Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 243 · 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 sum of the first 6 terms of the AP 10, 13, 16, …? (a) 105 (b) 114 (c) 210 (d) 25
2. 2.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 55 (d) 66
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
4. 4.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
5. 5.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 115° (c) 65° (d) 50°
6. 6.How many factors does 78 have? (a) 9 (b) 8 (c) 6 (d) 7
7. 7.In a class of 24 children, 11 like maths, 16 like science and 7 like both. How many like at least one of the two? (a) 20 (b) 13 (c) 24 (d) 27
8. 8.A bag has 10 blue balls and 6 green 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) 7 (c) 16 (d) 11
9. 9.In a class of 14 children, 8 like dance, 7 like music and 3 like both. How many like only dance? (a) 8 (b) 7 (c) 4 (d) 5
10. 10.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 12 (c) 13 (d) 24
11. 11.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 110° (c) 145° (d) 55°
12. 12.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 42 (c) 117 (d) 39
13. 13.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 56 (d) 28
14. 14.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/2 (c) 3/4 (d) 1/4
15. 15.What is the median of 18, 21, 37, 3, 6, 39 and 13? (a) 13 (b) 3 (c) 18 (d) 21
16. 16.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 150 cu cm (b) 16 cu cm (c) 12 cu cm (d) 108 cu cm
17. 17.What is the prime factorisation of 14? (a) 2 × 7² (b) 2 × 7 (c) 2³ × 7 (d) 2² × 7
18. 18.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
19. 19.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/4 (d) 3/8
20. 20.How many factors does 40 have? (a) 8 (b) 9 (c) 7 (d) 6
21. 21.8 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 96 (b) 56 (c) 48 (d) 14
22. 22.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 2/3 (b) 1/3 (c) 5/6 (d) 1/4
23. 23.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 32) (b) (x + 1)(x + 11) (c) (x − 4)(x − 8) (d) (x + 4)(x + 8)
24. 24.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
25. 25.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 165° (b) 160° (c) 15° (d) 35°
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.There are 4 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 8 (b) 32 (c) 16 (d) 20
28. 28.A cuboid is 8 cm long, 6 cm wide and 7 cm high. What is its volume? (a) 292 cu cm (b) 48 cu cm (c) 336 cu cm (d) 21 cu cm
29. 29.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 45 (d) 20
30. 30.What is the sum of all the whole numbers from 1 to 69? (a) 2416 (b) 2415 (c) 2346 (d) 4830
31. 31.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 256 cu cm (d) 384 cu cm
32. 32.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
33. 33.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 475 (b) 474 (c) 465 (d) 388
34. 34.In a class of 47 children, 20 like tea, 26 like coffee and 9 like neither. How many like both? (a) 9 (b) 38 (c) 8 (d) 7
35. 35.In which quadrant does the point (−3, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
36. 36.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 122 (c) 131 (d) 132
37. 37.In a class of 45 children, 21 like dance, 23 like music and 9 like both. How many like neither? (a) 9 (b) 1 (c) 19 (d) 10
38. 38.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
39. 39.What is the mode of 16, 7, 15, 3, 3, 16 and 3? (a) 16 (b) 7 (c) 15 (d) 3
40. 40.In a class of 37 children, 31 like maths, 16 like science and 11 like both. How many like at least one of the two? (a) 47 (b) 36 (c) 25 (d) 37

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