Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 868 · 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 straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 310° (c) 40° (d) 130°
2. 2.What is the mode of 18, 1, 1, 18, 5, 4 and 18? (a) 5 (b) 1 (c) 18 (d) 4
3. 3.In a class of 35 children, 14 like dance, 21 like music and 5 like neither. How many like both? (a) 4 (b) 5 (c) 6 (d) 30
4. 4.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
5. 5.A drawer has lots of white, red 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) 2 (b) 3 (c) 4 (d) 6
6. 6.What is the sum of the roots of x² − 12x + 32 = 0? (a) 32 (b) 12 (c) 11 (d) 13
7. 7.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 23 (c) 69 (d) 72
8. 8.Using (a + b)² = a² + 2ab + b², what is 51²? (a) 2601 (b) 2401 (c) 2611 (d) 2501
9. 9.8 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 32 (c) 11 (d) 48
10. 10.In a class of 25 children, 13 like tea, 16 like coffee and 4 like neither. How many like both? (a) 8 (b) 9 (c) 21 (d) 4
11. 11.How many factors does 89 have? (a) 1 (b) 3 (c) 4 (d) 2
12. 12.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 90 (d) 20
13. 13.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 864 sq cm (c) 144 sq cm (d) 1728 sq cm
14. 14.What is the 18th term of the AP 6, 8, 10, 12, …? (a) 40 (b) 36 (c) 34 (d) 42
15. 15.What is the median of 18, 14, 39, 13, 40, 21 and 11? (a) 18 (b) 13 (c) 21 (d) 14
16. 16.What is the midpoint of the line joining (7, 10) and (9, 18)? (a) (14, 8) (b) (8, 14) (c) (16, 28) (d) (1, 4)
17. 17.A bag has 7 red balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 9 (c) 12 (d) 8
18. 18.If a + b = 9 and ab = 18, what is (a − b)²? (a) 3 (b) 81 (c) 9 (d) 45
19. 19.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 28 (b) 27 (c) 30 (d) 26
20. 20.What are the roots of x² − 14x + 45 = 0? (a) 3 and 15 (b) 1 and 13 (c) 1 and 45 (d) 5 and 9
21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 15 (b) 16 (c) 4 (d) 14
22. 22.A drawer has lots of yellow, red 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) 6 (b) 3 (c) 2 (d) 4
23. 23.What is the mean of 12, 6, 16 and 14? (a) 16 (b) 12 (c) 13 (d) 11
24. 24.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 270° (c) 90° (d) 120°
25. 25.How many factors does 102 have? (a) 8 (b) 7 (c) 9 (d) 6
26. 26.What is the sum of all the whole numbers from 1 to 52? (a) 1378 (b) 1326 (c) 2756 (d) 1352
27. 27.A bag has 12 black balls and 10 green 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) 11 (c) 13 (d) 22
28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 17 (d) 18
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/18 (c) 1/36 (d) 1/12
30. 30.What is the sum of the roots of x² − 17x + 72 = 0? (a) 18 (b) 72 (c) 17 (d) 16
31. 31.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) 29 (c) 28 (d) 22
32. 32.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/3 (d) 1/4
33. 33.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 30 (d) 15
34. 34.In a class of 20 children, 7 like mangoes, 12 like bananas and 3 like both. How many like only mangoes? (a) 4 (b) 7 (c) 9 (d) 8
35. 35.How many prime numbers are there between 90 and 100? (a) 1 (b) 2 (c) 0 (d) 3
36. 36.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 384 sq cm (c) 512 sq cm (d) 64 sq cm
37. 37.How many factors does 67 have? (a) 3 (b) 4 (c) 2 (d) 1
38. 38.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 24 sq cm (d) 8 sq cm
39. 39.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 16 (d) 12
40. 40.What is the missing term in the AP 6, 13, 20, ?, 34? (a) 28 (b) 34 (c) 27 (d) 26

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