Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 398 · 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.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2 × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
2. 2.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/2 (d) 1/3
3. 3.A bag has 7 white, 5 yellow and 6 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 11/18 (b) 7/18 (c) 1/3 (d) 7/11
4. 4.The mean of 8 numbers is 20. When the number 47 is added to them, what is the new mean? (a) 24 (b) 23 (c) 22 (d) 20
5. 5.In a class of 36 children, 23 like tea, 21 like coffee and 3 like neither. How many like both? (a) 33 (b) 3 (c) 11 (d) 8
6. 6.In which quadrant does the point (5, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
7. 7.What is the median of 1, 32, 9, 14 and 29? (a) 14 (b) 29 (c) 9 (d) 17
8. 8.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 15° (c) 110° (d) 85°
9. 9.The mean of 8 numbers is 11. When the number 20 is added to them, what is the new mean? (a) 11 (b) 14 (c) 12 (d) 13
10. 10.A drawer has lots of green, yellow, black 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) 2 (b) 4 (c) 8 (d) 5
11. 11.What is the midpoint of the line joining (8, 10) and (20, 2)? (a) (6, 14) (b) (28, 12) (c) (6, 4) (d) (14, 6)
12. 12.A drawer has lots of 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) 5 (b) 2 (c) 4 (d) 3
13. 13.In which quadrant does the point (−8, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
14. 14.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
15. 15.What is the median of 5, 39, 10, 4, 34, 19 and 12? (a) 19 (b) 4 (c) 12 (d) 10
16. 16.Which term of the AP 6, 14, 22, 30, … is 254? (a) 33rd (b) 31st (c) 34th (d) 32nd
17. 17.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
18. 18.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 30 (c) 81 (d) 27
19. 19.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 30 (d) 15
20. 20.In a class of 28 children, 17 like cricket, 10 like football and 4 like neither. How many like both? (a) 4 (b) 3 (c) 2 (d) 24
21. 21.What is the midpoint of the line joining (7, 5) and (9, 17)? (a) (11, 8) (b) (8, 11) (c) (1, 6) (d) (16, 22)
22. 22.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
23. 23.What is the smallest prime factor of 341? (a) 11 (b) 31 (c) 1 (d) 2
24. 24.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) 8 (c) 15 (d) 14
25. 25.A bag has 5 white balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 7 (c) 6 (d) 8
26. 26.A bag has 3 red balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 4 (c) 2 (d) 5
27. 27.In a class of 29 children, 16 like maths, 15 like science and 12 like both. How many like at least one of the two? (a) 31 (b) 7 (c) 19 (d) 29
28. 28.What is the 29th term of the AP 18, 27, 36, 45, …? (a) 261 (b) 252 (c) 270 (d) 279
29. 29.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 150° (b) 85° (c) 115° (d) 95°
30. 30.The mean of 9 numbers is 10. When the number 40 is added to them, what is the new mean? (a) 10 (b) 13 (c) 25 (d) 14
31. 31.What is the mean of 13, 17, 7 and 7? (a) 12 (b) 11 (c) 13 (d) 10
32. 32.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 49 (d) 42
33. 33.What is the 22nd term of the AP 4, 7, 10, 13, …? (a) 63 (b) 70 (c) 66 (d) 67
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
35. 35.In which quadrant does the point (−7, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 6 (b) 8 (c) 9 (d) 4
37. 37.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 30 (d) 15
38. 38.The mean of 6 numbers is 34. When the number 6 is added to them, what is the new mean? (a) 30 (b) 20 (c) 31 (d) 34
39. 39.There are 8 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 64 (c) 12 (d) 32
40. 40.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm

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