Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 912 · 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.In a class of 30 children, 20 like tea, 9 like coffee and 5 like both. How many like at least one of the two? (a) 29 (b) 19 (c) 30 (d) 24
2. 2.What is the mean of 8, 15, 13, 15 and 4? (a) 13 (b) 12 (c) 11 (d) 10
3. 3.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) 25 (c) 24 (d) 13
4. 4.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
5. 5.What is the smallest prime factor of 403? (a) 1 (b) 13 (c) 31 (d) 2
6. 6.In a class of 41 children, 18 like tea, 21 like coffee and 4 like both. How many like neither? (a) 4 (b) 6 (c) 10 (d) 2
7. 7.What is the 30th term of the AP 16, 23, 30, 37, …? (a) 226 (b) 203 (c) 219 (d) 210
8. 8.If a + b = 16 and ab = 63, what is a² + b²? (a) 130 (b) 256 (c) 382 (d) 193
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/36 (c) 1/11 (d) 1/12
10. 10.What is the prime factorisation of 15? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3 × 5
11. 11.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 12 (c) 5 (d) 9
12. 12.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
13. 13.The mean of 8 numbers is 14. When the number 23 is added to them, what is the new mean? (a) 15 (b) 16 (c) 17 (d) 14
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
15. 15.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 85° (b) 95° (c) 110° (d) 155°
16. 16.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2 × 3² × 5 (c) 2 × 3² × 5² (d) 2³ × 3² × 5
17. 17.What is the mode of 10, 10, 13, 5, 13, 3 and 13? (a) 3 (b) 5 (c) 10 (d) 13
18. 18.What is the smallest prime factor of 39? (a) 13 (b) 3 (c) 1 (d) 2
19. 19.The mean of 9 numbers is 34. When the number 44 is added to them, what is the new mean? (a) 36 (b) 35 (c) 34 (d) 39
20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 2 (b) 1 (c) 3 (d) 4
21. 21.In a class of 29 children, 16 like dance, 16 like music and 10 like both. How many like at least one of the two? (a) 12 (b) 22 (c) 29 (d) 32
22. 22.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 150° (c) 31° (d) 30°
23. 23.A bag has 8 blue balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 9 (c) 2 (d) 16
24. 24.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 30° (b) 150° (c) 60° (d) 31°
25. 25.What is the median of 11, 1, 10, 40, 13, 24 and 33? (a) 11 (b) 40 (c) 13 (d) 24
26. 26.Using (a + b)² = a² + 2ab + b², what is 45²? (a) 2025 (b) 1225 (c) 1625 (d) 2035
27. 27.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 22 (c) 28 (d) 29
28. 28.What is the distance between the points (3, 17) and (8, 5)? (a) 17 (b) 169 (c) 14 (d) 13
29. 29.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 78 (c) 156 (d) 169
30. 30.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
31. 31.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 225 (d) 120
32. 32.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 12 cu cm (b) 84 cu cm (c) 122 cu cm (d) 14 cu cm
33. 33.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2⁴ × 3 (c) 2³ × 3 (d) 2² × 3
34. 34.What is the smallest prime factor of 143? (a) 13 (b) 2 (c) 11 (d) 1
35. 35.What is the mode of 11, 6, 11, 11, 14, 2 and 2? (a) 6 (b) 11 (c) 2 (d) 14
36. 36.In a class of 28 children, 12 like cricket, 15 like football and 6 like both. How many like at least one of the two? (a) 28 (b) 15 (c) 21 (d) 27
37. 37.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 60° (d) 120°
38. 38.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 21 (d) 42
39. 39.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 60 (c) 11 (d) 30
40. 40.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 11 (c) 99 (d) 36

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