Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 503 · 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.In a class of 36 children, 20 like mangoes, 12 like bananas and 5 like both. How many like neither? (a) 5 (b) 9 (c) 14 (d) 4
2. 2.In which quadrant does the point (6, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
3. 3.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 15 (c) 8 (d) 18
4. 4.If a + b = 13 and ab = 42, what is a² + b²? (a) 85 (b) 253 (c) 127 (d) 169
5. 5.A bag has 6 green, 9 blue and 7 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 15/22 (c) 7/22 (d) 7/15
6. 6.In a class of 36 children, 20 like mangoes, 13 like bananas and 9 like neither. How many like both? (a) 27 (b) 7 (c) 9 (d) 6
7. 7.A drawer has lots of red and blue 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) 2 (d) 3
8. 8.What is the 15th term of the AP 7, 15, 23, 31, …? (a) 127 (b) 112 (c) 120 (d) 119
9. 9.A bag has 10 green balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 11 (c) 2 (d) 15
10. 10.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) 4 (b) 5 (c) 3 (d) 2
11. 11.7 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 35 (c) 11 (d) 56
12. 12.What is the mode of 12, 6, 5, 6, 20, 12 and 6? (a) 12 (b) 6 (c) 5 (d) 20
13. 13.What is the 17th term of the AP 18, 26, 34, 42, …? (a) 146 (b) 136 (c) 128 (d) 154
14. 14.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 335° (c) 65° (d) 25°
15. 15.There are 5 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 50 (c) 25 (d) 10
16. 16.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 57 (d) 162
17. 17.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 484 cu cm (d) 726 cu cm
18. 18.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 454 (c) 573 (d) 574
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 1/12 (d) 2/11
20. 20.What is the midpoint of the line joining (6, 10) and (14, 20)? (a) (20, 30) (b) (10, 15) (c) (4, 5) (d) (15, 10)
21. 21.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 155° (c) 45° (d) 135°
22. 22.How many factors does 107 have? (a) 1 (b) 2 (c) 3 (d) 4
23. 23.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
24. 24.Which term of the AP 4, 13, 22, 31, … is 229? (a) 28th (b) 27th (c) 25th (d) 26th
25. 25.Using (a − b)² = a² − 2ab + b², what is 48²? (a) 2314 (b) 2304 (c) 2704 (d) 2496
26. 26.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
27. 27.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 15 (c) 25 (d) 10
28. 28.Which is the correct factorisation of x² + 8x + 12? (a) (x + 1)(x + 12) (b) (x + 2)(x + 6) (c) (x − 2)(x − 6) (d) (x + 1)(x + 7)
29. 29.What is the smallest prime factor of 133? (a) 19 (b) 1 (c) 2 (d) 7
30. 30.What is the distance between the points (2, 16) and (10, 1)? (a) 23 (b) 18 (c) 289 (d) 17
31. 31.A drawer has lots of black, yellow, white and blue 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) 4 (c) 8 (d) 5
32. 32.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
33. 33.A drawer has lots of green, yellow 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) 4 (b) 2 (c) 3 (d) 6
34. 34.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 132 (d) 66
35. 35.A bag has 4 black balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 5 (c) 11 (d) 6
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
37. 37.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 105° (b) 160° (c) 85° (d) 95°
38. 38.What is the mode of 3, 1, 16, 8, 8, 8 and 3? (a) 1 (b) 3 (c) 8 (d) 16
39. 39.A bag has 7 black balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 8 (b) 13 (c) 9 (d) 2
40. 40.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 1)(x + 16) (d) (x + 8)(x + 9)

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