Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 942 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/11 (c) 1/18 (d) 1/12
2. 2.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 85° (d) 10°
3. 3.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 75 (c) 76 (d) 66
4. 4.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 261 (c) 262 (d) 252
5. 5.What is the smallest prime factor of 221? (a) 17 (b) 1 (c) 2 (d) 13
6. 6.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
7. 7.In a class of 42 children, 24 like tea, 19 like coffee and 7 like both. How many like only tea? (a) 23 (b) 12 (c) 24 (d) 17
8. 8.A bag has 3 blue balls and 5 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) 8 (c) 4 (d) 6
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 1/11 (c) 1/12 (d) 3/11
10. 10.A bag has 10 black balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 22 (b) 11 (c) 12 (d) 2
11. 11.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 108 (c) 28 (d) 93
12. 12.A bag has 2 blue, 3 yellow and 7 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 3/4 (b) 1/4 (c) 1/3 (d) 5/6
13. 13.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
14. 14.What is the smallest prime factor of 35? (a) 2 (b) 5 (c) 7 (d) 1
15. 15.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 150° (c) 155° (d) 55°
16. 16.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 300° (c) 120° (d) 60°
17. 17.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 125° (b) 145° (c) 160° (d) 55°
18. 18.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 160° (b) 115° (c) 95° (d) 85°
19. 19.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 153 (c) 51 (d) 54
20. 20.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 115° (c) 66° (d) 65°
21. 21.In a class of 48 children, 29 like dance, 20 like music and 9 like both. How many like neither? (a) 7 (b) 17 (c) 9 (d) 8
22. 22.The mean of 3 numbers is 34. When the number 26 is added to them, what is the new mean? (a) 30 (b) 32 (c) 33 (d) 34
23. 23.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
24. 24.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x − 7)(x − 9) (c) (x + 1)(x + 15) (d) (x + 7)(x + 9)
25. 25.What is the mean of 8, 14, 19, 4 and 20? (a) 12 (b) 14 (c) 15 (d) 13
26. 26.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
27. 27.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 15° (c) 16° (d) 165°
28. 28.In a class of 43 children, 28 like mangoes, 22 like bananas and 8 like both. How many like at least one of the two? (a) 43 (b) 34 (c) 50 (d) 42
29. 29.A bag has 6 white balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 7 (d) 8
30. 30.What is the distance between the points (4, 13) and (10, 5)? (a) 11 (b) 100 (c) 10 (d) 14
31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 16 (b) 17 (c) 5 (d) 15
32. 32.What is the midpoint of the line joining (10, 4) and (16, 8)? (a) (6, 13) (b) (13, 6) (c) (3, 2) (d) (26, 12)
33. 33.What are the roots of x² − 9x + 14 = 0? (a) 1 and 8 (b) 1 and 14 (c) 3 and 6 (d) 2 and 7
34. 34.A bag has 8 green balls and 11 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) 2 (c) 9 (d) 19
35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 231 (d) 41
36. 36.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) 28 (b) 29 (c) 21 (d) 22
37. 37.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 45° (c) 135° (d) 91°
38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 13 (c) 15 (d) 14
39. 39.A bag has 12 red balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 13 (d) 21
40. 40.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm

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