Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 411 · 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 34 children, 20 like maths, 18 like science and 7 like neither. How many like both? (a) 4 (b) 11 (c) 27 (d) 7
2. 2.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 95° (b) 85° (c) 125° (d) 140°
3. 3.Using (a − b)² = a² − 2ab + b², what is 55²? (a) 3035 (b) 4225 (c) 3025 (d) 3575
4. 4.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 1099 (b) 909 (c) 729 (d) 1089
5. 5.If a + b = 13 and ab = 40, what is a² + b²? (a) 89 (b) 169 (c) 249 (d) 129
6. 6.A drawer has lots of red 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) 3 (b) 5 (c) 2 (d) 4
7. 7.What is the distance between the points (0, 0) and (4, 3)? (a) 6 (b) 7 (c) 25 (d) 5
8. 8.A drawer has lots of black, red, 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) 8 (c) 5 (d) 2
9. 9.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) 18 (b) 36 (c) 24 (d) 9
10. 10.What are the roots of x² − 8x + 15 = 0? (a) 1 and 7 (b) 2 and 6 (c) 1 and 15 (d) 3 and 5
11. 11.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 210° (b) 30° (c) 60° (d) 150°
12. 12.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 25 (d) 120
13. 13.What is the prime factorisation of 28? (a) 2 × 7 (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7²
14. 14.What is the mean of 14, 11, 7, 9, 15 and 16? (a) 14 (b) 11 (c) 12 (d) 13
15. 15.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 150° (c) 31° (d) 210°
16. 16.How many factors does 99 have? (a) 7 (b) 6 (c) 4 (d) 5
17. 17.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 1/4 (d) 5/6
18. 18.A bag has 8 blue balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 18 (c) 2 (d) 9
19. 19.In a class of 40 children, 15 like maths, 22 like science and 2 like both. How many like at least one of the two? (a) 40 (b) 35 (c) 37 (d) 33
20. 20.What is the mode of 6, 6, 4, 1, 6, 18 and 4? (a) 18 (b) 6 (c) 4 (d) 1
21. 21.What is the distance between the points (4, 3) and (16, 8)? (a) 17 (b) 14 (c) 13 (d) 169
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 2/11 (c) 1/11 (d) 1/12
23. 23.A bag has 3 white balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 4 (c) 14 (d) 2
24. 24.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
25. 25.A bag has 4 red balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 6 (c) 11 (d) 2
26. 26.Which is the correct factorisation of x² + 7x + 12? (a) (x + 1)(x + 12) (b) (x + 1)(x + 6) (c) (x − 3)(x − 4) (d) (x + 3)(x + 4)
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) 42 (c) 49 (d) 14
28. 28.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 91 (d) 105
29. 29.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
30. 30.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 40° (b) 85° (c) 140° (d) 135°
31. 31.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 11 cu cm (b) 40 cu cm (c) 8 cu cm (d) 76 cu cm
32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 6 (b) 5 (c) 7 (d) 4
33. 33.The mean of 7 numbers is 11. When the number 3 is added to them, what is the new mean? (a) 10 (b) 7 (c) 9 (d) 11
34. 34.In a class of 31 children, 15 like dance, 24 like music and 12 like both. How many like at least one of the two? (a) 39 (b) 31 (c) 15 (d) 27
35. 35.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 48 (d) 24
36. 36.How many factors does 110 have? (a) 8 (b) 6 (c) 9 (d) 7
37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 2 (d) 4
38. 38.Which term of the AP 1, 9, 17, 25, … is 89? (a) 13th (b) 12th (c) 14th (d) 11th
39. 39.What is the midpoint of the line joining (2, 14) and (6, 8)? (a) (2, 3) (b) (4, 11) (c) (11, 4) (d) (8, 22)
40. 40.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 90 (b) 48 (c) 10 (d) 45

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