Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 894 · 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 7 blue, 2 white and 8 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 10/17 (c) 7/17 (d) 11/17
2. 2.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 42 (d) 49
3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 13 (b) 3 (c) 11 (d) 12
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/12 (c) 1/18 (d) 1/36
5. 5.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
6. 6.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 16 cu cm (d) 8 cu cm
7. 7.If a + b = 15 and ab = 56, what is a² + b²? (a) 113 (b) 337 (c) 225 (d) 169
8. 8.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 338 (c) 325 (d) 351
9. 9.The mean of 7 numbers is 33. When the number 1 is added to them, what is the new mean? (a) 29 (b) 30 (c) 33 (d) 17
10. 10.A drawer has lots of green, white, blue and yellow 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) 8 (d) 5
11. 11.If a + b = 11 and ab = 10, what is a² + b²? (a) 141 (b) 111 (c) 121 (d) 101
12. 12.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 125° (d) 100°
13. 13.Which term of the AP 1, 5, 9, 13, … is 85? (a) 21st (b) 23rd (c) 24th (d) 22nd
14. 14.In which quadrant does the point (−2, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
15. 15.What is the mean of 4, 6, 4 and 18? (a) 9 (b) 8 (c) 7 (d) 10
16. 16.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 140° (b) 120° (c) 60° (d) 100°
17. 17.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) 8 (b) 15 (c) 7 (d) 14
18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 3 (b) 12 (c) 10 (d) 11
19. 19.A bag has 9 white, 4 red and 8 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 3/7 (b) 13/21 (c) 1/3 (d) 4/7
20. 20.A drawer has lots of red 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) 4 (d) 3
21. 21.A drawer has lots of red, green 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) 6 (b) 3 (c) 4 (d) 2
22. 22.What is the midpoint of the line joining (9, 17) and (19, 9)? (a) (28, 26) (b) (14, 13) (c) (13, 14) (d) (5, 4)
23. 23.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
24. 24.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
25. 25.A bag has 7 black balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 9 (c) 16 (d) 8
26. 26.Using (a − b)² = a² − 2ab + b², what is 56²? (a) 4096 (b) 3584 (c) 3136 (d) 3146
27. 27.6 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 36 (c) 9 (d) 18
28. 28.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 105° (b) 45° (c) 135° (d) 120°
29. 29.In a class of 29 children, 18 like maths, 14 like science and 2 like neither. How many like both? (a) 27 (b) 5 (c) 3 (d) 2
30. 30.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) 72 (d) 27
31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
32. 32.What is the smallest prime factor of 217? (a) 2 (b) 31 (c) 7 (d) 1
33. 33.What is the 39th term of the AP 19, 26, 33, 40, …? (a) 292 (b) 273 (c) 266 (d) 285
34. 34.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 80° (d) 160°
35. 35.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
36. 36.How many factors does 69 have? (a) 2 (b) 3 (c) 5 (d) 4
37. 37.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)
38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 16 (b) 15 (c) 5 (d) 17
39. 39.In a class of 17 children, 9 like maths, 10 like science and 5 like both. How many like neither? (a) 5 (b) 3 (c) 8 (d) 4
40. 40.What is the 29th term of the AP 7, 13, 19, 25, …? (a) 174 (b) 175 (c) 168 (d) 181

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