Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 979 · 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 bag has 6 blue, 7 white and 3 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 5/8 (b) 7/16 (c) 1/3 (d) 9/16
2. 2.What is the mode of 6, 10, 3, 6, 3, 17 and 6? (a) 10 (b) 6 (c) 17 (d) 3
3. 3.In a class of 32 children, 13 like cricket, 20 like football and 2 like both. How many like neither? (a) 0 (b) 1 (c) 3 (d) 2
4. 4.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/2 (c) 1/4 (d) 1/3
5. 5.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 14) (b) (x − 6)(x − 9) (c) (x + 1)(x + 54) (d) (x + 6)(x + 9)
6. 6.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) 28 (b) 29 (c) 21 (d) 22
7. 7.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 24 (c) 32 (d) 48
8. 8.How many prime numbers are there between 10 and 40? (a) 8 (b) 9 (c) 7 (d) 10
9. 9.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 132 (c) 144 (d) 66
10. 10.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
11. 11.What is the smallest prime factor of 143? (a) 1 (b) 2 (c) 11 (d) 13
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
13. 13.A bag has 4 red balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 4 (c) 2 (d) 5
14. 14.A drawer has lots of black, yellow, green 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) 4 (b) 8 (c) 2 (d) 5
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 month? (a) 48 (b) 36 (c) 49 (d) 37
16. 16.The mean of 4 numbers is 22. When the number 17 is added to them, what is the new mean? (a) 21 (b) 23 (c) 20 (d) 22
17. 17.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
18. 18.What is the mode of 10, 8, 15, 10, 1, 10 and 1? (a) 10 (b) 8 (c) 15 (d) 1
19. 19.In a class of 37 children, 21 like maths, 15 like science and 9 like both. How many like neither? (a) 10 (b) 9 (c) 19 (d) 1
20. 20.A bag has 5 blue, 5 green and 9 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 5/19 (b) 1/3 (c) 14/19 (d) 5/14
21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/11 (d) 1/12
23. 23.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 130 (b) 19 (c) 68 (d) 65
24. 24.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
25. 25.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
26. 26.A bag has 3 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) 2 (b) 9 (c) 4 (d) 7
27. 27.Which is the correct factorisation of x² + 14x + 45? (a) (x + 1)(x + 45) (b) (x − 5)(x − 9) (c) (x + 5)(x + 9) (d) (x + 1)(x + 13)
28. 28.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
29. 29.What is the mean of 6, 7, 3, 5, 11 and 22? (a) 8 (b) 10 (c) 11 (d) 9
30. 30.In which quadrant does the point (−5, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
31. 31.What are the roots of x² − 16x + 63 = 0? (a) 3 and 21 (b) 1 and 15 (c) 7 and 9 (d) 1 and 63
32. 32.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
33. 33.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 249 (c) 238 (d) 240
34. 34.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
35. 35.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
36. 36.A bag has 11 white balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 12 (b) 23 (c) 13 (d) 2
37. 37.Which is the correct factorisation of x² + 8x + 12? (a) (x + 2)(x + 6) (b) (x + 1)(x + 12) (c) (x − 2)(x − 6) (d) (x + 1)(x + 7)
38. 38.A bag has 3 green balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 2 (c) 7 (d) 5
39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 5 (c) 4 (d) 2
40. 40.A cuboid is 8 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 16 cu cm (b) 152 cu cm (c) 96 cu cm (d) 48 cu cm

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