Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 681 · 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.A drawer has lots of white, green, red 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) 2 (c) 8 (d) 4
2. 2.What are the roots of x² − 8x + 15 = 0? (a) 1 and 7 (b) 3 and 5 (c) 1 and 15 (d) 2 and 6
3. 3.What is the distance between the points (5, 2) and (11, 10)? (a) 14 (b) 10 (c) 11 (d) 100
4. 4.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
5. 5.A bag has 7 yellow, 7 green and 4 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 11/18 (b) 7/11 (c) 7/18 (d) 1/3
6. 6.In a class of 49 children, 26 like maths, 26 like science and 6 like both. How many like only maths? (a) 6 (b) 23 (c) 26 (d) 20
7. 7.What is the median of 36, 18, 4, 33 and 6? (a) 33 (b) 4 (c) 6 (d) 18
8. 8.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
9. 9.What is the mode of 2, 12, 19, 6, 19, 19 and 12? (a) 12 (b) 6 (c) 2 (d) 19
10. 10.What is the median of 5, 13, 40, 9 and 17? (a) 13 (b) 40 (c) 17 (d) 9
11. 11.What are the roots of x² − 9x + 20 = 0? (a) 1 and 8 (b) 4 and 5 (c) 1 and 20 (d) 2 and 10
12. 12.Which is the correct factorisation of x² + 5x + 6? (a) (x + 1)(x + 6) (b) (x + 2)(x + 3) (c) (x + 1)(x + 4) (d) (x − 2)(x − 3)
13. 13.What is the median of 40, 15, 9, 35 and 14? (a) 35 (b) 9 (c) 14 (d) 15
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
15. 15.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 16 (d) 24
16. 16.Which is the correct factorisation of x² + 13x + 40? (a) (x + 5)(x + 8) (b) (x + 1)(x + 40) (c) (x − 5)(x − 8) (d) (x + 1)(x + 12)
17. 17.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
18. 18.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 145° (d) 75°
19. 19.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 756 (d) 729
20. 20.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 55 (d) 121
21. 21.A bag has 10 red balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 22 (d) 13
22. 22.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 216 (b) 408 (c) 204 (d) 28
23. 23.What is the distance between the points (3, 9) and (11, 24)? (a) 18 (b) 289 (c) 23 (d) 17
24. 24.3 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) 18 (b) 12 (c) 6 (d) 9
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
26. 26.In a class of 31 children, 18 like maths, 10 like science and 7 like both. How many like only maths? (a) 18 (b) 21 (c) 3 (d) 11
27. 27.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
28. 28.In a class of 38 children, 17 like mangoes, 22 like bananas and 5 like neither. How many like both? (a) 1 (b) 6 (c) 5 (d) 33
29. 29.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 8 (c) 7 (d) 15
30. 30.What is the midpoint of the line joining (2, 14) and (12, 2)? (a) (5, 6) (b) (7, 8) (c) (14, 16) (d) (8, 7)
31. 31.In which quadrant does the point (2, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
32. 32.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 2/3 (c) 5/6 (d) 1/3
33. 33.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 24 (c) 75 (d) 72
34. 34.What is the product of the roots of x² − 7x + 10 = 0? (a) 10 (b) 7 (c) 9 (d) 11
35. 35.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 37 (b) 49 (c) 36 (d) 48
36. 36.Two angles of a triangle are 25° and 60°. What is the third angle? (a) 95° (b) 85° (c) 155° (d) 120°
37. 37.In a class of 31 children, 20 like tea, 15 like coffee and 9 like both. How many like at least one of the two? (a) 17 (b) 26 (c) 35 (d) 31
38. 38.In a class of 49 children, 32 like mangoes, 19 like bananas and 12 like both. How many like neither? (a) 22 (b) 12 (c) 11 (d) 10
39. 39.A bag has 4 blue balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 6 (b) 13 (c) 5 (d) 2
40. 40.What is the median of 10, 15, 38, 21, 36, 26 and 37? (a) 21 (b) 26 (c) 36 (d) 27

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