Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 982 · 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.If a + b = 10 and ab = 24, what is (a − b)²? (a) 2 (b) 52 (c) 100 (d) 4
2. 2.What is the mean of 3, 11, 5, 3, 2 and 12? (a) 6 (b) 8 (c) 5 (d) 7
3. 3.How many prime numbers are there between 80 and 110? (a) 6 (b) 8 (c) 9 (d) 7
4. 4.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 120° (c) 60° (d) 30°
5. 5.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 120° (d) 160°
6. 6.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 65° (b) 105° (c) 140° (d) 115°
7. 7.What is the 35th term of the AP 3, 12, 21, 30, …? (a) 318 (b) 309 (c) 315 (d) 306
8. 8.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
9. 9.The mean of 7 numbers is 39. When the number 31 is added to them, what is the new mean? (a) 39 (b) 37 (c) 35 (d) 38
10. 10.What is the mode of 17, 11, 11, 4, 9, 11 and 17? (a) 4 (b) 17 (c) 9 (d) 11
11. 11.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 52 cu cm (b) 6 cu cm (c) 9 cu cm (d) 24 cu cm
12. 12.What is the distance between the points (3, 8) and (9, 16)? (a) 11 (b) 100 (c) 14 (d) 10
13. 13.In which quadrant does the point (−1, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
14. 14.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 21 (c) 18 (d) 6
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 15 (b) 16 (c) 5 (d) 14
16. 16.What is the mean of 16, 5, 3 and 20? (a) 13 (b) 10 (c) 11 (d) 12
17. 17.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 150° (d) 125°
18. 18.What is the median of 17, 8, 20, 4, 27, 39 and 5? (a) 8 (b) 17 (c) 20 (d) 4
19. 19.How many factors does 49 have? (a) 2 (b) 1 (c) 4 (d) 3
20. 20.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
21. 21.In a class of 33 children, 19 like maths, 11 like science and 4 like both. How many like neither? (a) 3 (b) 11 (c) 4 (d) 7
22. 22.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
23. 23.What is the median of 17, 39, 31, 16 and 34? (a) 34 (b) 17 (c) 32 (d) 31
24. 24.A bag has 12 yellow balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 6 (d) 17
25. 25.A drawer has lots of red, 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) 5 (b) 10 (c) 6 (d) 2
26. 26.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
27. 27.A bag has 3 red 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) 2 (b) 12 (c) 4 (d) 14
28. 28.What is the distance between the points (3, 14) and (15, 5)? (a) 225 (b) 16 (c) 15 (d) 21
29. 29.What is the median of 30, 21, 13, 8 and 5? (a) 14 (b) 8 (c) 13 (d) 21
30. 30.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 55 (b) 56 (c) 13 (d) 110
31. 31.Using (a − b)² = a² − 2ab + b², what is 89²? (a) 8099 (b) 8281 (c) 7921 (d) 7931
32. 32.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 30° (c) 120° (d) 60°
33. 33.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 145° (b) 120° (c) 95° (d) 85°
34. 34.If a + b = 10 and ab = 21, what is (a − b)²? (a) 58 (b) 100 (c) 4 (d) 16
35. 35.A cuboid is 8 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 208 sq cm (b) 192 sq cm (c) 104 sq cm (d) 416 sq cm
36. 36.Using (a − b)² = a² − 2ab + b², what is 75²? (a) 6375 (b) 5635 (c) 5625 (d) 7225
37. 37.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 14 (d) 42
38. 38.In a class of 41 children, 16 like dance, 17 like music and 2 like both. How many like at least one of the two? (a) 41 (b) 31 (c) 33 (d) 29
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 1/6 (c) 5/36 (d) 5/11
40. 40.What is the midpoint of the line joining (0, 18) and (8, 8)? (a) (13, 4) (b) (4, 5) (c) (8, 26) (d) (4, 13)

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