Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 184 · 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.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 230° (c) 130° (d) 50°
2. 2.In a class of 21 children, 12 like cricket, 9 like football and 4 like both. How many like at least one of the two? (a) 21 (b) 18 (c) 13 (d) 17
3. 3.In a class of 32 children, 16 like cricket, 19 like football and 5 like both. How many like neither? (a) 7 (b) 3 (c) 5 (d) 2
4. 4.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 226 (c) 222 (d) 231
5. 5.What is the mean of 20, 15, 19 and 6? (a) 15 (b) 12 (c) 20 (d) 16
6. 6.How many factors does 22 have? (a) 2 (b) 3 (c) 4 (d) 5
7. 7.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 50° (c) 25° (d) 130°
8. 8.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 1/4 (d) 3/8
9. 9.How many factors does 13 have? (a) 2 (b) 4 (c) 3 (d) 1
10. 10.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
11. 11.A bag has 11 green balls and 5 yellow 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) 16 (c) 12 (d) 6
12. 12.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 1190 (c) 578 (d) 561
13. 13.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 94 sq cm (b) 168 sq cm (c) 376 sq cm (d) 188 sq cm
14. 14.How many prime numbers are there between 70 and 80? (a) 4 (b) 5 (c) 2 (d) 3
15. 15.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) 12 (d) 13
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 16 (b) 14 (c) 15 (d) 4
17. 17.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
18. 18.If a + b = 5 and ab = 4, what is a² + b²? (a) 17 (b) 33 (c) 21 (d) 25
19. 19.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
20. 20.A bag has 5 red balls and 11 green 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) 6 (c) 12 (d) 16
21. 21.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
22. 22.A bag has 9 blue balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 20 (c) 2 (d) 10
23. 23.What is the median of 6, 3, 32, 10 and 23? (a) 10 (b) 23 (c) 6 (d) 32
24. 24.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 33 (c) 10 (d) 90
25. 25.If a + b = 4 and ab = 3, what is (a − b)²? (a) 4 (b) 2 (c) 10 (d) 16
26. 26.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 205° (c) 25° (d) 26°
27. 27.In a class of 26 children, 19 like maths, 14 like science and 9 like both. How many like at least one of the two? (a) 26 (b) 33 (c) 24 (d) 15
28. 28.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
29. 29.A drawer has lots of white, yellow, 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) 2 (b) 5 (c) 8 (d) 4
30. 30.A drawer has lots of white, green, 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) 4 (c) 5 (d) 2
31. 31.What is the sum of the roots of x² − 15x + 56 = 0? (a) 15 (b) 14 (c) 56 (d) 16
32. 32.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
33. 33.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 20 (d) 25
34. 34.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 15 (c) 36 (d) 12
35. 35.In a class of 33 children, 18 like dance, 10 like music and 3 like both. How many like at least one of the two? (a) 33 (b) 28 (c) 25 (d) 22
36. 36.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 25 (d) 240
37. 37.The mean of 3 numbers is 29. When the number 17 is added to them, what is the new mean? (a) 26 (b) 27 (c) 23 (d) 29
38. 38.What is the mean of 5, 7, 5, 2 and 11? (a) 8 (b) 5 (c) 6 (d) 7
39. 39.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 20 (d) 10
40. 40.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 110° (b) 130° (c) 70° (d) 160°

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