Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 685 · 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 smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 24 (c) 25 (d) 12
2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 5 (b) 3 (c) 4 (d) 6
3. 3.What are the roots of x² − 5x + 6 = 0? (a) 1 and 4 (b) 1 and 6 (c) 2 and 3 (d) 2 and 4
4. 4.In a class of 44 children, 28 like tea, 20 like coffee and 9 like both. How many like only tea? (a) 11 (b) 24 (c) 28 (d) 19
5. 5.What is the smallest prime factor of 57? (a) 19 (b) 1 (c) 3 (d) 2
6. 6.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
7. 7.In a class of 30 children, 8 like tea, 18 like coffee and 6 like neither. How many like both? (a) 6 (b) 24 (c) 3 (d) 2
8. 8.What is the 10th term of the AP 5, 11, 17, 23, …? (a) 59 (b) 65 (c) 54 (d) 60
9. 9.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
10. 10.If a + b = 14 and ab = 48, what is (a − b)²? (a) 100 (b) 4 (c) 196 (d) 2
11. 11.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/3 (c) 1/4 (d) 2/3
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
13. 13.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 64 sq cm (c) 384 sq cm (d) 512 sq cm
14. 14.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 65° (b) 115° (c) 105° (d) 140°
15. 15.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) 22 (b) 29 (c) 21 (d) 28
16. 16.In a class of 43 children, 29 like tea, 22 like coffee and 10 like both. How many like only tea? (a) 29 (b) 21 (c) 12 (d) 19
17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20
18. 18.In which quadrant does the point (7, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
19. 19.What is the midpoint of the line joining (0, 3) and (4, 5)? (a) (4, 2) (b) (4, 8) (c) (2, 4) (d) (2, 1)
20. 20.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 275 (b) 40 (c) 278 (d) 550
21. 21.What is the median of 9, 8, 7, 30, 29, 28 and 19? (a) 19 (b) 9 (c) 28 (d) 30
22. 22.In which quadrant does the point (9, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
23. 23.Using (a − b)² = a² − 2ab + b², what is 79²? (a) 6561 (b) 6399 (c) 6251 (d) 6241
24. 24.The mean of 4 numbers is 22. When the number 12 is added to them, what is the new mean? (a) 17 (b) 22 (c) 21 (d) 20
25. 25.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 8)(x + 9) (c) (x + 1)(x + 16) (d) (x + 1)(x + 72)
26. 26.What is the distance between the points (4, 8) and (13, 20)? (a) 16 (b) 15 (c) 225 (d) 21
27. 27.How many prime numbers are there between 60 and 90? (a) 7 (b) 9 (c) 6 (d) 8
28. 28.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
29. 29.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 100° (b) 145° (c) 115° (d) 35°
30. 30.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 50 (c) 26 (d) 25
31. 31.What is the mode of 6, 17, 17, 8, 16, 16 and 16? (a) 17 (b) 8 (c) 16 (d) 6
32. 32.What is the mean of 20, 4, 8 and 20? (a) 14 (b) 12 (c) 13 (d) 15
33. 33.Which is the correct factorisation of x² + 9x + 14? (a) (x + 1)(x + 14) (b) (x + 1)(x + 8) (c) (x + 2)(x + 7) (d) (x − 2)(x − 7)
34. 34.In which quadrant does the point (7, 6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
35. 35.A drawer has lots of black, green 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) 2 (b) 6 (c) 3 (d) 4
36. 36.What is the midpoint of the line joining (2, 12) and (12, 10)? (a) (5, 1) (b) (7, 11) (c) (14, 22) (d) (11, 7)
37. 37.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
38. 38.What is the mean of 19, 16, 11 and 6? (a) 13 (b) 14 (c) 15 (d) 12
39. 39.The mean of 5 numbers is 38. When the number 62 is added to them, what is the new mean? (a) 50 (b) 38 (c) 43 (d) 42
40. 40.In which quadrant does the point (−7, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

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