Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 240 · 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.A bag has 4 blue balls and 9 yellow 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) 5 (c) 10 (d) 13
2. 2.A bag has 4 red balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 13 (c) 6 (d) 2
3. 3.What is the sum of all the whole numbers from 1 to 92? (a) 4186 (b) 8556 (c) 4278 (d) 4232
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
5. 5.What is the product of the roots of x² − 11x + 30 = 0? (a) 11 (b) 30 (c) 31 (d) 29
6. 6.What is the 22nd term of the AP 16, 20, 24, 28, …? (a) 100 (b) 84 (c) 104 (d) 88
7. 7.A bag has 11 white balls and 6 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) 7 (c) 17 (d) 12
8. 8.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/3 (b) 5/6 (c) 2/3 (d) 1/4
9. 9.In a class of 41 children, 28 like dance, 14 like music and 7 like neither. How many like both? (a) 7 (b) 34 (c) 1 (d) 8
10. 10.A drawer has lots of yellow 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) 5 (b) 4 (c) 2 (d) 3
11. 11.A bag has 5 green balls and 9 yellow 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) 10 (c) 14 (d) 6
12. 12.What is the mean of 16, 14, 2, 2, 14 and 6? (a) 10 (b) 11 (c) 8 (d) 9
13. 13.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
14. 14.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 145° (b) 135° (c) 80° (d) 45°
15. 15.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
16. 16.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 105° (b) 145° (c) 70° (d) 110°
17. 17.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 11035 (b) 10025 (c) 11025 (d) 9025
18. 18.In which quadrant does the point (9, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
19. 19.A bag has 11 black balls and 9 yellow 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) 10 (c) 20 (d) 2
20. 20.How many factors does 42 have? (a) 6 (b) 9 (c) 7 (d) 8
21. 21.What is the sum of the roots of x² − 10x + 16 = 0? (a) 11 (b) 9 (c) 16 (d) 10
22. 22.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
23. 23.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
24. 24.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 19 (b) 18 (c) 17 (d) 26
25. 25.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
26. 26.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 25 (d) 20
27. 27.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 30° (c) 105° (d) 15°
28. 28.How many factors does 62 have? (a) 5 (b) 3 (c) 2 (d) 4
29. 29.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 5/6 (d) 1/4
30. 30.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
31. 31.What is the median of 16, 30, 4, 24 and 2? (a) 17 (b) 24 (c) 4 (d) 16
32. 32.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 72 (c) 24 (d) 8
33. 33.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 155° (b) 45° (c) 160° (d) 135°
34. 34.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 29 (b) 28 (c) 36 (d) 27
35. 35.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
36. 36.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 36 (d) 12
37. 37.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 280° (c) 100° (d) 10°
38. 38.The mean of 7 numbers is 40. When the number 56 is added to them, what is the new mean? (a) 42 (b) 40 (c) 43 (d) 48
39. 39.If a + b = 19 and ab = 88, what is (a − b)²? (a) 185 (b) 361 (c) 9 (d) 3
40. 40.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) 37 (c) 24 (d) 36

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