Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 840 · 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.How many factors does 31 have? (a) 2 (b) 3 (c) 4 (d) 1
2. 2.A drawer has lots of yellow 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) 5 (c) 3 (d) 4
3. 3.A bag has 3 white, 5 green and 7 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 3/5 (b) 7/15 (c) 1/3 (d) 8/15
4. 4.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 56 (c) 74 (d) 66
5. 5.In a class of 38 children, 19 like cricket, 15 like football and 3 like both. How many like only cricket? (a) 19 (b) 23 (c) 12 (d) 16
6. 6.What is the distance between the points (0, 14) and (12, 9)? (a) 14 (b) 13 (c) 169 (d) 17
7. 7.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 25 (c) 20 (d) 10
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
9. 9.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 2525 (b) 2025 (c) 3025 (d) 3035
10. 10.What is the midpoint of the line joining (3, 3) and (13, 5)? (a) (8, 4) (b) (5, 1) (c) (16, 8) (d) (4, 8)
11. 11.In which quadrant does the point (2, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
12. 12.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 22 (d) 55
13. 13.What is the median of 15, 12, 4, 36 and 13? (a) 16 (b) 4 (c) 13 (d) 15
14. 14.What is the mode of 8, 2, 2, 2, 8, 20 and 13? (a) 13 (b) 20 (c) 8 (d) 2
15. 15.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 110 (c) 220 (d) 20
16. 16.In a class of 34 children, 21 like cricket, 17 like football and 10 like both. How many like only cricket? (a) 21 (b) 7 (c) 17 (d) 11
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
18. 18.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 95° (d) 145°
19. 19.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 14 (b) 16 (c) 15 (d) 4
21. 21.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 70 (b) 888 (c) 480 (d) 444
22. 22.In a class of 11 children, 5 like maths, 7 like science and 2 like both. How many like only maths? (a) 5 (b) 2 (c) 4 (d) 3
23. 23.In a class of 40 children, 16 like maths, 23 like science and 7 like both. How many like at least one of the two? (a) 25 (b) 40 (c) 32 (d) 39
24. 24.What is the midpoint of the line joining (1, 4) and (11, 14)? (a) (12, 18) (b) (9, 6) (c) (6, 9) (d) (5, 5)
25. 25.If a + b = 7 and ab = 12, what is (a − b)²? (a) 37 (b) 1 (c) 49 (d) 25
26. 26.What is the mean of 6, 19, 8, 16 and 16? (a) 14 (b) 12 (c) 15 (d) 13
27. 27.6 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 84 (b) 48 (c) 13 (d) 42
28. 28.In a class of 50 children, 24 like tea, 26 like coffee and 9 like both. How many like at least one of the two? (a) 50 (b) 32 (c) 42 (d) 41
29. 29.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7 (d) 2 × 5 × 7²
30. 30.How many prime numbers are there between 90 and 110? (a) 4 (b) 6 (c) 7 (d) 5
31. 31.What is the mean of 13, 15, 12 and 12? (a) 12 (b) 14 (c) 13 (d) 15
32. 32.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 45 (d) 90
33. 33.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 24 (c) 8 (d) 72
34. 34.In a class of 27 children, 17 like tea, 8 like coffee and 5 like both. How many like at least one of the two? (a) 20 (b) 27 (c) 15 (d) 25
35. 35.How many factors does 76 have? (a) 6 (b) 4 (c) 7 (d) 5
36. 36.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 95° (c) 265° (d) 85°
37. 37.What is the 23rd term of the AP 7, 15, 23, 31, …? (a) 176 (b) 183 (c) 191 (d) 184
38. 38.What is the smallest prime factor of 69? (a) 2 (b) 23 (c) 3 (d) 1
39. 39.What is the midpoint of the line joining (9, 19) and (11, 7)? (a) (1, 6) (b) (20, 26) (c) (13, 10) (d) (10, 13)
40. 40.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 378 (c) 387 (d) 388

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