Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 916 · 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 circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
2. 2.How many factors does 95 have? (a) 3 (b) 4 (c) 2 (d) 5
3. 3.A bag has 9 green, 3 yellow and 7 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 9/19 (c) 10/19 (d) 9/10
4. 4.If a + b = 8 and ab = 7, what is a² + b²? (a) 64 (b) 50 (c) 78 (d) 57
5. 5.Which term of the AP 18, 23, 28, 33, … is 183? (a) 33rd (b) 35th (c) 34th (d) 36th
6. 6.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
7. 7.If a + b = 17 and ab = 72, what is a² + b²? (a) 145 (b) 289 (c) 217 (d) 433
8. 8.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 30° (c) 120° (d) 40°
9. 9.What is the midpoint of the line joining (9, 1) and (13, 3)? (a) (11, 2) (b) (2, 11) (c) (2, 1) (d) (22, 4)
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
11. 11.A drawer has lots of green 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) 4 (b) 3 (c) 5 (d) 2
12. 12.The mean of 6 numbers is 32. When the number 53 is added to them, what is the new mean? (a) 36 (b) 34 (c) 35 (d) 32
13. 13.What is the mean of 5, 7, 18, 17, 9 and 10? (a) 10 (b) 13 (c) 11 (d) 12
14. 14.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 28 (c) 22 (d) 21
15. 15.A drawer has lots of white, yellow, blue, red 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) 10 (b) 2 (c) 6 (d) 5
16. 16.A bag has 5 red balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 6 (b) 2 (c) 17 (d) 7
17. 17.The mean of 6 numbers is 12. When the number 33 is added to them, what is the new mean? (a) 12 (b) 16 (c) 15 (d) 14
18. 18.How many prime numbers are there between 10 and 20? (a) 3 (b) 4 (c) 6 (d) 5
19. 19.A drawer has lots of blue, 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) 4 (b) 2 (c) 3 (d) 6
20. 20.In a class of 31 children, 20 like tea, 19 like coffee and 10 like both. How many like at least one of the two? (a) 19 (b) 29 (c) 39 (d) 31
21. 21.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4
22. 22.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 6 (d) 12
23. 23.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 13 (d) 12
24. 24.The numbers 5 to 13 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) 30 (c) 81 (d) 9
25. 25.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
26. 26.What is the 12th term of the AP 11, 13, 15, 17, …? (a) 22 (b) 35 (c) 33 (d) 24
27. 27.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1378 (c) 1326 (d) 1352
28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 17 (b) 19 (c) 8 (d) 18
29. 29.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
30. 30.What is the median of 4, 1, 12, 40 and 21? (a) 12 (b) 4 (c) 21 (d) 13
31. 31.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 11 (d) 2
32. 32.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 121 (d) 21
33. 33.How many prime numbers are there between 80 and 90? (a) 4 (b) 2 (c) 3 (d) 1
34. 34.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 1331 sq cm (c) 484 sq cm (d) 121 sq cm
35. 35.How many factors does 84 have? (a) 11 (b) 13 (c) 12 (d) 10
36. 36.What is the smallest prime factor of 377? (a) 13 (b) 1 (c) 29 (d) 2
37. 37.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 16 (d) 28
38. 38.Which is the correct factorisation of x² + 7x + 10? (a) (x + 2)(x + 5) (b) (x + 1)(x + 10) (c) (x + 1)(x + 6) (d) (x − 2)(x − 5)
39. 39.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 3 (b) 9 (c) 11 (d) 10

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