Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 59 · 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. 1.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 11 (b) 56 (c) 28 (d) 32
2. 2.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 7/8 (d) 3/8
3. 3.How many prime numbers are there between 90 and 120? (a) 8 (b) 7 (c) 5 (d) 6
4. 4.What is the product of the roots of x² − 7x + 12 = 0? (a) 12 (b) 13 (c) 7 (d) 11
5. 5.What is the median of 26, 8, 7, 33 and 37? (a) 33 (b) 7 (c) 26 (d) 8
6. 6.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
7. 7.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 1)(x + 14) (c) (x + 1)(x + 56) (d) (x + 7)(x + 8)
8. 8.What is the smallest prime factor of 51? (a) 17 (b) 3 (c) 1 (d) 2
9. 9.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
10. 10.A bag has 8 white, 2 blue and 8 green balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 17/18 (b) 8/9 (c) 1/3 (d) 1/9
11. 11.A bag has 11 black balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 17 (c) 13 (d) 12
12. 12.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
14. 14.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4
15. 15.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 398 (c) 490 (d) 489
16. 16.In a class of 32 children, 24 like mangoes, 12 like bananas and 2 like neither. How many like both? (a) 30 (b) 6 (c) 4 (d) 2
17. 17.How many prime numbers are there between 90 and 110? (a) 7 (b) 4 (c) 5 (d) 6
18. 18.In a class of 34 children, 20 like dance, 10 like music and 6 like both. How many like at least one of the two? (a) 18 (b) 30 (c) 34 (d) 24
19. 19.A drawer has lots of blue, green, yellow, 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) 10 (b) 2 (c) 5 (d) 6
20. 20.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
21. 21.What is the median of 22, 3, 36, 10 and 35? (a) 35 (b) 36 (c) 22 (d) 10
22. 22.Two angles of a triangle are 45° and 80°. What is the third angle? (a) 55° (b) 125° (c) 135° (d) 100°
23. 23.A bag has 5 black balls and 6 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) 6 (c) 7 (d) 11
24. 24.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 40° (c) 20° (d) 140°
25. 25.How many factors does 23 have? (a) 2 (b) 1 (c) 3 (d) 4
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 18 (b) 19 (c) 17 (d) 7
27. 27.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 63 (c) 64 (d) 54
28. 28.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
29. 29.What is the 40th term of the AP 2, 4, 6, 8, …? (a) 80 (b) 78 (c) 82 (d) 81
30. 30.A bag has 9 red, 9 white and 3 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 19/21 (c) 1/7 (d) 6/7
31. 31.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 5 (d) 6
32. 32.How many factors does 25 have? (a) 1 (b) 4 (c) 2 (d) 3
33. 33.What is the midpoint of the line joining (7, 3) and (11, 1)? (a) (18, 4) (b) (2, 1) (c) (9, 2) (d) (2, 9)
34. 34.What is the midpoint of the line joining (3, 10) and (5, 12)? (a) (8, 22) (b) (4, 11) (c) (11, 4) (d) (1, 1)
35. 35.In which quadrant does the point (−6, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 15 (d) 16
37. 37.The mean of 8 numbers is 33. When the number 69 is added to them, what is the new mean? (a) 51 (b) 37 (c) 33 (d) 38
38. 38.A bag has 6 green balls and 3 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) 7 (c) 4 (d) 9
39. 39.A drawer has lots of yellow, green, blue 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) 8 (b) 5 (c) 4 (d) 2
40. 40.If a + b = 20 and ab = 99, what is a² + b²? (a) 400 (b) 202 (c) 598 (d) 301

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