Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 407 · 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.In a class of 43 children, 27 like mangoes, 19 like bananas and 8 like both. How many like only mangoes? (a) 19 (b) 11 (c) 27 (d) 24
2. 2.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
3. 3.A bag has 8 red balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 9 (b) 20 (c) 10 (d) 2
4. 4.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 324 cu cm (c) 486 cu cm (d) 27 cu cm
5. 5.What is the mean of 20, 7, 6 and 15? (a) 13 (b) 11 (c) 12 (d) 16
6. 6.In a class of 43 children, 20 like cricket, 22 like football and 3 like both. How many like at least one of the two? (a) 43 (b) 36 (c) 42 (d) 39
7. 7.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 26 (b) 24 (c) 33 (d) 25
8. 8.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
10. 10.What is the smallest prime factor of 87? (a) 3 (b) 29 (c) 1 (d) 2
11. 11.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 702 (c) 338 (d) 325
12. 12.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
13. 13.What is the 22nd term of the AP 2, 7, 12, 17, …? (a) 112 (b) 105 (c) 110 (d) 107
14. 14.A drawer has lots of green, blue 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) 6 (b) 3 (c) 2 (d) 4
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 9 (b) 21 (c) 19 (d) 20
16. 16.How many factors does 118 have? (a) 3 (b) 2 (c) 5 (d) 4
17. 17.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 110° (c) 145° (d) 35°
18. 18.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 120 (d) 240
19. 19.A drawer has lots of red 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) 5 (b) 3 (c) 4 (d) 2
20. 20.In a class of 37 children, 14 like maths, 18 like science and 2 like both. How many like only maths? (a) 14 (b) 19 (c) 12 (d) 16
21. 21.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
22. 22.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2 × 3 × 5⁴
23. 23.What is the 36th term of the AP 10, 13, 16, 19, …? (a) 108 (b) 118 (c) 115 (d) 105
24. 24.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
25. 25.The mean of 6 numbers is 13. When the number 20 is added to them, what is the new mean? (a) 16 (b) 15 (c) 14 (d) 13
26. 26.There are 6 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 36 (c) 9 (d) 24
27. 27.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 16 (b) 17 (c) 18 (d) 21
28. 28.What is the missing term in the AP 19, 25, ?, 37, 43? (a) 37 (b) 30 (c) 32 (d) 31
29. 29.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
30. 30.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 30° (d) 75°
31. 31.A bag has 7 white balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 9 (d) 8
32. 32.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) 12 (b) 25 (c) 13 (d) 24
33. 33.In a class of 32 children, 25 like dance, 13 like music and 7 like both. How many like neither? (a) 7 (b) 8 (c) 1 (d) 2
34. 34.Which is the correct factorisation of x² + 10x + 21? (a) (x + 3)(x + 7) (b) (x − 3)(x − 7) (c) (x + 1)(x + 21) (d) (x + 1)(x + 9)
35. 35.In which quadrant does the point (−8, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
36. 36.In a class of 24 children, 11 like cricket, 13 like football and 6 like both. How many like only cricket? (a) 11 (b) 6 (c) 7 (d) 5
37. 37.In a class of 38 children, 21 like cricket, 19 like football and 3 like both. How many like neither? (a) 4 (b) 3 (c) 2 (d) 1
38. 38.A bag has 3 white balls and 5 blue 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) 4 (c) 6 (d) 8
39. 39.In a class of 15 children, 6 like maths, 11 like science and 1 like neither. How many like both? (a) 14 (b) 2 (c) 1 (d) 3
40. 40.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 619 (c) 618 (d) 609

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