Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 456 · 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 5 terms of the AP 10, 12, 14, …? (a) 75 (b) 18 (c) 70 (d) 140
2. 2.What is the 11th term of the AP 8, 14, 20, 26, …? (a) 74 (b) 60 (c) 66 (d) 68
3. 3.A bag has 7 white balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 9 (c) 16 (d) 8
4. 4.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
5. 5.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
6. 6.What is the median of 10, 29, 36, 25 and 26? (a) 26 (b) 25 (c) 36 (d) 29
7. 7.A drawer has lots of green, yellow, red, blue 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) 5 (c) 2 (d) 10
8. 8.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/4 (d) 1/3
9. 9.A cuboid is 12 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 288 sq cm (b) 576 sq cm (c) 144 sq cm (d) 289 sq cm
10. 10.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
11. 11.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1369 (b) 1849 (c) 1379 (d) 1591
12. 12.The mean of 8 numbers is 38. When the number 74 is added to them, what is the new mean? (a) 43 (b) 42 (c) 56 (d) 38
13. 13.In a class of 25 children, 10 like mangoes, 17 like bananas and 4 like neither. How many like both? (a) 6 (b) 2 (c) 4 (d) 21
14. 14.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 180 (b) 360 (c) 36 (d) 198
15. 15.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 159 (c) 168 (d) 160
16. 16.8 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 80 (b) 13 (c) 40 (d) 48
17. 17.How many prime numbers are there between 50 and 70? (a) 6 (b) 3 (c) 4 (d) 5
18. 18.What is the distance between the points (4, 21) and (16, 5)? (a) 21 (b) 20 (c) 28 (d) 400
19. 19.What is the midpoint of the line joining (3, 7) and (13, 5)? (a) (5, 1) (b) (16, 12) (c) (8, 6) (d) (6, 8)
20. 20.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 80 (c) 71 (d) 62
21. 21.A bag has 5 blue balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 6 (b) 16 (c) 2 (d) 7
22. 22.A drawer has lots of blue, green 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) 2 (b) 3 (c) 4 (d) 6
23. 23.What is the median of 4, 5, 18, 34, 35, 38 and 25? (a) 26 (b) 25 (c) 18 (d) 34
24. 24.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 36 cu cm (c) 27 cu cm (d) 9 cu cm
25. 25.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/7 (c) 1/8 (d) 1/4
26. 26.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
27. 27.What is the midpoint of the line joining (1, 7) and (3, 3)? (a) (2, 5) (b) (1, 2) (c) (4, 10) (d) (5, 2)
28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 4 (b) 6 (c) 7 (d) 5
29. 29.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
30. 30.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
31. 31.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 36 (c) 12 (d) 108
32. 32.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7² (c) 2² × 7 (d) 2 × 7
33. 33.A bag has 6 black balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 8 (c) 2 (d) 7
34. 34.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 95° (c) 160° (d) 85°
35. 35.Which term of the AP 11, 16, 21, 26, … is 141? (a) 27th (b) 26th (c) 29th (d) 28th
36. 36.How many factors does 30 have? (a) 9 (b) 7 (c) 6 (d) 8
37. 37.There are 3 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) 12 (b) 7 (c) 24 (d) 15
38. 38.A drawer has lots of white, green, black, red and yellow 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) 10 (c) 6 (d) 2
39. 39.What is the median of 32, 39, 33, 4, 7, 31 and 21? (a) 32 (b) 21 (c) 4 (d) 31
40. 40.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 5 (c) 9 (d) 6

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