Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 884 · 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.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) 63 (b) 60 (c) 180 (d) 20
2. 2.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 345 (c) 302 (d) 336
3. 3.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 137 (b) 128 (c) 138 (d) 146
4. 4.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 70° (b) 250° (c) 110° (d) 140°
5. 5.What is the mean of 5, 7, 12, 5, 5 and 14? (a) 9 (b) 10 (c) 8 (d) 7
6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 4 (d) 1
7. 7.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 235° (b) 55° (c) 125° (d) 110°
8. 8.A bag has 10 black balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 17 (c) 11 (d) 12
9. 9.If a + b = 21 and ab = 108, what is (a − b)²? (a) 9 (b) 3 (c) 441 (d) 225
10. 10.A bag has 7 red balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 15 (b) 2 (c) 8 (d) 9
11. 11.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
12. 12.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 140° (c) 80° (d) 41°
13. 13.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) 7 (b) 15 (c) 8 (d) 14
14. 14.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 8281 (b) 8101 (c) 7921 (d) 8291
15. 15.The mean of 5 numbers is 25. When the number 49 is added to them, what is the new mean? (a) 37 (b) 30 (c) 25 (d) 29
16. 16.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
17. 17.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1601 (b) 1521 (c) 1691 (d) 1681
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
19. 19.A bag has 8 blue, 6 green and 5 white balls. One ball is taken out without looking. What is the probability that it is blue? (a) 8/11 (b) 11/19 (c) 8/19 (d) 1/3
20. 20.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
21. 21.In a class of 46 children, 17 like cricket, 25 like football and 6 like both. How many like only cricket? (a) 21 (b) 19 (c) 11 (d) 17
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/36 (c) 1/18 (d) 1/12
23. 23.A bag has 5 red balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 6 (c) 7 (d) 10
24. 24.The mean of 4 numbers is 20. When the number 40 is added to them, what is the new mean? (a) 24 (b) 25 (c) 20 (d) 30
25. 25.How many prime numbers are there between 90 and 120? (a) 7 (b) 6 (c) 8 (d) 5
26. 26.A bag has 3 white, 6 red and 4 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 8/13 (b) 1/3 (c) 7/13 (d) 6/13
27. 27.How many prime numbers are there between 10 and 30? (a) 5 (b) 7 (c) 6 (d) 8
28. 28.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
29. 29.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
30. 30.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 210 (c) 105 (d) 196
31. 31.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 132 (c) 123 (d) 124
32. 32.What is the smallest prime factor of 35? (a) 7 (b) 5 (c) 2 (d) 1
33. 33.What are the roots of x² − 9x + 20 = 0? (a) 1 and 8 (b) 2 and 10 (c) 4 and 5 (d) 1 and 20
34. 34.In a class of 20 children, 10 like maths, 14 like science and 6 like both. How many like at least one of the two? (a) 12 (b) 18 (c) 24 (d) 20
35. 35.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 204 (c) 195 (d) 208
36. 36.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 73 (c) 17 (d) 72
37. 37.A drawer has lots of green, yellow, black, blue 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
38. 38.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 21 (d) 49
39. 39.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
40. 40.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 100 (d) 45

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