Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 2 · 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 circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
2. 2.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 25° (c) 130° (d) 50°
3. 3.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 12 (d) 36
4. 4.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 50° (c) 40° (d) 310°
5. 5.How many factors does 65 have? (a) 4 (b) 5 (c) 3 (d) 2
6. 6.How many factors does 72 have? (a) 13 (b) 11 (c) 10 (d) 12
7. 7.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 50° (c) 155° (d) 130°
8. 8.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
9. 9.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 120° (b) 105° (c) 135° (d) 45°
10. 10.What is the mode of 10, 12, 11, 19, 11, 19 and 19? (a) 19 (b) 11 (c) 12 (d) 10
11. 11.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) 54 (b) 57 (c) 18 (d) 162
12. 12.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 240 (d) 25
13. 13.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 110° (d) 70°
14. 14.What is the distance between the points (2, 2) and (18, 14)? (a) 28 (b) 400 (c) 21 (d) 20
15. 15.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
16. 16.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 10 (b) 16 (c) 11 (d) 12
17. 17.What is the product of the roots of x² − 12x + 32 = 0? (a) 31 (b) 12 (c) 33 (d) 32
18. 18.In a class of 19 children, 7 like dance, 13 like music and 2 like neither. How many like both? (a) 17 (b) 3 (c) 2 (d) 1
19. 19.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
20. 20.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x + 1)(x + 16) (c) (x − 8)(x − 9) (d) (x + 1)(x + 72)
21. 21.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) 21 (b) 22 (c) 28 (d) 29
22. 22.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 6 (c) 12 (d) 9
23. 23.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 12 (d) 16
24. 24.In a class of 27 children, 18 like dance, 15 like music and 9 like both. How many like neither? (a) 12 (b) 4 (c) 9 (d) 3
25. 25.What is the midpoint of the line joining (4, 5) and (6, 15)? (a) (10, 20) (b) (10, 5) (c) (1, 5) (d) (5, 10)
26. 26.In a class of 43 children, 19 like tea, 22 like coffee and 9 like neither. How many like both? (a) 7 (b) 34 (c) 9 (d) 8
27. 27.5 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 40 (b) 20 (c) 25 (d) 9
28. 28.What is the mean of 20, 13, 6 and 9? (a) 13 (b) 11 (c) 12 (d) 16
29. 29.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 155° (d) 110°
30. 30.What is the mean of 13, 18, 15, 5 and 9? (a) 13 (b) 15 (c) 12 (d) 10
31. 31.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 20° (d) 40°
32. 32.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 100° (c) 80° (d) 40°
33. 33.A drawer has lots of green, red, blue, 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) 5 (b) 10 (c) 2 (d) 6
34. 34.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 70 (c) 52 (d) 62
35. 35.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5³ (d) 2³ × 3² × 5
36. 36.In a class of 27 children, 15 like tea, 15 like coffee and 4 like both. How many like neither? (a) 5 (b) 4 (c) 1 (d) 2
37. 37.In a class of 25 children, 19 like mangoes, 9 like bananas and 4 like both. How many like only mangoes? (a) 16 (b) 5 (c) 15 (d) 19
38. 38.Using (a − b)² = a² − 2ab + b², what is 79²? (a) 6561 (b) 6251 (c) 6399 (d) 6241
39. 39.What is the distance between the points (1, 18) and (6, 6)? (a) 169 (b) 13 (c) 14 (d) 17
40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 42 (d) 21

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