Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 87 · 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 angles of a triangle are 65° and 95°. What is the third angle? (a) 115° (b) 20° (c) 85° (d) 160°
2. 2.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
3. 3.Which is the correct factorisation of x² + 11x + 18? (a) (x − 2)(x − 9) (b) (x + 2)(x + 9) (c) (x + 1)(x + 10) (d) (x + 1)(x + 18)
4. 4.If a + b = 10 and ab = 21, what is a² + b²? (a) 100 (b) 79 (c) 142 (d) 58
5. 5.What is the mode of 5, 13, 9, 13, 5, 13 and 4? (a) 9 (b) 13 (c) 4 (d) 5
6. 6.A bag has 12 white balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 20 (b) 14 (c) 2 (d) 13
7. 7.What is the mean of 11, 10, 2, 2, 13 and 16? (a) 8 (b) 9 (c) 10 (d) 11
8. 8.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 21 (b) 20 (c) 22 (d) 25
9. 9.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
10. 10.Which term of the AP 5, 9, 13, 17, … is 125? (a) 30th (b) 33rd (c) 31st (d) 32nd
11. 11.In which quadrant does the point (−5, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
12. 12.How many prime numbers are there between 60 and 70? (a) 4 (b) 2 (c) 3 (d) 1
13. 13.What is the 39th term of the AP 20, 22, 24, 26, …? (a) 76 (b) 98 (c) 78 (d) 96
14. 14.How many factors does 64 have? (a) 5 (b) 8 (c) 7 (d) 6
15. 15.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 41° (c) 40° (d) 220°
16. 16.What is the distance between the points (8, 20) and (13, 8)? (a) 14 (b) 169 (c) 17 (d) 13
17. 17.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 7 (b) 9 (c) 8 (d) 6
18. 18.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
19. 19.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
20. 20.What is the midpoint of the line joining (0, 9) and (10, 17)? (a) (10, 26) (b) (13, 5) (c) (5, 13) (d) (5, 4)
21. 21.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 372 (c) 451 (d) 441
22. 22.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 15° (c) 85° (d) 110°
23. 23.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 140° (d) 50°
24. 24.In a class of 28 children, 19 like maths, 17 like science and 9 like both. How many like neither? (a) 10 (b) 9 (c) 1 (d) 2
25. 25.Which is the correct factorisation of x² + 9x + 14? (a) (x − 2)(x − 7) (b) (x + 2)(x + 7) (c) (x + 1)(x + 8) (d) (x + 1)(x + 14)
26. 26.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) 18 (b) 54 (c) 6 (d) 21
27. 27.A bag has 9 yellow balls and 10 red 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) 19 (c) 10 (d) 11
28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 20 (b) 8 (c) 19 (d) 18
29. 29.A drawer has lots of blue 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) 3 (c) 2 (d) 4
30. 30.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
31. 31.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
32. 32.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
33. 33.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
34. 34.A cuboid is 11 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 19 cu cm (b) 200 cu cm (c) 66 cu cm (d) 132 cu cm
35. 35.A bag has 11 yellow balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 12 (c) 13 (d) 15
36. 36.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
37. 37.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 216 (b) 112 (c) 17 (d) 108
38. 38.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 160° (b) 80° (c) 120° (d) 100°
39. 39.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 75° (d) 110°
40. 40.What is the midpoint of the line joining (3, 14) and (11, 2)? (a) (14, 16) (b) (7, 8) (c) (8, 7) (d) (4, 6)

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