Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 807 · 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 mode of 10, 5, 10, 20, 10, 5 and 6? (a) 20 (b) 10 (c) 5 (d) 6
2. 2.What is the mean of 12, 3, 11 and 6? (a) 7 (b) 10 (c) 9 (d) 8
3. 3.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 70° (c) 36° (d) 145°
4. 4.In a class of 47 children, 17 like tea, 31 like coffee and 11 like both. How many like at least one of the two? (a) 47 (b) 26 (c) 48 (d) 37
5. 5.What is the smallest prime factor of 169? (a) 3 (b) 13 (c) 1 (d) 2
6. 6.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 156 (b) 23 (c) 90 (d) 78
7. 7.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
8. 8.A drawer has lots of blue, red, white, black 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) 10 (b) 2 (c) 5 (d) 6
9. 9.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 81° (c) 80° (d) 100°
10. 10.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 390 (c) 332 (d) 381
11. 11.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 42 (d) 49
12. 12.What is the mean of 6, 8, 16 and 10? (a) 11 (b) 10 (c) 8 (d) 9
13. 13.8 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) 48 (c) 40 (d) 13
14. 14.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 1/3 (c) 5/6 (d) 1/5
15. 15.What is the sum of the roots of x² − 12x + 32 = 0? (a) 32 (b) 11 (c) 13 (d) 12
16. 16.A bag has 7 white balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 12 (c) 9 (d) 2
17. 17.How many factors does 77 have? (a) 5 (b) 3 (c) 4 (d) 2
18. 18.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
19. 19.A bag has 4 blue balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 7 (c) 2 (d) 10
20. 20.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
21. 21.In a class of 31 children, 15 like tea, 14 like coffee and 6 like neither. How many like both? (a) 6 (b) 4 (c) 5 (d) 25
22. 22.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 66 (c) 55 (d) 110
23. 23.In which quadrant does the point (5, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
24. 24.A drawer has lots of black, green, blue 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) 2 (b) 8 (c) 5 (d) 4
25. 25.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 209 (b) 220 (c) 418 (d) 29
26. 26.How many factors does 113 have? (a) 4 (b) 3 (c) 2 (d) 1
27. 27.In a class of 29 children, 16 like dance, 10 like music and 8 like neither. How many like both? (a) 21 (b) 8 (c) 6 (d) 5
28. 28.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
29. 29.In a class of 37 children, 23 like mangoes, 18 like bananas and 2 like neither. How many like both? (a) 2 (b) 6 (c) 35 (d) 4
30. 30.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/8 (c) 3/5 (d) 5/8
31. 31.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
32. 32.What is the midpoint of the line joining (3, 5) and (13, 13)? (a) (9, 8) (b) (8, 9) (c) (16, 18) (d) (5, 4)
33. 33.How many prime numbers are there between 70 and 90? (a) 7 (b) 5 (c) 6 (d) 4
34. 34.What is the mean of 7, 18, 12 and 19? (a) 14 (b) 15 (c) 16 (d) 13
35. 35.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 125° (c) 55° (d) 305°
36. 36.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
37. 37.In a class of 37 children, 20 like dance, 24 like music and 8 like both. How many like at least one of the two? (a) 28 (b) 37 (c) 36 (d) 44
38. 38.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 72 (d) 24
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 4/11 (c) 5/36 (d) 1/11
40. 40.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14

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