Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 587 · 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 book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 597 (c) 470 (d) 588
2. 2.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 3/8 (d) 7/8
3. 3.A drawer has lots of white and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 3 (d) 2
4. 4.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 61° (c) 120° (d) 240°
5. 5.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
6. 6.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 144 (c) 66 (d) 132
7. 7.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 75° (d) 150°
8. 8.In a class of 40 children, 24 like cricket, 11 like football and 4 like both. How many like neither? (a) 5 (b) 13 (c) 4 (d) 9
9. 9.In a class of 29 children, 11 like mangoes, 19 like bananas and 4 like both. How many like at least one of the two? (a) 26 (b) 30 (c) 29 (d) 22
10. 10.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 20 (d) 25
11. 11.In a class of 28 children, 7 like dance, 13 like music and 2 like both. How many like only dance? (a) 11 (b) 15 (c) 5 (d) 7
12. 12.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
13. 13.In a class of 42 children, 15 like maths, 22 like science and 9 like neither. How many like both? (a) 9 (b) 5 (c) 33 (d) 4
14. 14.A bag has 6 black balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 7 (c) 2 (d) 5
15. 15.The mean of 4 numbers is 31. When the number 11 is added to them, what is the new mean? (a) 28 (b) 31 (c) 27 (d) 21
16. 16.What is the median of 17, 12, 15, 3 and 29? (a) 12 (b) 15 (c) 17 (d) 16
17. 17.What is the 39th term of the AP 4, 6, 8, 10, …? (a) 80 (b) 78 (c) 82 (d) 76
18. 18.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
20. 20.In a class of 27 children, 17 like maths, 19 like science and 10 like both. How many like only maths? (a) 8 (b) 17 (c) 9 (d) 7
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/11 (c) 1/6 (d) 7/36
22. 22.In which quadrant does the point (−1, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
23. 23.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 60° (b) 31° (c) 150° (d) 30°
24. 24.The mean of 8 numbers is 28. When the number 37 is added to them, what is the new mean? (a) 28 (b) 31 (c) 30 (d) 29
25. 25.There are 3 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 21 (b) 24 (c) 42 (d) 10
26. 26.A bag has 11 black balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 15 (c) 2 (d) 5
27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 4 (b) 2 (c) 5 (d) 3
28. 28.In a class of 34 children, 19 like mangoes, 14 like bananas and 6 like both. How many like neither? (a) 1 (b) 6 (c) 7 (d) 13
29. 29.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
30. 30.A bag has 10 green balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 15 (c) 11 (d) 2
31. 31.A bag has 6 green balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 13 (c) 2 (d) 8
32. 32.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 24 (c) 63 (d) 21
33. 33.What is the product of the roots of x² − 8x + 15 = 0? (a) 8 (b) 14 (c) 15 (d) 16
34. 34.What is the smallest prime factor of 55? (a) 11 (b) 1 (c) 5 (d) 2
35. 35.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
36. 36.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
37. 37.In a class of 45 children, 20 like tea, 25 like coffee and 10 like both. How many like at least one of the two? (a) 36 (b) 35 (c) 25 (d) 45
38. 38.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 384 cu cm (c) 256 cu cm (d) 512 cu cm
39. 39.If a + b = 21 and ab = 108, what is (a − b)²? (a) 9 (b) 225 (c) 3 (d) 441
40. 40.Using (a + b)² = a² + 2ab + b², what is 65²? (a) 3025 (b) 4225 (c) 3625 (d) 4235

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