Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 581 · 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.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 7 (d) 9
2. 2.In which quadrant does the point (7, −4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
3. 3.In a class of 40 children, 28 like mangoes, 14 like bananas and 8 like both. How many like at least one of the two? (a) 26 (b) 34 (c) 42 (d) 40
4. 4.What is the mean of 20, 7, 4, 20, 6 and 9? (a) 13 (b) 10 (c) 11 (d) 12
5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 5 (d) 2
6. 6.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 51 (c) 572 (d) 286
7. 7.How many prime numbers are there between 20 and 30? (a) 2 (b) 1 (c) 4 (d) 3
8. 8.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 100° (d) 40°
9. 9.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
10. 10.If a + b = 13 and ab = 30, what is a² + b²? (a) 109 (b) 139 (c) 169 (d) 229
11. 11.A bag has 9 yellow balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 20 (b) 10 (c) 12 (d) 2
12. 12.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 11) (b) (x + 3)(x + 9) (c) (x + 1)(x + 27) (d) (x − 3)(x − 9)
13. 13.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3² × 7 (c) 3 × 7² (d) 3 × 7
14. 14.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 20 (d) 240
15. 15.What is the sum of the roots of x² − 11x + 30 = 0? (a) 10 (b) 11 (c) 30 (d) 12
16. 16.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
17. 17.A bag has 4 white balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 7 (b) 2 (c) 6 (d) 5
18. 18.A bag has 10 white balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 18 (c) 9 (d) 2
19. 19.In a class of 30 children, 6 like maths, 20 like science and 3 like both. How many like at least one of the two? (a) 30 (b) 26 (c) 23 (d) 20
20. 20.What is the mean of 9, 2, 19, 11, 7 and 12? (a) 11 (b) 9 (c) 10 (d) 12
21. 21.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
22. 22.A cuboid is 10 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 536 sq cm (b) 134 sq cm (c) 240 sq cm (d) 268 sq cm
23. 23.What is the 15th term of the AP 17, 23, 29, 35, …? (a) 107 (b) 101 (c) 90 (d) 84
24. 24.What is the midpoint of the line joining (5, 0) and (7, 6)? (a) (3, 6) (b) (6, 3) (c) (1, 3) (d) (12, 6)
25. 25.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 56 (c) 16 (d) 64
26. 26.What is the mean of 19, 12, 6 and 3? (a) 10 (b) 9 (c) 11 (d) 8
27. 27.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 531 (c) 540 (d) 541
28. 28.How many factors does 52 have? (a) 5 (b) 4 (c) 6 (d) 7
29. 29.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 820 (c) 800 (d) 780
30. 30.In a class of 40 children, 21 like cricket, 23 like football and 5 like both. How many like at least one of the two? (a) 34 (b) 40 (c) 44 (d) 39
31. 31.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 110° (b) 135° (c) 115° (d) 70°
32. 32.What is the mode of 9, 9, 6, 6, 2, 16 and 9? (a) 2 (b) 9 (c) 16 (d) 6
33. 33.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 37 (c) 49 (d) 36
34. 34.What is the mode of 3, 12, 3, 12, 5, 7 and 12? (a) 3 (b) 5 (c) 12 (d) 7
35. 35.A bag has 8 white balls and 3 yellow 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) 11 (c) 4 (d) 9
36. 36.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 60° (b) 130° (c) 110° (d) 120°
37. 37.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 35° (d) 110°
38. 38.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
39. 39.A cuboid is 8 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 118 sq cm (b) 236 sq cm (c) 240 sq cm (d) 472 sq cm
40. 40.In a class of 39 children, 22 like cricket, 24 like football and 4 like neither. How many like both? (a) 7 (b) 35 (c) 11 (d) 4

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