Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 698 · 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 an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 35° (d) 145°
2. 2.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7² (c) 2² × 7 (d) 2 × 7
3. 3.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
4. 4.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 14 (c) 8 (d) 15
5. 5.What is the midpoint of the line joining (7, 7) and (15, 15)? (a) (12, 11) (b) (22, 22) (c) (11, 11) (d) (4, 4)
6. 6.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 12 (c) 7 (d) 16
7. 7.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 576 (b) 384 (c) 256 (d) 266
8. 8.A drawer has lots of white, yellow 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) 4 (c) 3 (d) 2
9. 9.What are the roots of x² − 13x + 40 = 0? (a) 1 and 12 (b) 1 and 40 (c) 5 and 8 (d) 2 and 20
10. 10.What is the smallest prime factor of 115? (a) 23 (b) 1 (c) 5 (d) 2
11. 11.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 574 (c) 573 (d) 564
12. 12.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 5 (b) 12 (c) 6 (d) 9
13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 18 (b) 19 (c) 17 (d) 7
14. 14.What is the 40th term of the AP 1, 7, 13, 19, …? (a) 240 (b) 235 (c) 234 (d) 241
15. 15.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 16 (d) 12
16. 16.What is the 28th term of the AP 8, 10, 12, 14, …? (a) 54 (b) 56 (c) 64 (d) 62
17. 17.A bag has 2 white, 5 blue and 5 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 7/12 (b) 2/3 (c) 1/3 (d) 5/12
18. 18.What is the median of 5, 12, 24, 35 and 28? (a) 24 (b) 12 (c) 28 (d) 25
19. 19.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
20. 20.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 17 (b) 130 (c) 125 (d) 250
21. 21.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 50° (d) 65°
22. 22.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 217 sq cm (c) 144 sq cm (d) 36 sq cm
23. 23.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 150 cu cm (c) 100 cu cm (d) 15 cu cm
24. 24.In a class of 36 children, 24 like mangoes, 8 like bananas and 4 like both. How many like at least one of the two? (a) 36 (b) 24 (c) 28 (d) 32
25. 25.Which term of the AP 19, 26, 33, 40, … is 82? (a) 11th (b) 9th (c) 10th (d) 12th
26. 26.How many factors does 82 have? (a) 2 (b) 3 (c) 4 (d) 5
27. 27.What is the prime factorisation of 20? (a) 2² × 5 (b) 2 × 5² (c) 2 × 5 (d) 2³ × 5
28. 28.What is the 29th term of the AP 16, 19, 22, 25, …? (a) 103 (b) 84 (c) 87 (d) 100
29. 29.In which quadrant does the point (−1, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
30. 30.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 37 (c) 24 (d) 25
31. 31.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
32. 32.How many factors does 16 have? (a) 5 (b) 4 (c) 6 (d) 3
33. 33.Which is the correct factorisation of x² + 12x + 35? (a) (x + 1)(x + 35) (b) (x + 1)(x + 11) (c) (x + 5)(x + 7) (d) (x − 5)(x − 7)
34. 34.A drawer has lots of black, blue, 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) 8 (b) 2 (c) 4 (d) 5
35. 35.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 5/6 (d) 1/4
36. 36.What is the mode of 3, 17, 4, 10, 4, 4 and 10? (a) 3 (b) 17 (c) 4 (d) 10
37. 37.A bag has 2 red, 9 green and 4 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 13/15 (c) 2/13 (d) 2/15
38. 38.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
39. 39.What is the 24th term of the AP 20, 27, 34, 41, …? (a) 188 (b) 181 (c) 161 (d) 168
40. 40.A drawer has lots of blue, white, yellow 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) 5 (b) 2 (c) 4 (d) 8

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