Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 274 · 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.How many factors does 75 have? (a) 7 (b) 5 (c) 6 (d) 4
2. 2.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 196 (d) 182
3. 3.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 55 (c) 22 (d) 110
4. 4.A bag has 5 black balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 12 (c) 6 (d) 7
5. 5.A drawer has lots of green, red, white, 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) 2 (b) 5 (c) 10 (d) 6
6. 6.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 95° (b) 150° (c) 85° (d) 115°
7. 7.A bag has 7 yellow, 8 red and 9 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 17/24 (b) 7/24 (c) 1/3 (d) 7/17
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/18 (c) 1/12 (d) 1/36
9. 9.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
10. 10.In a class of 29 children, 13 like mangoes, 23 like bananas and 2 like neither. How many like both? (a) 7 (b) 2 (c) 9 (d) 27
11. 11.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 55° (c) 90° (d) 45°
12. 12.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
13. 13.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) 24 (c) 13 (d) 12
14. 14.In a class of 45 children, 19 like tea, 19 like coffee and 2 like both. How many like only tea? (a) 17 (b) 26 (c) 19 (d) 2
15. 15.What are the roots of x² − 16x + 63 = 0? (a) 3 and 21 (b) 7 and 9 (c) 1 and 63 (d) 1 and 15
16. 16.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 8)(x + 9) (c) (x + 1)(x + 72) (d) (x − 8)(x − 9)
17. 17.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
18. 18.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 33 (c) 30 (d) 10
19. 19.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 8372 (c) 4095 (d) 4186
20. 20.Which term of the AP 4, 6, 8, 10, … is 32? (a) 16th (b) 14th (c) 17th (d) 15th
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 1/11 (c) 6/11 (d) 7/36
22. 22.In a class of 29 children, 11 like dance, 18 like music and 5 like both. How many like at least one of the two? (a) 24 (b) 19 (c) 29 (d) 25
23. 23.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
24. 24.What is the distance between the points (1, 0) and (4, 4)? (a) 6 (b) 5 (c) 25 (d) 7
25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 6 (b) 9 (c) 8 (d) 7
26. 26.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 56 (d) 28
27. 27.What is the mean of 16, 18, 15 and 11? (a) 20 (b) 15 (c) 16 (d) 12
28. 28.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 5 (d) 6
29. 29.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 35 (b) 26 (c) 27 (d) 25
30. 30.If a + b = 19 and ab = 88, what is (a − b)²? (a) 185 (b) 361 (c) 9 (d) 3
31. 31.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 100° (d) 140°
32. 32.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 110 (d) 100
33. 33.What is the 40th term of the AP 20, 27, 34, 41, …? (a) 300 (b) 273 (c) 280 (d) 293
34. 34.There are 3 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 36 (b) 21 (c) 9 (d) 18
35. 35.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2³ × 5 (c) 2⁴ × 5 (d) 2² × 5
36. 36.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 49 (d) 42
37. 37.In a class of 47 children, 24 like cricket, 21 like football and 6 like neither. How many like both? (a) 5 (b) 4 (c) 41 (d) 6
38. 38.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
39. 39.What is the mode of 5, 13, 5, 19, 17, 5 and 13? (a) 19 (b) 5 (c) 13 (d) 17
40. 40.A bag has 5 yellow, 4 green and 6 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 1/2 (c) 2/5 (d) 2/3

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