Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 857 · 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 40? (a) 4 (b) 2 (c) 3 (d) 1
2. 2.In a class of 54 children, 25 like cricket, 27 like football and 8 like both. How many like neither? (a) 18 (b) 8 (c) 2 (d) 10
3. 3.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 135° (c) 60° (d) 120°
4. 4.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 60° (d) 150°
5. 5.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 16° (c) 15° (d) 165°
6. 6.In which quadrant does the point (7, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
7. 7.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 7/8 (c) 1/4 (d) 1/8
8. 8.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/3 (c) 1/2 (d) 2/3
9. 9.A bag has 8 yellow balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 13 (b) 2 (c) 10 (d) 9
10. 10.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
11. 11.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
12. 12.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 85° (b) 120° (c) 60° (d) 155°
13. 13.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 7 (d) 2
14. 14.What is the mean of 9, 2, 19 and 18? (a) 11 (b) 16 (c) 13 (d) 12
15. 15.Which is the correct factorisation of x² + 11x + 24? (a) (x + 1)(x + 10) (b) (x + 3)(x + 8) (c) (x + 1)(x + 24) (d) (x − 3)(x − 8)
16. 16.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 3/8 (c) 1/8 (d) 1/4
17. 17.A bag has 8 blue balls and 10 green 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) 9 (c) 18 (d) 11
18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 20 (d) 8
19. 19.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 15° (c) 75° (d) 105°
20. 20.Which term of the AP 2, 10, 18, 26, … is 146? (a) 21st (b) 19th (c) 18th (d) 20th
21. 21.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
22. 22.What is the sum of the roots of x² − 11x + 24 = 0? (a) 24 (b) 10 (c) 12 (d) 11
23. 23.How many factors does 20 have? (a) 5 (b) 7 (c) 6 (d) 4
24. 24.What is the 14th term of the AP 2, 4, 6, 8, …? (a) 28 (b) 29 (c) 30 (d) 26
25. 25.What is the distance between the points (1, 0) and (7, 8)? (a) 100 (b) 10 (c) 14 (d) 11
26. 26.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 552 (c) 276 (d) 529
27. 27.There are 6 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 24 (c) 9 (d) 36
28. 28.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
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
30. 30.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) 25 (c) 37 (d) 36
31. 31.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
32. 32.A bag has 7 blue balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 8 (b) 15 (c) 9 (d) 2
33. 33.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 30° (d) 40°
34. 34.A bag has 8 blue balls and 12 white 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) 2 (c) 9 (d) 13
35. 35.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 48 (d) 16
36. 36.How many prime numbers are there between 20 and 40? (a) 3 (b) 6 (c) 4 (d) 5
37. 37.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
38. 38.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 55° (c) 125° (d) 56°
39. 39.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/18 (c) 1/11 (d) 1/12

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