Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 575 · 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.A bag has 6 white balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 7 (b) 2 (c) 16 (d) 8
2. 2.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 60° (b) 135° (c) 105° (d) 120°
3. 3.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 95° (c) 155° (d) 85°
4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
5. 5.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 10 (c) 24 (d) 32
6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 7 (d) 16
7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 4 (d) 1
8. 8.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 55° (b) 125° (c) 145° (d) 160°
9. 9.What is the mean of 16, 11, 19 and 18? (a) 16 (b) 17 (c) 18 (d) 15
10. 10.What is the 17th term of the AP 1, 4, 7, 10, …? (a) 51 (b) 48 (c) 49 (d) 52
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
12. 12.What is the median of 11, 30, 35, 9 and 4? (a) 9 (b) 11 (c) 35 (d) 30
13. 13.What is the 39th term of the AP 16, 24, 32, 40, …? (a) 312 (b) 304 (c) 328 (d) 320
14. 14.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 55° (c) 20° (d) 70°
15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 7 (b) 17 (c) 16 (d) 18
16. 16.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 6 cu cm (b) 72 cu cm (c) 11 cu cm (d) 36 cu cm
17. 17.How many prime numbers are there between 10 and 20? (a) 3 (b) 6 (c) 4 (d) 5
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 5/36 (c) 1/9 (d) 4/11
19. 19.What is the 17th term of the AP 10, 12, 14, 16, …? (a) 34 (b) 32 (c) 42 (d) 44
20. 20.The mean of 7 numbers is 22. When the number 6 is added to them, what is the new mean? (a) 14 (b) 22 (c) 20 (d) 21
21. 21.How many factors does 30 have? (a) 6 (b) 9 (c) 7 (d) 8
22. 22.What is the mean of 13, 18, 20, 19, 8 and 18? (a) 15 (b) 16 (c) 17 (d) 18
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/12 (c) 1/9 (d) 1/11
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/6 (c) 5/11 (d) 1/11
25. 25.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1369 (b) 1591 (c) 1849 (d) 1379
26. 26.In a class of 47 children, 18 like maths, 29 like science and 9 like both. How many like neither? (a) 10 (b) 0 (c) 18 (d) 9
27. 27.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) 12 (b) 24 (c) 25 (d) 13
28. 28.What is the sum of the roots of x² − 13x + 42 = 0? (a) 13 (b) 12 (c) 14 (d) 42
29. 29.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 15° (b) 165° (c) 155° (d) 40°
30. 30.In a class of 31 children, 19 like maths, 19 like science and 2 like neither. How many like both? (a) 9 (b) 2 (c) 7 (d) 29
31. 31.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 42 (c) 49 (d) 14
32. 32.How many factors does 34 have? (a) 5 (b) 4 (c) 2 (d) 3
33. 33.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 12 (c) 36 (d) 39
34. 34.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 130° (d) 25°
35. 35.In a class of 32 children, 14 like dance, 17 like music and 9 like both. How many like at least one of the two? (a) 32 (b) 22 (c) 13 (d) 31
36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 17 (d) 7
37. 37.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
38. 38.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) 24 (b) 8 (c) 27 (d) 72
39. 39.What is the mean of 4, 15, 18, 14, 19 and 8? (a) 14 (b) 15 (c) 13 (d) 12
40. 40.If a + b = 18 and ab = 77, what is a² + b²? (a) 324 (b) 170 (c) 478 (d) 247

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