 sq cm (b) 66 sq cm (c) 132 sq cm (d) 80 sq cm
7. 7.In a class of 41 children, 23 like cricket, 24 like football and 7 like both. How many like at least one of the two? (a) 40 (b) 41 (c) 33 (d) 47
8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 5 (b) 2 (c) 3 (d) 4
9. 9.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
10. 10.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 48 (b) 252 (c) 504 (d) 257
11. 11.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 3/4 (c) 1/4 (d) 1/8
12. 12.In a class of 48 children, 31 like dance, 22 like music and 12 like both. How many like only dance? (a) 31 (b) 10 (c) 19 (d) 26
13. 13.What is the smallest prime factor of 21? (a) 3 (b) 7 (c) 2 (d) 1
14. 14.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 66 (c) 69 (d) 22
15. 15.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
16. 16.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 27 (b) 75 (c) 150 (d) 90
17. 17.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 50° (d) 65°
18. 18.What is the distance between the points (2, 6) and (10, 21)? (a) 18 (b) 289 (c) 23 (d) 17
19. 19.What is the sum of all the whole numbers from 1 to 90? (a) 4095 (b) 4005 (c) 8190 (d) 4050
20. 20.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 25° (c) 65° (d) 335°
21. 21.What is the mode of 3, 17, 10, 17, 10, 17 and 1? (a) 17 (b) 3 (c) 1 (d) 10
22. 22.In a class of 40 children, 13 like cricket, 26 like football and 8 like neither. How many like both? (a) 7 (b) 32 (c) 6 (d) 8
23. 23.What is the distance between the points (0, 2) and (6, 10)? (a) 10 (b) 100 (c) 11 (d) 14
24. 24.Which is the correct factorisation of x² + 11x + 28? (a) (x + 1)(x + 10) (b) (x + 1)(x + 28) (c) (x − 4)(x − 7) (d) (x + 4)(x + 7)
25. 25.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 70° (c) 35° (d) 55°
26. 26.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 14 (d) 21
27. 27.How many factors does 100 have? (a) 10 (b) 8 (c) 7 (d) 9
28. 28.In a class of 34 children, 20 like mangoes, 17 like bananas and 5 like both. How many like at least one of the two? (a) 37 (b) 32 (c) 27 (d) 34
29. 29.How many factors does 32 have? (a) 7 (b) 6 (c) 5 (d) 4
30. 30.A drawer has lots of 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) 2 (b) 3 (c) 4 (d) 6
31. 31.What is the 37th term of the AP 7, 10, 13, 16, …? (a) 108 (b) 115 (c) 111 (d) 118
32. 32.A bag has 9 blue 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) 2 (b) 10 (c) 19 (d) 11
33. 33.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 81 (d) 45
34. 34.What is the 40th term of the AP 9, 17, 25, 33, …? (a) 320 (b) 312 (c) 321 (d) 329
35. 35.Which is the correct factorisation of x² + 16x + 63? (a) (x − 7)(x − 9) (b) (x + 7)(x + 9) (c) (x + 1)(x + 15) (d) (x + 1)(x + 63)
36. 36.In a class of 21 children, 10 like cricket, 14 like football and 4 like neither. How many like both? (a) 4 (b) 17 (c) 7 (d) 3
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 5/36 (c) 1/11 (d) 5/11
38. 38.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 24 (d) 48
39. 39.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) 2 times (c) 4 times (d) 8 times
40. 40.What is the mean of 15, 9, 12 and 12? (a) 16 (b) 11 (c) 13 (d) 12

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