Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 24 · 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.Using (a + b)² = a² + 2ab + b², what is 51²? (a) 2601 (b) 2611 (c) 2501 (d) 2401
2. 2.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 100 (d) 90
3. 3.If a + b = 12 and ab = 35, what is a² + b²? (a) 144 (b) 109 (c) 214 (d) 74
4. 4.In a class of 29 children, 17 like maths, 17 like science and 10 like both. How many like neither? (a) 6 (b) 5 (c) 15 (d) 10
5. 5.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 739 (b) 729 (c) 1089 (d) 891
6. 6.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 631 (c) 595 (d) 630
7. 7.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 115° (b) 140° (c) 65° (d) 155°
8. 8.A drawer has lots of green, white, blue 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
9. 9.What is the mode of 7, 15, 4, 4, 1, 1 and 1? (a) 15 (b) 7 (c) 1 (d) 4
10. 10.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 120 (d) 20
11. 11.How many prime numbers are there between 20 and 50? (a) 8 (b) 9 (c) 6 (d) 7
12. 12.How many factors does 42 have? (a) 6 (b) 9 (c) 8 (d) 7
13. 13.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 206 (c) 202 (d) 201
14. 14.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 25 (d) 10
15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 19 (d) 20
16. 16.What is the mean of 5, 12, 12 and 19? (a) 12 (b) 16 (c) 11 (d) 13
17. 17.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 80° (c) 135° (d) 100°
18. 18.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 37 (c) 36 (d) 48
19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 4 (c) 14 (d) 15
20. 20.A bag has 3 green balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 4 (b) 2 (c) 6 (d) 5
21. 21.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 812 (d) 784
22. 22.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 186 (c) 185 (d) 194
23. 23.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 55° (b) 80° (c) 125° (d) 155°
24. 24.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 24 (c) 27 (d) 8
25. 25.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 21 (c) 189 (d) 63
26. 26.In a class of 34 children, 11 like dance, 24 like music and 3 like neither. How many like both? (a) 4 (b) 31 (c) 3 (d) 1
27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
28. 28.The mean of 6 numbers is 38. When the number 66 is added to them, what is the new mean? (a) 52 (b) 43 (c) 38 (d) 42
29. 29.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 25 (d) 120
30. 30.Which term of the AP 3, 6, 9, 12, … is 30? (a) 9th (b) 10th (c) 12th (d) 11th
31. 31.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
32. 32.What is the median of 8, 15, 2, 38, 40, 29 and 5? (a) 15 (b) 38 (c) 29 (d) 8
33. 33.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 15 (c) 8 (d) 7
34. 34.In a class of 43 children, 18 like cricket, 29 like football and 11 like both. How many like neither? (a) 11 (b) 18 (c) 8 (d) 7
35. 35.What is the mean of 20, 11, 8 and 13? (a) 15 (b) 12 (c) 13 (d) 14
36. 36.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 609 (c) 600 (d) 478
37. 37.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
38. 38.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
39. 39.What is the smallest prime factor of 87? (a) 3 (b) 29 (c) 2 (d) 1
40. 40.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 85° (c) 86° (d) 95°

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