Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 141 · 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 mode of 14, 14, 2, 16, 2, 13 and 2? (a) 2 (b) 13 (c) 16 (d) 14
2. 2.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
3. 3.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 294 sq cm (c) 49 sq cm (d) 196 sq cm
4. 4.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
5. 5.In a class of 23 children, 11 like mangoes, 11 like bananas and 4 like neither. How many like both? (a) 2 (b) 19 (c) 4 (d) 3
6. 6.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
7. 7.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/12 (c) 1/18 (d) 1/11
9. 9.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 32 (b) 200 (c) 370 (d) 185
10. 10.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) 30 (b) 81 (c) 27 (d) 9
11. 11.How many prime numbers are there between 50 and 60? (a) 3 (b) 4 (c) 2 (d) 1
12. 12.What is the prime factorisation of 35? (a) 5 × 7 (b) 5² × 7 (c) 5³ × 7 (d) 5 × 7²
13. 13.A bag has 12 black balls and 13 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 14 (c) 2 (d) 25
14. 14.A bag has 7 blue balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 9 (b) 15 (c) 2 (d) 8
15. 15.What is the mode of 13, 16, 8, 5, 5, 8 and 5? (a) 5 (b) 8 (c) 16 (d) 13
16. 16.What is the sum of the roots of x² − 11x + 30 = 0? (a) 11 (b) 10 (c) 12 (d) 30
17. 17.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
18. 18.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
19. 19.What is the median of 38, 7, 35, 32 and 25? (a) 35 (b) 33 (c) 32 (d) 25
20. 20.What is the mean of 13, 2, 5, 7, 9 and 12? (a) 9 (b) 7 (c) 10 (d) 8
21. 21.What is the distance between the points (6, 13) and (15, 1)? (a) 21 (b) 16 (c) 15 (d) 225
22. 22.What is the mean of 4, 5, 15 and 12? (a) 12 (b) 10 (c) 8 (d) 9
23. 23.What is the distance between the points (9, 14) and (21, 9)? (a) 14 (b) 17 (c) 13 (d) 169
24. 24.A bag has 11 blue balls and 3 yellow 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) 12 (c) 14 (d) 4
25. 25.What is the distance between the points (6, 0) and (12, 8)? (a) 11 (b) 14 (c) 10 (d) 100
26. 26.A bag has 12 white balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 14 (b) 15 (c) 2 (d) 13
27. 27.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 14 (c) 42 (d) 49
28. 28.The mean of 5 numbers is 25. When the number 1 is added to them, what is the new mean? (a) 21 (b) 13 (c) 25 (d) 22
29. 29.A bag has 3 black balls and 9 green 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) 10 (c) 12 (d) 4
30. 30.There are 6 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 24 (c) 36 (d) 18
31. 31.What is the median of 6, 16, 28, 26 and 25? (a) 28 (b) 16 (c) 25 (d) 26
32. 32.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 95° (b) 150° (c) 125° (d) 85°
33. 33.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 35° (d) 145°
34. 34.In a class of 42 children, 20 like tea, 27 like coffee and 11 like both. How many like only tea? (a) 9 (b) 20 (c) 15 (d) 16
35. 35.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 10° (b) 170° (c) 160° (d) 30°
36. 36.3 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) 5 (b) 6 (c) 9 (d) 12
37. 37.In a class of 43 children, 22 like mangoes, 20 like bananas and 7 like neither. How many like both? (a) 6 (b) 36 (c) 7 (d) 5
38. 38.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) 15 (c) 8 (d) 14
39. 39.In a class of 43 children, 22 like maths, 19 like science and 8 like both. How many like only maths? (a) 24 (b) 14 (c) 11 (d) 22
40. 40.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7³ (c) 2³ × 3 × 7 (d) 2² × 3 × 7

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