Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 665 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/18 (c) 1/11 (d) 1/12
2. 2.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 112 (b) 20 (c) 208 (d) 104
3. 3.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
4. 4.What is the mean of 17, 2, 19 and 14? (a) 12 (b) 15 (c) 14 (d) 13
5. 5.The mean of 8 numbers is 21. When the number 48 is added to them, what is the new mean? (a) 24 (b) 23 (c) 21 (d) 25
6. 6.In which quadrant does the point (−8, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
7. 7.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 65° (d) 25°
8. 8.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 105 (c) 120 (d) 210
9. 9.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
10. 10.Which term of the AP 8, 14, 20, 26, … is 98? (a) 15th (b) 17th (c) 16th (d) 18th
11. 11.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 6 (d) 21
12. 12.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
13. 13.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7²
14. 14.In which quadrant does the point (−2, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
15. 15.What is the mean of 2, 7, 6, 6 and 4? (a) 5 (b) 4 (c) 7 (d) 6
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 16 (d) 15
17. 17.What is the mean of 11, 8, 3, 11, 19 and 20? (a) 14 (b) 11 (c) 13 (d) 12
18. 18.What is the median of 7, 16, 33, 40 and 10? (a) 17 (b) 10 (c) 33 (d) 16
19. 19.Which term of the AP 6, 8, 10, 12, … is 50? (a) 24th (b) 25th (c) 22nd (d) 23rd
20. 20.The numbers 3 to 11 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) 7 (c) 24 (d) 21
21. 21.A drawer has lots of black, yellow, white and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 4 (c) 2 (d) 5
22. 22.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
23. 23.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 3 (d) 12
24. 24.What is the smallest prime factor of 299? (a) 13 (b) 23 (c) 2 (d) 1
25. 25.In a class of 35 children, 15 like dance, 27 like music and 3 like neither. How many like both? (a) 32 (b) 10 (c) 7 (d) 3
26. 26.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) 25 (b) 13 (c) 12 (d) 24
27. 27.In which quadrant does the point (−9, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
28. 28.What is the mean of 18, 12, 7 and 19? (a) 16 (b) 13 (c) 14 (d) 15
29. 29.How many factors does 92 have? (a) 5 (b) 6 (c) 4 (d) 7
30. 30.What is the mean of 10, 2, 14, 13, 12 and 3? (a) 10 (b) 11 (c) 8 (d) 9
31. 31.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 55 (c) 100 (d) 90
32. 32.A bag has 4 yellow, 5 white and 5 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 5/7 (b) 1/3 (c) 2/5 (d) 2/7
33. 33.What is the smallest prime factor of 87? (a) 2 (b) 1 (c) 29 (d) 3
34. 34.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
35. 35.What is the 16th term of the AP 16, 24, 32, 40, …? (a) 128 (b) 136 (c) 144 (d) 120
36. 36.What is the mean of 9, 11, 8 and 16? (a) 10 (b) 13 (c) 12 (d) 11
37. 37.A bag has 5 yellow balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 6 (c) 15 (d) 11
38. 38.What is the mode of 19, 19, 8, 13, 14, 14 and 19? (a) 14 (b) 8 (c) 19 (d) 13
39. 39.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
40. 40.What is the 21st term of the AP 6, 14, 22, 30, …? (a) 174 (b) 168 (c) 160 (d) 166

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