Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 615 · 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 sum of the first 8 terms of the AP 9, 10, 11, …? (a) 100 (b) 200 (c) 104 (d) 16
2. 2.In a class of 38 children, 21 like mangoes, 20 like bananas and 9 like neither. How many like both? (a) 9 (b) 12 (c) 3 (d) 29
3. 3.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2² × 3 (c) 2⁴ × 3 (d) 2³ × 3
4. 4.A drawer has lots of white, yellow and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 4 (d) 3
5. 5.What is the distance between the points (8, 4) and (11, 0)? (a) 25 (b) 7 (c) 5 (d) 6
6. 6.A drawer has lots of black 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) 3 (d) 2
7. 7.What is the distance between the points (6, 5) and (10, 2)? (a) 25 (b) 7 (c) 6 (d) 5
8. 8.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 28 (d) 49
9. 9.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 477 (c) 390 (d) 478
10. 10.How many factors does 101 have? (a) 3 (b) 1 (c) 4 (d) 2
11. 11.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
12. 12.What is the smallest prime factor of 51? (a) 1 (b) 3 (c) 17 (d) 2
13. 13.A bag has 9 blue balls and 12 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) 13 (c) 10 (d) 21
14. 14.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 81 sq cm (d) 486 sq cm
15. 15.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3240 (c) 3321 (d) 3322
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
17. 17.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 45° (d) 35°
18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 18 (d) 19
19. 19.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 4 times (d) 8 times
20. 20.A bag has 9 black balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 10 (c) 2 (d) 16
21. 21.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 156 (c) 147 (d) 148
22. 22.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
23. 23.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
24. 24.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
25. 25.Which is the correct factorisation of x² + 5x + 6? (a) (x − 2)(x − 3) (b) (x + 1)(x + 4) (c) (x + 1)(x + 6) (d) (x + 2)(x + 3)
26. 26.The mean of 3 numbers is 35. When the number 51 is added to them, what is the new mean? (a) 35 (b) 39 (c) 40 (d) 43
27. 27.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 961 (b) 899 (c) 841 (d) 851
28. 28.A drawer has lots of yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 4 (d) 3
29. 29.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 164 (c) 163 (d) 154
30. 30.How many prime numbers are there between 80 and 110? (a) 9 (b) 6 (c) 8 (d) 7
31. 31.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4
32. 32.Which term of the AP 7, 10, 13, 16, … is 115? (a) 36th (b) 38th (c) 37th (d) 39th
33. 33.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/8 (c) 1/7 (d) 7/8
34. 34.In which quadrant does the point (−4, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
35. 35.In a class of 29 children, 11 like mangoes, 19 like bananas and 5 like both. How many like neither? (a) 4 (b) 5 (c) 3 (d) 9
36. 36.How many factors does 22 have? (a) 4 (b) 3 (c) 5 (d) 2
37. 37.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 52 (c) 44 (d) 43
38. 38.In a class of 41 children, 23 like mangoes, 21 like bananas and 6 like neither. How many like both? (a) 6 (b) 3 (c) 9 (d) 35
39. 39.The mean of 3 numbers is 29. When the number 17 is added to them, what is the new mean? (a) 27 (b) 29 (c) 26 (d) 23
40. 40.How many prime numbers are there between 90 and 100? (a) 1 (b) 0 (c) 3 (d) 2

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