Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 300 · 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 mean of 6, 14, 6, 20 and 4? (a) 11 (b) 10 (c) 12 (d) 9
2. 2.How many prime numbers are there between 60 and 90? (a) 6 (b) 7 (c) 9 (d) 8
3. 3.In a class of 17 children, 11 like maths, 13 like science and 1 like neither. How many like both? (a) 16 (b) 7 (c) 1 (d) 8
4. 4.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 501 (c) 511 (d) 510
5. 5.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
6. 6.Which term of the AP 12, 15, 18, 21, … is 42? (a) 14th (b) 11th (c) 12th (d) 10th
7. 7.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 21 (c) 30 (d) 36
8. 8.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
9. 9.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
10. 10.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 3042 (c) 3081 (d) 6162
11. 11.A bag has 4 blue balls and 6 red 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) 10 (d) 5
12. 12.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 10° (c) 85° (d) 95°
13. 13.In a class of 22 children, 8 like tea, 7 like coffee and 3 like both. How many like only tea? (a) 5 (b) 4 (c) 8 (d) 15
14. 14.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 10°
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 1/11 (c) 5/36 (d) 1/9
16. 16.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 75° (b) 155° (c) 25° (d) 130°
17. 17.A bag has 4 yellow balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 8 (c) 6 (d) 5
18. 18.In a class of 26 children, 13 like tea, 16 like coffee and 4 like both. How many like only tea? (a) 10 (b) 12 (c) 13 (d) 9
19. 19.Which term of the AP 1, 3, 5, 7, … is 55? (a) 28th (b) 30th (c) 29th (d) 27th
20. 20.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) 37 (b) 25 (c) 24 (d) 36
21. 21.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 16 (b) 7 (c) 18 (d) 17
23. 23.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 36 (d) 81
24. 24.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
25. 25.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
26. 26.In which quadrant does the point (−2, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
27. 27.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 90° (b) 140° (c) 130° (d) 40°
28. 28.Which is the correct factorisation of x² + 15x + 56? (a) (x + 7)(x + 8) (b) (x − 7)(x − 8) (c) (x + 1)(x + 56) (d) (x + 1)(x + 14)
29. 29.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 120° (d) 121°
31. 31.A bag has 3 red balls and 9 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) 4 (d) 10
32. 32.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
33. 33.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 75° (c) 105° (d) 120°
34. 34.What is the prime factorisation of 336? (a) 2 × 3 × 7⁴ (b) 2⁴ × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁵ × 3 × 7
35. 35.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 64 (c) 16 (d) 28
36. 36.A bag has 6 white balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 7 (c) 11 (d) 2
37. 37.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 625 (b) 235 (c) 225 (d) 375
38. 38.The mean of 4 numbers is 34. When the number 44 is added to them, what is the new mean? (a) 39 (b) 34 (c) 37 (d) 36
39. 39.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 225 (c) 228 (d) 234
40. 40.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 1331 cu cm (d) 33 cu cm

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