Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 108 · 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 37 children, 26 like dance, 17 like music and 8 like both. How many like at least one of the two? (a) 43 (b) 37 (c) 35 (d) 27
2. 2.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 36 (c) 81 (d) 72
3. 3.What is the midpoint of the line joining (10, 18) and (18, 10)? (a) (28, 28) (b) (15, 14) (c) (4, 4) (d) (14, 14)
4. 4.In which quadrant does the point (3, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
5. 5.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 70 sq cm (b) 59 sq cm (c) 118 sq cm (d) 236 sq cm
6. 6.In which quadrant does the point (9, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
7. 7.There are 4 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) 20 (b) 16 (c) 8 (d) 32
8. 8.What is the 35th term of the AP 19, 23, 27, 31, …? (a) 136 (b) 159 (c) 140 (d) 155
9. 9.A drawer has lots of white, blue, yellow 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) 2 (b) 8 (c) 5 (d) 4
10. 10.A bag has 4 green balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 15 (b) 2 (c) 6 (d) 5
11. 11.What is the mean of 13, 15, 8, 4 and 10? (a) 9 (b) 10 (c) 12 (d) 11
12. 12.What is the sum of the roots of x² − 5x + 6 = 0? (a) 6 (b) 4 (c) 7 (d) 5
13. 13.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
14. 14.In a class of 41 children, 25 like cricket, 21 like football and 10 like both. How many like neither? (a) 6 (b) 10 (c) 15 (d) 5
15. 15.What is the distance between the points (3, 7) and (15, 2)? (a) 17 (b) 14 (c) 169 (d) 13
16. 16.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
18. 18.In a class of 22 children, 8 like dance, 8 like music and 2 like both. How many like only dance? (a) 8 (b) 2 (c) 6 (d) 14
19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
20. 20.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 85° (b) 145° (c) 130° (d) 95°
21. 21.A drawer has lots of black, yellow, green 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) 8 (c) 5 (d) 2
22. 22.What is the 23rd term of the AP 4, 11, 18, 25, …? (a) 161 (b) 165 (c) 154 (d) 158
23. 23.A drawer has lots of blue, black, white 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) 2 (c) 5 (d) 8
24. 24.What is the mean of 10, 6, 16 and 4? (a) 8 (b) 12 (c) 9 (d) 10
25. 25.If a + b = 11 and ab = 30, what is (a − b)²? (a) 121 (b) 61 (c) 1 (d) 91
26. 26.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 90° (c) 125° (d) 270°
27. 27.In a class of 40 children, 23 like dance, 19 like music and 5 like both. How many like at least one of the two? (a) 32 (b) 40 (c) 42 (d) 37
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/12 (d) 1/11
29. 29.What is the 22nd term of the AP 3, 7, 11, 15, …? (a) 91 (b) 88 (c) 87 (d) 84
30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
31. 31.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 14 (b) 96 (c) 56 (d) 48
32. 32.What is the midpoint of the line joining (4, 9) and (16, 5)? (a) (6, 2) (b) (7, 10) (c) (20, 14) (d) (10, 7)
33. 33.A bag has 2 green, 9 yellow and 5 blue balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 7/16 (b) 7/9 (c) 9/16 (d) 1/3
34. 34.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 25 (d) 11
35. 35.In a class of 45 children, 25 like maths, 24 like science and 6 like both. How many like at least one of the two? (a) 37 (b) 43 (c) 45 (d) 49
36. 36.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
37. 37.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 54 (c) 162 (d) 57
38. 38.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 9 (b) 11 (c) 10 (d) 8
40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18

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