Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 33 · 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 11 cm. What is its volume? (a) 484 cu cm (b) 33 cu cm (c) 1331 cu cm (d) 726 cu cm
2. 2.In a class of 41 children, 22 like cricket, 20 like football and 3 like both. How many like only cricket? (a) 19 (b) 17 (c) 21 (d) 22
3. 3.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
4. 4.A bag has 3 black balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 2 (c) 5 (d) 4
5. 5.A bag has 7 red, 3 green and 7 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 10/17 (c) 7/17 (d) 11/17
6. 6.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 15 (b) 17 (c) 16 (d) 20
7. 7.In a class of 29 children, 14 like tea, 21 like coffee and 4 like neither. How many like both? (a) 25 (b) 6 (c) 4 (d) 10
8. 8.In a class of 39 children, 19 like maths, 27 like science and 8 like both. How many like at least one of the two? (a) 30 (b) 38 (c) 39 (d) 46
9. 9.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
10. 10.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 260° (b) 80° (c) 160° (d) 100°
11. 11.A bag has 11 black balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 12 (b) 2 (c) 13 (d) 16
12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 21 (d) 9
13. 13.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 84 (c) 42 (d) 13
14. 14.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
15. 15.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) 37 (b) 25 (c) 24 (d) 36
16. 16.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 468 (c) 478 (d) 477
17. 17.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 28 (c) 22 (d) 29
18. 18.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 9 (c) 81 (d) 27
19. 19.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
20. 20.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 110° (b) 100° (c) 150° (d) 70°
21. 21.What is the mean of 5, 9, 8 and 14? (a) 9 (b) 12 (c) 8 (d) 10
22. 22.What is the prime factorisation of 63? (a) 3 × 7² (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7
23. 23.What is the sum of the roots of x² − 10x + 21 = 0? (a) 21 (b) 9 (c) 10 (d) 11
24. 24.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 50° (d) 100°
25. 25.What is the product of the roots of x² − 13x + 42 = 0? (a) 43 (b) 41 (c) 42 (d) 13
26. 26.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 12) (b) (x − 5)(x − 8) (c) (x + 1)(x + 40) (d) (x + 5)(x + 8)
27. 27.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
28. 28.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 7225 (b) 8125 (c) 9025 (d) 9035
29. 29.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 18 (c) 36 (d) 81
30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
31. 31.There are 4 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) 20 (b) 40 (c) 24 (d) 9
32. 32.If a + b = 16 and ab = 48, what is a² + b²? (a) 160 (b) 256 (c) 352 (d) 208
33. 33.In a class of 43 children, 16 like cricket, 22 like football and 2 like both. How many like at least one of the two? (a) 38 (b) 36 (c) 34 (d) 43
34. 34.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 75° (d) 15°
35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
36. 36.In a class of 41 children, 28 like mangoes, 14 like bananas and 9 like both. How many like only mangoes? (a) 19 (b) 27 (c) 28 (d) 5
37. 37.A drawer has lots of yellow and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 4 (c) 5 (d) 2
38. 38.In a class of 39 children, 19 like cricket, 28 like football and 2 like neither. How many like both? (a) 8 (b) 37 (c) 10 (d) 2
39. 39.What is the 30th term of the AP 17, 24, 31, 38, …? (a) 227 (b) 203 (c) 220 (d) 210
40. 40.If a + b = 4 and ab = 3, what is a² + b²? (a) 13 (b) 10 (c) 22 (d) 16

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