Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 580 · 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.What is the missing term in the AP 19, 24, 29, ?, 39? (a) 34 (b) 33 (c) 35 (d) 39
2. 2.How many prime numbers are there between 30 and 60? (a) 9 (b) 7 (c) 6 (d) 8
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
4. 4.A bag has 12 white balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 21 (b) 2 (c) 13 (d) 10
5. 5.In a class of 23 children, 7 like dance, 16 like music and 3 like both. How many like neither? (a) 6 (b) 4 (c) 3 (d) 0
6. 6.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 16 (d) 24
7. 7.There are 5 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 50 (c) 25 (d) 30
8. 8.If a + b = 15 and ab = 50, what is (a − b)²? (a) 5 (b) 225 (c) 25 (d) 125
9. 9.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
10. 10.What are the roots of x² − 14x + 45 = 0? (a) 1 and 13 (b) 1 and 45 (c) 5 and 9 (d) 3 and 15
11. 11.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
12. 12.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 36 (c) 45 (d) 72
13. 13.If a + b = 10 and ab = 24, what is a² + b²? (a) 148 (b) 76 (c) 52 (d) 100
14. 14.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 68 (c) 76 (d) 67
15. 15.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 28 (d) 49
16. 16.A bag has 3 red, 7 green and 4 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 3/14 (c) 6/7 (d) 11/14
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/18 (d) 1/12
18. 18.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 45 (c) 100 (d) 55
19. 19.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
20. 20.What is the mode of 18, 13, 20, 11, 18, 13 and 13? (a) 18 (b) 13 (c) 20 (d) 11
21. 21.A bag has 8 blue balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 20 (b) 10 (c) 9 (d) 2
22. 22.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 150°
23. 23.A cuboid is 6 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 72 sq cm (b) 120 sq cm (c) 240 sq cm (d) 60 sq cm
24. 24.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) 24 (b) 37 (c) 36 (d) 25
25. 25.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 225° (b) 45° (c) 135° (d) 90°
26. 26.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
27. 27.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
28. 28.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 24 (c) 32 (d) 16
29. 29.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 9 (b) 44 (c) 88 (d) 48
30. 30.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 15° (b) 140° (c) 55° (d) 165°
31. 31.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 354 (c) 308 (d) 355
32. 32.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 10° (d) 50°
33. 33.The mean of 9 numbers is 22. When the number 32 is added to them, what is the new mean? (a) 24 (b) 23 (c) 27 (d) 22
34. 34.How many prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 6 (d) 5
35. 35.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 90° (b) 150° (c) 120° (d) 270°
36. 36.How many prime numbers are there between 60 and 70? (a) 3 (b) 2 (c) 4 (d) 1
37. 37.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 484 (d) 506
38. 38.What is the 30th term of the AP 20, 28, 36, 44, …? (a) 252 (b) 260 (c) 232 (d) 240
39. 39.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
40. 40.In a class of 28 children, 11 like maths, 17 like science and 3 like both. How many like only maths? (a) 8 (b) 14 (c) 11 (d) 3

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