Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 787 · 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 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) 8 (b) 24 (c) 27 (d) 72
2. 2.In a class of 13 children, 6 like dance, 9 like music and 3 like both. How many like at least one of the two? (a) 13 (b) 15 (c) 12 (d) 9
3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 14 (b) 12 (c) 15 (d) 7
4. 4.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4
5. 5.There are 3 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 21 (c) 10 (d) 42
6. 6.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 115° (c) 295° (d) 65°
7. 7.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 121 (c) 22 (d) 55
8. 8.A drawer has lots of white 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) 5 (b) 4 (c) 3 (d) 2
9. 9.The mean of 7 numbers is 20. When the number 12 is added to them, what is the new mean? (a) 16 (b) 18 (c) 19 (d) 20
10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 16 (b) 15 (c) 5 (d) 14
11. 11.What is the 10th term of the AP 4, 8, 12, 16, …? (a) 36 (b) 41 (c) 44 (d) 40
12. 12.If a + b = 13 and ab = 40, what is (a − b)²? (a) 89 (b) 169 (c) 9 (d) 3
13. 13.A drawer has lots of white, yellow 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) 2 (c) 3 (d) 6
14. 14.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 36 (d) 45
15. 15.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 150° (b) 30° (c) 300° (d) 120°
16. 16.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
17. 17.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
18. 18.What is the sum of the roots of x² − 15x + 56 = 0? (a) 15 (b) 14 (c) 56 (d) 16
19. 19.In a class of 35 children, 25 like cricket, 16 like football and 12 like both. How many like neither? (a) 18 (b) 7 (c) 12 (d) 6
20. 20.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2⁵ × 5 (c) 2³ × 5 (d) 2⁴ × 5
21. 21.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 5/6 (b) 1/5 (c) 1/3 (d) 1/6
22. 22.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 16 sq cm (d) 64 sq cm
23. 23.In a class of 32 children, 13 like dance, 24 like music and 6 like both. How many like at least one of the two? (a) 25 (b) 37 (c) 31 (d) 32
24. 24.In a class of 35 children, 24 like tea, 17 like coffee and 12 like both. How many like neither? (a) 6 (b) 7 (c) 12 (d) 18
25. 25.What is the 30th term of the AP 16, 24, 32, 40, …? (a) 256 (b) 240 (c) 248 (d) 232
26. 26.The mean of 6 numbers is 34. When the number 27 is added to them, what is the new mean? (a) 34 (b) 32 (c) 35 (d) 33
27. 27.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) 28 (b) 29 (c) 22 (d) 21
28. 28.A bag has 3 white, 8 yellow and 5 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 5/16 (b) 11/16 (c) 3/4 (d) 1/3
29. 29.What is the median of 18, 25, 36, 22 and 21? (a) 21 (b) 25 (c) 22 (d) 36
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/11 (c) 7/36 (d) 1/6
31. 31.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
32. 32.If a + b = 18 and ab = 80, what is (a − b)²? (a) 4 (b) 2 (c) 324 (d) 164
33. 33.How many factors does 82 have? (a) 3 (b) 4 (c) 2 (d) 5
34. 34.Which term of the AP 6, 9, 12, 15, … is 102? (a) 32nd (b) 33rd (c) 35th (d) 34th
35. 35.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 381 (c) 372 (d) 326
36. 36.Which term of the AP 19, 27, 35, 43, … is 171? (a) 22nd (b) 21st (c) 19th (d) 20th
37. 37.A bag has 10 black balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 17 (d) 8
38. 38.What is the 18th term of the AP 16, 25, 34, 43, …? (a) 169 (b) 178 (c) 162 (d) 153
39. 39.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 55° (c) 145° (d) 125°
40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 12 (b) 14 (c) 13 (d) 5

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