Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 370 · 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 straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 61° (c) 240° (d) 60°
2. 2.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 135° (c) 45° (d) 91°
3. 3.Which term of the AP 6, 11, 16, 21, … is 161? (a) 31st (b) 32nd (c) 33rd (d) 34th
4. 4.What is the 35th term of the AP 4, 10, 16, 22, …? (a) 208 (b) 204 (c) 210 (d) 214
5. 5.A bag has 6 white balls and 4 black 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) 5 (d) 7
6. 6.In a class of 34 children, 15 like tea, 21 like coffee and 12 like both. How many like only tea? (a) 9 (b) 3 (c) 13 (d) 15
7. 7.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 25 (d) 20
8. 8.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 165 (b) 176 (c) 330 (d) 25
9. 9.Using (a + b)² = a² + 2ab + b², what is 64²? (a) 4106 (b) 3136 (c) 3616 (d) 4096
10. 10.The mean of 9 numbers is 31. When the number 21 is added to them, what is the new mean? (a) 26 (b) 30 (c) 31 (d) 29
11. 11.In which quadrant does the point (6, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
12. 12.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 95° (d) 60°
13. 13.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 556 (c) 546 (d) 555
14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 20 (d) 21
15. 15.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/4 (c) 5/6 (d) 1/3
16. 16.What is the 29th term of the AP 9, 13, 17, 21, …? (a) 121 (b) 116 (c) 125 (d) 112
17. 17.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 90 (d) 55
18. 18.In a class of 40 children, 20 like dance, 18 like music and 3 like both. How many like at least one of the two? (a) 32 (b) 38 (c) 35 (d) 40
19. 19.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 6 (d) 5
20. 20.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 55° (b) 130° (c) 105° (d) 125°
21. 21.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3³ × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7
22. 22.What is the smallest prime factor of 65? (a) 2 (b) 13 (c) 1 (d) 5
23. 23.What is the mean of 14, 17, 18 and 11? (a) 12 (b) 16 (c) 15 (d) 20
24. 24.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) 28 (b) 22 (c) 21 (d) 29
25. 25.6 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) 24 (b) 18 (c) 8 (d) 12
26. 26.What is the mode of 19, 10, 19, 19, 13, 17 and 17? (a) 19 (b) 10 (c) 13 (d) 17
27. 27.In a class of 27 children, 11 like maths, 15 like science and 8 like both. How many like neither? (a) 17 (b) 9 (c) 1 (d) 8
28. 28.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) 14 (b) 15 (c) 8 (d) 7
29. 29.What is the midpoint of the line joining (9, 1) and (13, 11)? (a) (6, 11) (b) (22, 12) (c) (2, 5) (d) (11, 6)
30. 30.What is the mode of 18, 18, 7, 7, 7, 6 and 14? (a) 6 (b) 18 (c) 14 (d) 7
31. 31.What is the mean of 19, 6, 8, 2 and 20? (a) 11 (b) 10 (c) 12 (d) 13
32. 32.What is the median of 25, 27, 7, 36 and 21? (a) 7 (b) 25 (c) 21 (d) 27
33. 33.What is the distance between the points (5, 7) and (8, 3)? (a) 7 (b) 25 (c) 5 (d) 6
34. 34.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 144 (d) 66
35. 35.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 18 sq cm (b) 42 sq cm (c) 84 sq cm (d) 21 sq cm
36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 19 (d) 7
37. 37.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 80? (a) 10 (b) 9 (c) 7 (d) 8
39. 39.What is the smallest prime factor of 169? (a) 3 (b) 2 (c) 13 (d) 1
40. 40.Which is the correct factorisation of x² + 13x + 42? (a) (x − 6)(x − 7) (b) (x + 6)(x + 7) (c) (x + 1)(x + 42) (d) (x + 1)(x + 12)

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