Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 527 · 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.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 136° (c) 45° (d) 135°
2. 2.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 8 (d) 18
4. 4.How many factors does 115 have? (a) 5 (b) 4 (c) 3 (d) 2
5. 5.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 5/8 (c) 1/4 (d) 3/5
6. 6.In a class of 37 children, 15 like dance, 14 like music and 10 like neither. How many like both? (a) 27 (b) 10 (c) 2 (d) 3
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/12 (c) 2/11 (d) 1/18
8. 8.A bag has 11 white balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 18 (c) 12 (d) 2
9. 9.What is the smallest prime factor of 51? (a) 17 (b) 1 (c) 3 (d) 2
10. 10.A drawer has lots of yellow 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) 3 (b) 2 (c) 5 (d) 4
11. 11.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 37 (c) 46 (d) 28
12. 12.What is the mean of 15, 14, 3 and 8? (a) 9 (b) 10 (c) 11 (d) 8
13. 13.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
14. 14.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 635 (b) 425 (c) 225 (d) 625
15. 15.5 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) 20 (b) 25 (c) 9 (d) 40
16. 16.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 240° (d) 121°
17. 17.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 290° (c) 145° (d) 35°
18. 18.What is the smallest prime factor of 121? (a) 1 (b) 11 (c) 2 (d) 3
19. 19.A bag has 8 yellow balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 9 (b) 18 (c) 10 (d) 2
20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 19 (d) 18
21. 21.The mean of 6 numbers is 22. When the number 15 is added to them, what is the new mean? (a) 21 (b) 22 (c) 20 (d) 23
22. 22.A bag has 9 green, 8 white and 3 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 2/3 (b) 3/5 (c) 2/5 (d) 1/3
23. 23.What is the median of 6, 39, 4, 22 and 7? (a) 7 (b) 6 (c) 4 (d) 22
24. 24.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) 3 (c) 2 (d) 4
25. 25.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 18 (c) 54 (d) 6
26. 26.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 12 (c) 42 (d) 72
27. 27.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 15 (d) 30
28. 28.What is the median of 19, 25, 12, 39, 16, 6 and 11? (a) 16 (b) 39 (c) 12 (d) 19
29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 3 (b) 4 (c) 1 (d) 2
30. 30.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
31. 31.What is the 12th term of the AP 13, 21, 29, 37, …? (a) 88 (b) 96 (c) 101 (d) 109
32. 32.What is the distance between the points (0, 8) and (16, 20)? (a) 20 (b) 28 (c) 400 (d) 21
33. 33.Which is the correct factorisation of x² + 7x + 12? (a) (x + 1)(x + 6) (b) (x + 1)(x + 12) (c) (x + 3)(x + 4) (d) (x − 3)(x − 4)
34. 34.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 75° (d) 125°
35. 35.What is the 18th term of the AP 20, 22, 24, 26, …? (a) 34 (b) 56 (c) 36 (d) 54
36. 36.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 120° (d) 160°
37. 37.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5² × 7 (c) 5 × 7² (d) 5 × 7
38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 5 (b) 10 (c) 8 (d) 11
39. 39.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 176 (b) 88 (c) 13 (d) 89
40. 40.6 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) 42 (c) 13 (d) 48

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