Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 107 · 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 fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
2. 2.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 152 sq cm (b) 40 sq cm (c) 38 sq cm (d) 76 sq cm
3. 3.What is the midpoint of the line joining (10, 4) and (12, 2)? (a) (22, 6) (b) (11, 3) (c) (1, 1) (d) (3, 11)
4. 4.There are 8 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 12 (c) 32 (d) 64
5. 5.In a class of 38 children, 19 like tea, 22 like coffee and 12 like both. How many like at least one of the two? (a) 41 (b) 38 (c) 17 (d) 29
6. 6.A bag has 10 yellow balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 20 (b) 2 (c) 11 (d) 12
7. 7.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
8. 8.A drawer has lots of white and green 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) 3 (c) 4 (d) 5
9. 9.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
10. 10.A bag has 12 blue balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 14 (b) 20 (c) 13 (d) 2
11. 11.A bag has 8 white balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 10 (c) 9 (d) 16
12. 12.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 45 (c) 15 (d) 48
13. 13.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
14. 14.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 125° (c) 150° (d) 30°
15. 15.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
16. 16.What is the mean of 20, 17, 10 and 13? (a) 20 (b) 15 (c) 16 (d) 12
17. 17.A bag has 3 black balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 4 (b) 2 (c) 5 (d) 6
18. 18.What is the mean of 19, 13, 20, 12, 2 and 18? (a) 13 (b) 15 (c) 14 (d) 12
19. 19.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 55° (b) 85° (c) 150° (d) 125°
20. 20.In which quadrant does the point (5, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
21. 21.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
22. 22.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 25 (c) 240 (d) 20
23. 23.The mean of 3 numbers is 15. When the number 11 is added to them, what is the new mean? (a) 14 (b) 15 (c) 13 (d) 16
24. 24.Which is the correct factorisation of x² + 10x + 21? (a) (x + 1)(x + 21) (b) (x − 3)(x − 7) (c) (x + 3)(x + 7) (d) (x + 1)(x + 9)
25. 25.What is the mean of 18, 12, 5 and 5? (a) 10 (b) 8 (c) 9 (d) 11
26. 26.What is the smallest prime factor of 95? (a) 1 (b) 19 (c) 2 (d) 5
27. 27.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 16 (c) 12 (d) 6
28. 28.If a + b = 16 and ab = 48, what is (a − b)²? (a) 256 (b) 8 (c) 160 (d) 64
29. 29.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 165 (c) 166 (d) 174
30. 30.In a class of 41 children, 20 like maths, 31 like science and 12 like both. How many like neither? (a) 3 (b) 14 (c) 2 (d) 12
31. 31.What is the distance between the points (8, 20) and (17, 8)? (a) 16 (b) 225 (c) 15 (d) 21
32. 32.A bag has 8 black balls and 5 white 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) 6 (d) 9
33. 33.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 2/3 (c) 1/3 (d) 1/2
34. 34.In which quadrant does the point (−6, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
35. 35.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 144 (b) 84 (c) 72 (d) 22
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
37. 37.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
38. 38.In which quadrant does the point (−3, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
39. 39.The mean of 7 numbers is 18. When the number 2 is added to them, what is the new mean? (a) 17 (b) 10 (c) 16 (d) 18
40. 40.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 130° (b) 50° (c) 155° (d) 75°

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