Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 417 · 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 = 12 and ab = 27, what is (a − b)²? (a) 6 (b) 144 (c) 36 (d) 90
2. 2.How many prime numbers are there between 30 and 40? (a) 4 (b) 3 (c) 2 (d) 1
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
4. 4.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 55 (d) 110
5. 5.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 75° (c) 150° (d) 60°
6. 6.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 15 (b) 17 (c) 13 (d) 14
7. 7.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 69 (c) 66 (d) 198
8. 8.A bag has 5 green balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 11 (c) 2 (d) 7
9. 9.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
10. 10.In a class of 24 children, 12 like tea, 6 like coffee and 8 like neither. How many like both? (a) 2 (b) 8 (c) 16 (d) 3
11. 11.Using (a + b)² = a² + 2ab + b², what is 73²? (a) 4909 (b) 5339 (c) 4489 (d) 5329
12. 12.A drawer has lots of black and red 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) 4 (c) 2 (d) 3
13. 13.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 24 (c) 42 (d) 33
14. 14.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 11 (c) 30 (d) 36
15. 15.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 124 cu cm (b) 72 cu cm (c) 8 cu cm (d) 15 cu cm
16. 16.What is the distance between the points (3, 3) and (15, 19)? (a) 20 (b) 21 (c) 400 (d) 28
17. 17.A drawer has lots of yellow, green, black and white 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) 2 (c) 8 (d) 4
18. 18.What is the sum of the first 10 terms of the AP 7, 12, 17, …? (a) 320 (b) 590 (c) 52 (d) 295
19. 19.A bag has 3 red balls and 4 white 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) 5 (c) 7 (d) 4
20. 20.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 171 (c) 342 (d) 153
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/12 (d) 1/18
22. 22.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 36 (c) 39 (d) 108
23. 23.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 70 (b) 20 (c) 73 (d) 140
24. 24.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 140° (d) 155°
25. 25.What is the prime factorisation of 20? (a) 2 × 5² (b) 2² × 5 (c) 2 × 5 (d) 2³ × 5
26. 26.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 6 times (d) 2 times
27. 27.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 71° (c) 110° (d) 70°
28. 28.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 40° (d) 80°
29. 29.If a + b = 3 and ab = 2, what is a² + b²? (a) 9 (b) 13 (c) 7 (d) 5
30. 30.A bag has 3 blue balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 4 (b) 6 (c) 2 (d) 5
31. 31.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/6 (c) 6/11 (d) 1/11
33. 33.Which term of the AP 15, 21, 27, 33, … is 111? (a) 17th (b) 19th (c) 18th (d) 16th
34. 34.What is the distance between the points (0, 6) and (7, 30)? (a) 31 (b) 26 (c) 625 (d) 25
35. 35.A bag has 11 white balls and 9 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) 20 (c) 10 (d) 12
36. 36.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 1)(x + 16) (c) (x − 8)(x − 9) (d) (x + 8)(x + 9)
37. 37.What is the distance between the points (6, 13) and (14, 7)? (a) 10 (b) 11 (c) 100 (d) 14
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
39. 39.How many prime numbers are there between 80 and 100? (a) 5 (b) 4 (c) 3 (d) 2
40. 40.What is the midpoint of the line joining (0, 5) and (6, 17)? (a) (3, 6) (b) (3, 11) (c) (11, 3) (d) (6, 22)

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