Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 762 · 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 21 children, 15 like tea, 15 like coffee and 12 like both. How many like neither? (a) 12 (b) 3 (c) 15 (d) 4
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
3. 3.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 24 (c) 37 (d) 36
4. 4.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
5. 5.A bag has 5 yellow, 5 white and 6 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 11/16 (c) 5/11 (d) 5/16
6. 6.The mean of 6 numbers is 38. When the number 52 is added to them, what is the new mean? (a) 40 (b) 41 (c) 45 (d) 38
7. 7.A bag has 6 blue balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 16 (b) 8 (c) 2 (d) 7
8. 8.A bag has 8 green, 8 blue and 4 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 3/5 (b) 2/5 (c) 1/3 (d) 13/20
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/12 (c) 1/36 (d) 1/11
10. 10.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 75° (b) 130° (c) 155° (d) 105°
11. 11.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
12. 12.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 135° (c) 90° (d) 45°
13. 13.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
14. 14.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
15. 15.What is the median of 31, 8, 4, 32 and 35? (a) 22 (b) 31 (c) 4 (d) 32
16. 16.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 42 (c) 39 (d) 13
17. 17.In a class of 30 children, 21 like dance, 8 like music and 5 like both. How many like only dance? (a) 22 (b) 21 (c) 16 (d) 3
18. 18.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 110 (b) 220 (c) 125 (d) 34
19. 19.The mean of 4 numbers is 31. When the number 46 is added to them, what is the new mean? (a) 33 (b) 35 (c) 34 (d) 31
20. 20.The mean of 4 numbers is 23. When the number 3 is added to them, what is the new mean? (a) 20 (b) 19 (c) 13 (d) 23
21. 21.In which quadrant does the point (7, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
22. 22.Which is the correct factorisation of x² + 11x + 30? (a) (x − 5)(x − 6) (b) (x + 5)(x + 6) (c) (x + 1)(x + 30) (d) (x + 1)(x + 10)
23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 18 (d) 20
24. 24.How many factors does 90 have? (a) 11 (b) 10 (c) 13 (d) 12
25. 25.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
26. 26.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/11 (c) 1/12 (d) 1/36
28. 28.If a + b = 6 and ab = 8, what is (a − b)²? (a) 20 (b) 36 (c) 4 (d) 2
29. 29.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
30. 30.In a class of 42 children, 25 like cricket, 15 like football and 8 like both. How many like at least one of the two? (a) 42 (b) 40 (c) 24 (d) 32
31. 31.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
32. 32.A bag has 8 black balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 18 (c) 2 (d) 10
33. 33.What is the median of 3, 18, 40, 8, 38, 28 and 13? (a) 18 (b) 8 (c) 28 (d) 13
34. 34.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 28 (c) 22 (d) 29
35. 35.The mean of 5 numbers is 22. When the number 40 is added to them, what is the new mean? (a) 26 (b) 31 (c) 22 (d) 25
36. 36.In a class of 18 children, 7 like maths, 7 like science and 3 like both. How many like only maths? (a) 11 (b) 4 (c) 3 (d) 7
37. 37.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 215° (b) 70° (c) 145° (d) 35°
38. 38.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 120 (d) 20
39. 39.A bag has 4 green, 7 yellow and 5 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 7/16 (b) 9/16 (c) 1/3 (d) 7/9
40. 40.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 7/8 (c) 1/8 (d) 1/4

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