Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 292 · 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 9, 9, 14, 9, 12, 12 and 15? (a) 9 (b) 15 (c) 12 (d) 14
2. 2.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 10 (d) 20
3. 3.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 81 (c) 36 (d) 72
4. 4.A bag has 7 blue, 2 yellow and 3 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/12
5. 5.What is the 13th term of the AP 16, 24, 32, 40, …? (a) 120 (b) 96 (c) 104 (d) 112
6. 6.What is the mean of 17, 14, 9 and 8? (a) 11 (b) 16 (c) 12 (d) 13
7. 7.A drawer has lots of 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) 3 (c) 2 (d) 4
8. 8.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
9. 9.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 210 (d) 105
10. 10.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 150° (b) 95° (c) 115° (d) 30°
11. 11.What is the mode of 8, 5, 8, 15, 9, 15 and 15? (a) 5 (b) 15 (c) 8 (d) 9
12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 3 (b) 15 (c) 14 (d) 13
13. 13.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁵ × 7 (c) 2³ × 7 (d) 2⁴ × 7
14. 14.A bag has 5 black balls and 6 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) 11 (c) 7 (d) 6
15. 15.Which term of the AP 12, 15, 18, 21, … is 57? (a) 15th (b) 17th (c) 16th (d) 19th
16. 16.A drawer has lots of red, black, blue, yellow and white 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) 10 (d) 6
17. 17.A drawer has lots of blue, red, green and white 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) 4 (d) 8
18. 18.How many prime numbers are there between 50 and 70? (a) 5 (b) 3 (c) 6 (d) 4
19. 19.If a + b = 8 and ab = 7, what is a² + b²? (a) 57 (b) 78 (c) 64 (d) 50
20. 20.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 23 (b) 101 (c) 196 (d) 98
21. 21.What is the midpoint of the line joining (7, 11) and (19, 1)? (a) (6, 5) (b) (13, 6) (c) (6, 13) (d) (26, 12)
22. 22.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 12 cu cm (d) 96 cu cm
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
24. 24.In a class of 49 children, 20 like cricket, 27 like football and 7 like both. How many like neither? (a) 9 (b) 7 (c) 2 (d) 16
25. 25.What is the distance between the points (2, 27) and (9, 3)? (a) 625 (b) 26 (c) 25 (d) 31
26. 26.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 604 (c) 603 (d) 474
27. 27.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3872 (c) 7832 (d) 3916
28. 28.What is the prime factorisation of 15? (a) 3 × 5² (b) 3 × 5 (c) 3³ × 5 (d) 3² × 5
29. 29.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 35° (b) 115° (c) 100° (d) 145°
30. 30.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/4 (c) 1/2 (d) 1/3
31. 31.Which is the correct factorisation of x² + 9x + 20? (a) (x + 4)(x + 5) (b) (x + 1)(x + 20) (c) (x − 4)(x − 5) (d) (x + 1)(x + 8)
32. 32.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 65° (b) 245° (c) 115° (d) 130°
33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 7 (b) 6 (c) 9 (d) 8
34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 16 (d) 5
35. 35.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 63 (c) 24 (d) 21
36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 4 (b) 5 (c) 7 (d) 6
37. 37.What is the mode of 3, 5, 9, 8, 5, 5 and 9? (a) 9 (b) 8 (c) 3 (d) 5
38. 38.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 21 (c) 15 (d) 14
39. 39.If a + b = 11 and ab = 30, what is a² + b²? (a) 91 (b) 61 (c) 181 (d) 121
40. 40.The mean of 8 numbers is 18. When the number 9 is added to them, what is the new mean? (a) 18 (b) 17 (c) 16 (d) 19

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