Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 669 · 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 median of 3, 4, 18, 11 and 27? (a) 18 (b) 4 (c) 11 (d) 12
2. 2.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 7/8 (c) 1/4 (d) 1/7
3. 3.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
4. 4.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
5. 5.A drawer has lots of red, yellow, green, black 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) 10 (b) 2 (c) 5 (d) 6
6. 6.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) 265° (c) 85° (d) 95°
7. 7.What is the mean of 7, 6, 3 and 20? (a) 10 (b) 12 (c) 8 (d) 9
8. 8.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x − 8)(x − 9) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)
9. 9.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 20 (d) 120
10. 10.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 32 (b) 200 (c) 185 (d) 370
11. 11.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 8) (b) (x + 1)(x + 20) (c) (x − 4)(x − 5) (d) (x + 4)(x + 5)
12. 12.What is the distance between the points (9, 9) and (15, 17)? (a) 11 (b) 14 (c) 100 (d) 10
13. 13.What is the sum of the roots of x² − 15x + 54 = 0? (a) 54 (b) 16 (c) 14 (d) 15
14. 14.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
15. 15.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 2/3 (c) 1/4 (d) 1/3
16. 16.What is the 25th term of the AP 9, 18, 27, 36, …? (a) 226 (b) 234 (c) 216 (d) 225
17. 17.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
18. 18.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 125° (b) 140° (c) 55° (d) 95°
19. 19.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 70° (c) 340° (d) 160°
20. 20.Using (a − b)² = a² − 2ab + b², what is 56²? (a) 3136 (b) 3584 (c) 3146 (d) 4096
21. 21.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 216 cu cm (d) 217 cu cm
22. 22.How many factors does 90 have? (a) 10 (b) 12 (c) 13 (d) 11
23. 23.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) 2 (b) 4 (c) 3 (d) 5
24. 24.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2³ × 3 × 5 (c) 2⁵ × 3 × 5 (d) 2⁴ × 3 × 5
25. 25.Using (a + b)² = a² + 2ab + b², what is 93²? (a) 8659 (b) 8649 (c) 7569 (d) 8109
26. 26.A drawer has lots of red, green 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) 4 (b) 2 (c) 3 (d) 6
27. 27.If a + b = 17 and ab = 70, what is (a − b)²? (a) 289 (b) 9 (c) 149 (d) 3
28. 28.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 522 (c) 523 (d) 513
29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 3 (b) 9 (c) 10 (d) 11
30. 30.The mean of 3 numbers is 25. When the number 13 is added to them, what is the new mean? (a) 25 (b) 23 (c) 19 (d) 22
31. 31.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1378 (c) 1431 (d) 1432
32. 32.A drawer has lots of blue 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) 3 (b) 2 (c) 5 (d) 4
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/11 (c) 5/36 (d) 1/6
34. 34.What is the midpoint of the line joining (5, 2) and (11, 10)? (a) (8, 6) (b) (3, 4) (c) (6, 8) (d) (16, 12)
35. 35.In a class of 28 children, 19 like maths, 12 like science and 5 like both. How many like at least one of the two? (a) 28 (b) 31 (c) 21 (d) 26
36. 36.In a class of 35 children, 17 like cricket, 18 like football and 7 like both. How many like at least one of the two? (a) 35 (b) 21 (c) 28 (d) 29
37. 37.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
38. 38.A bag has 10 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 6 (d) 15
39. 39.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 70° (b) 110° (c) 130° (d) 160°
40. 40.A bag has 5 yellow balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 5 (c) 9 (d) 6

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