Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 227 · 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 how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 6 (d) 3
2. 2.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 130° (b) 110° (c) 120° (d) 60°
3. 3.A bag has 9 red, 4 green and 7 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 9/11 (b) 11/20 (c) 1/3 (d) 9/20
4. 4.What is the distance between the points (5, 0) and (21, 12)? (a) 400 (b) 21 (c) 20 (d) 28
5. 5.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 65° (d) 155°
6. 6.In which quadrant does the point (−7, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
7. 7.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 21 (d) 14
8. 8.A bag has 12 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 14 (b) 13 (c) 17 (d) 2
9. 9.In a class of 43 children, 23 like cricket, 21 like football and 9 like both. How many like only cricket? (a) 12 (b) 22 (c) 23 (d) 14
10. 10.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 54 sq cm (c) 9 sq cm (d) 27 sq cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
12. 12.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 45 (c) 135 (d) 48
13. 13.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 6 cu cm (b) 12 cu cm (c) 32 cu cm (d) 7 cu cm
14. 14.A drawer has lots of blue, green, yellow 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) 2 (b) 4 (c) 8 (d) 5
15. 15.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/36 (c) 1/11 (d) 1/18
17. 17.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 851 (b) 961 (c) 841 (d) 899
18. 18.There are 8 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) 56 (b) 112 (c) 15 (d) 64
19. 19.How many factors does 43 have? (a) 1 (b) 2 (c) 3 (d) 4
20. 20.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 55 (c) 110 (d) 66
21. 21.A bag has 7 yellow balls and 5 white 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) 2 (c) 6 (d) 8
22. 22.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
23. 23.A bag has 5 green, 4 white and 2 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 7/11 (b) 6/11 (c) 5/11 (d) 1/3
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/36 (c) 5/11 (d) 1/6
25. 25.In a class of 25 children, 10 like dance, 11 like music and 4 like both. How many like only dance? (a) 7 (b) 14 (c) 6 (d) 10
26. 26.A drawer has lots of black and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 4 (c) 3 (d) 5
27. 27.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 384 (b) 266 (c) 256 (d) 576
28. 28.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 75 (c) 216 (d) 72
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/9 (c) 1/11 (d) 1/12
30. 30.In a class of 38 children, 23 like maths, 18 like science and 3 like neither. How many like both? (a) 7 (b) 35 (c) 6 (d) 3
31. 31.A bag has 5 blue balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 6 (b) 2 (c) 16 (d) 7
32. 32.If a + b = 5 and ab = 4, what is a² + b²? (a) 25 (b) 17 (c) 33 (d) 21
33. 33.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
34. 34.What is the median of 25, 11, 27, 23, 12, 33 and 39? (a) 25 (b) 27 (c) 26 (d) 23
35. 35.What is the median of 10, 31, 3, 20 and 18? (a) 3 (b) 10 (c) 18 (d) 20
36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 9 (b) 20 (c) 21 (d) 19
37. 37.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 25 (d) 20
38. 38.A bag has 11 green balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 17 (b) 2 (c) 13 (d) 12
39. 39.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 140° (d) 50°
40. 40.In a class of 21 children, 8 like mangoes, 7 like bananas and 4 like both. How many like neither? (a) 10 (b) 4 (c) 14 (d) 6

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