Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 345 · 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 90 and 120? (a) 8 (b) 7 (c) 6 (d) 5
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
3. 3.In a class of 36 children, 22 like mangoes, 15 like bananas and 4 like both. How many like neither? (a) 7 (b) 2 (c) 3 (d) 4
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
5. 5.What is the mode of 15, 7, 7, 11, 15, 15 and 1? (a) 11 (b) 7 (c) 1 (d) 15
6. 6.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 238 (b) 119 (c) 124 (d) 32
7. 7.What is the 35th term of the AP 3, 6, 9, 12, …? (a) 102 (b) 108 (c) 106 (d) 105
8. 8.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 70° (d) 80°
9. 9.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 132 (c) 78 (d) 144
10. 10.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 16 (d) 48
11. 11.If a + b = 12 and ab = 20, what is (a − b)²? (a) 144 (b) 8 (c) 64 (d) 104
12. 12.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 24 cu cm (b) 9 cu cm (c) 12 cu cm (d) 52 cu cm
13. 13.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 368 (b) 208 (c) 184 (d) 44
14. 14.If a + b = 3 and ab = 2, what is (a − b)²? (a) 5 (b) 1 (c) 7 (d) 9
15. 15.A drawer has lots of white and red 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) 2 (d) 3
16. 16.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
17. 17.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
18. 18.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
19. 19.A bag has 6 green, 5 red and 2 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 12/13 (b) 11/13 (c) 2/13 (d) 1/3
20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 5 (b) 6 (c) 4 (d) 3
21. 21.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 28 (c) 21 (d) 14
22. 22.What is the sum of the roots of x² − 16x + 63 = 0? (a) 17 (b) 16 (c) 63 (d) 15
23. 23.In which quadrant does the point (−2, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
24. 24.What is the median of 33, 37, 31, 6, 21, 39 and 23? (a) 23 (b) 33 (c) 6 (d) 31
25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 8 (b) 5 (c) 6 (d) 7
26. 26.If a + b = 11 and ab = 18, what is (a − b)²? (a) 85 (b) 121 (c) 49 (d) 7
27. 27.Two angles of a triangle are 50° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 40° (c) 140° (d) 130°
28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 17 (d) 19
29. 29.There are 7 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 28 (b) 14 (c) 21 (d) 9
30. 30.Using (a − b)² = a² − 2ab + b², what is 46²? (a) 2116 (b) 2916 (c) 2484 (d) 2126
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 1/9 (c) 4/11 (d) 5/36
32. 32.If a + b = 15 and ab = 50, what is a² + b²? (a) 225 (b) 125 (c) 325 (d) 175
33. 33.What is the smallest prime factor of 57? (a) 19 (b) 1 (c) 2 (d) 3
34. 34.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 4/11 (c) 5/36 (d) 1/9
36. 36.In a class of 40 children, 13 like cricket, 20 like football and 9 like neither. How many like both? (a) 9 (b) 3 (c) 31 (d) 2
37. 37.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/2 (c) 3/4 (d) 1/3
38. 38.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) 49 (b) 37 (c) 36 (d) 48
39. 39.There are 4 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) 32 (b) 56 (c) 28 (d) 11
40. 40.What is the median of 15, 22, 20, 38 and 12? (a) 15 (b) 20 (c) 22 (d) 21

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