Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 959 · 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 sum of the first 10 terms of the AP 10, 11, 12, …? (a) 150 (b) 19 (c) 145 (d) 290
2. 2.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 130° (b) 75° (c) 155° (d) 50°
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 day of the week? (a) 7 (b) 14 (c) 8 (d) 15
4. 4.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
5. 5.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 100° (b) 160° (c) 260° (d) 80°
6. 6.Which term of the AP 12, 20, 28, 36, … is 268? (a) 34th (b) 35th (c) 32nd (d) 33rd
7. 7.A drawer has lots of white and green 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) 2 (c) 5 (d) 4
8. 8.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 46° (d) 45°
9. 9.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 48 (c) 16 (d) 144
10. 10.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 100 (c) 45 (d) 20
11. 11.A cuboid is 7 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 104 sq cm (b) 140 sq cm (c) 416 sq cm (d) 208 sq cm
12. 12.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 96 cu cm (d) 12 cu cm
13. 13.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 408 (b) 204 (c) 224 (d) 43
14. 14.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 35° (d) 90°
15. 15.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
16. 16.In a class of 22 children, 15 like mangoes, 12 like bananas and 6 like both. How many like at least one of the two? (a) 22 (b) 15 (c) 21 (d) 27
17. 17.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
18. 18.What is the midpoint of the line joining (0, 7) and (2, 3)? (a) (1, 5) (b) (2, 10) (c) (5, 1) (d) (1, 2)
19. 19.A bag has 10 blue balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 13 (c) 2 (d) 11
20. 20.What is the smallest prime factor of 133? (a) 2 (b) 7 (c) 1 (d) 19
21. 21.In a class of 43 children, 17 like cricket, 26 like football and 9 like neither. How many like both? (a) 34 (b) 8 (c) 10 (d) 9
22. 22.A drawer has lots of white, yellow, blue, green and black 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) 10 (c) 5 (d) 6
23. 23.In a class of 23 children, 14 like maths, 12 like science and 7 like both. How many like only maths? (a) 11 (b) 5 (c) 14 (d) 7
24. 24.In a class of 50 children, 24 like dance, 26 like music and 8 like both. How many like neither? (a) 0 (b) 9 (c) 8 (d) 16
25. 25.What is the mode of 7, 2, 4, 9, 4, 2 and 2? (a) 7 (b) 9 (c) 2 (d) 4
26. 26.There are 3 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 7 (b) 12 (c) 24 (d) 15
27. 27.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 72 (c) 24 (d) 216
28. 28.How many prime numbers are there between 60 and 90? (a) 7 (b) 6 (c) 9 (d) 8
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 1/12 (d) 2/11
30. 30.A bag has 5 yellow, 4 green and 4 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 9/13 (b) 1/3 (c) 10/13 (d) 4/13
31. 31.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 36) (b) (x + 1)(x + 12) (c) (x + 4)(x + 9) (d) (x − 4)(x − 9)
32. 32.A drawer has lots of white, green, black and blue 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) 2 (c) 5 (d) 8
33. 33.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 70° (d) 340°
34. 34.A bag has 10 yellow balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 12 (b) 21 (c) 2 (d) 11
35. 35.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
36. 36.What is the distance between the points (4, 33) and (11, 9)? (a) 26 (b) 625 (c) 25 (d) 31
37. 37.What is the mean of 4, 14, 17, 18 and 17? (a) 14 (b) 15 (c) 13 (d) 16
38. 38.What is the smallest prime factor of 91? (a) 2 (b) 7 (c) 1 (d) 13
39. 39.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 18 (c) 5 (d) 45
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) 99 (b) 33 (c) 36 (d) 11

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