Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 621 · 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 a class of 29 children, 10 like maths, 20 like science and 2 like both. How many like only maths? (a) 10 (b) 8 (c) 18 (d) 9
2. 2.What is the median of 9, 22, 24, 31 and 6? (a) 23 (b) 9 (c) 24 (d) 22
3. 3.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
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.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 16 (d) 24
6. 6.Using (a + b)² = a² + 2ab + b², what is 85²? (a) 6425 (b) 7225 (c) 7235 (d) 5625
7. 7.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) 22 (b) 28 (c) 29 (d) 21
8. 8.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) 4 (b) 3 (c) 2 (d) 5
9. 9.What is the mean of 17, 3, 7, 6 and 22? (a) 10 (b) 11 (c) 13 (d) 12
10. 10.What is the midpoint of the line joining (9, 10) and (21, 14)? (a) (15, 12) (b) (6, 2) (c) (12, 15) (d) (30, 24)
11. 11.A bag has 11 red balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 22 (b) 12 (c) 13 (d) 2
12. 12.Using (a + b)² = a² + 2ab + b², what is 102²? (a) 10004 (b) 9604 (c) 10414 (d) 10404
13. 13.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
14. 14.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
15. 15.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 12) (b) (x − 6)(x − 7) (c) (x + 6)(x + 7) (d) (x + 1)(x + 42)
16. 16.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 4 times (c) 6 times (d) 8 times
17. 17.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 115° (d) 95°
18. 18.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 30 (b) 5 (c) 16 (d) 15
19. 19.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
20. 20.How many prime numbers are there between 30 and 60? (a) 7 (b) 6 (c) 9 (d) 8
21. 21.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 12 (c) 8 (d) 6
22. 22.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 22 (d) 55
23. 23.A drawer has lots of black, 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) 3 (b) 4 (c) 2 (d) 6
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 7/36 (c) 1/6 (d) 6/11
25. 25.What is the distance between the points (9, 7) and (13, 10)? (a) 5 (b) 25 (c) 7 (d) 6
26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 5 (b) 6 (c) 4 (d) 3
27. 27.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 63 (c) 20 (d) 60
28. 28.A bag has 4 green, 8 white and 2 yellow balls. One ball is taken out without looking. What is the probability that it is white? (a) 9/14 (b) 1/3 (c) 4/7 (d) 3/7
29. 29.In a class of 41 children, 18 like cricket, 30 like football and 12 like both. How many like at least one of the two? (a) 48 (b) 24 (c) 36 (d) 41
30. 30.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 21 (d) 9
32. 32.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) 25 (c) 24 (d) 37
33. 33.What is the sum of the roots of x² − 15x + 56 = 0? (a) 15 (b) 16 (c) 56 (d) 14
34. 34.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 80° (d) 100°
35. 35.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
36. 36.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 25 (d) 120
37. 37.What is the 20th term of the AP 18, 24, 30, 36, …? (a) 138 (b) 132 (c) 120 (d) 114
38. 38.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 576 sq cm (c) 864 sq cm (d) 144 sq cm
39. 39.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
40. 40.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 1/4 (d) 5/6

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