Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 910 · 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.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 576 cu cm
2. 2.The mean of 6 numbers is 37. When the number 9 is added to them, what is the new mean? (a) 37 (b) 34 (c) 23 (d) 33
3. 3.A drawer has lots of blue, yellow, black, red 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) 6 (c) 5 (d) 10
4. 4.A cuboid is 11 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 308 sq cm (b) 298 sq cm (c) 596 sq cm (d) 149 sq cm
5. 5.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 8 (c) 24 (d) 72
6. 6.Using (a + b)² = a² + 2ab + b², what is 104²? (a) 10816 (b) 10826 (c) 9216 (d) 10016
7. 7.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
8. 8.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 73 (b) 960 (c) 480 (d) 516
9. 9.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
10. 10.How many factors does 31 have? (a) 1 (b) 3 (c) 4 (d) 2
11. 11.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 144 (d) 66
12. 12.If a + b = 7 and ab = 10, what is (a − b)²? (a) 9 (b) 29 (c) 49 (d) 3
13. 13.If a + b = 5 and ab = 6, what is a² + b²? (a) 13 (b) 19 (c) 37 (d) 25
14. 14.The numbers 20 to 28 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) 216 (c) 75 (d) 72
15. 15.How many factors does 59 have? (a) 3 (b) 2 (c) 4 (d) 1
16. 16.If a + b = 6 and ab = 5, what is a² + b²? (a) 31 (b) 26 (c) 46 (d) 36
17. 17.In a class of 55 children, 31 like mangoes, 30 like bananas and 12 like both. How many like neither? (a) 12 (b) 6 (c) 7 (d) 18
18. 18.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 192 (c) 200 (d) 183
19. 19.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 100° (d) 40°
20. 20.What is the mean of 5, 17, 5 and 9? (a) 12 (b) 8 (c) 10 (d) 9
21. 21.In a class of 38 children, 18 like cricket, 18 like football and 5 like both. How many like at least one of the two? (a) 36 (b) 26 (c) 38 (d) 31
22. 22.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 95° (d) 10°
23. 23.How many prime numbers are there between 50 and 80? (a) 9 (b) 6 (c) 7 (d) 8
24. 24.Which term of the AP 13, 21, 29, 37, … is 157? (a) 18th (b) 21st (c) 20th (d) 19th
25. 25.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
26. 26.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 5/6 (b) 1/5 (c) 1/3 (d) 1/6
27. 27.How many prime numbers are there between 70 and 100? (a) 7 (b) 8 (c) 5 (d) 6
28. 28.What is the mean of 17, 20, 5, 10, 6 and 8? (a) 10 (b) 12 (c) 11 (d) 13
29. 29.What is the smallest prime factor of 221? (a) 17 (b) 1 (c) 13 (d) 2
30. 30.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 95° (b) 55° (c) 125° (d) 140°
31. 31.There are 4 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) 28 (b) 10 (c) 24 (d) 48
32. 32.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/3 (d) 1/4
33. 33.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2 × 3² × 7
34. 34.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 672 (b) 360 (c) 336 (d) 50
35. 35.The mean of 9 numbers is 39. When the number 69 is added to them, what is the new mean? (a) 54 (b) 43 (c) 42 (d) 39
36. 36.What is the smallest prime factor of 115? (a) 2 (b) 23 (c) 5 (d) 1
37. 37.What is the mode of 9, 19, 15, 15, 16, 15 and 9? (a) 9 (b) 19 (c) 16 (d) 15
38. 38.What is the missing term in the AP 10, 15, 20, ?, 30? (a) 25 (b) 30 (c) 26 (d) 24
39. 39.The mean of 7 numbers is 10. When the number 42 is added to them, what is the new mean? (a) 15 (b) 10 (c) 26 (d) 14
40. 40.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3

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