Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 446 · 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.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
2. 2.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
3. 3.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 5 (c) 4 (d) 3
5. 5.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 225 (d) 29
6. 6.How many prime numbers are there between 80 and 100? (a) 4 (b) 5 (c) 2 (d) 3
7. 7.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 75° (c) 30° (d) 150°
8. 8.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 140 (c) 149 (d) 158
9. 9.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 110° (b) 105° (c) 70° (d) 145°
10. 10.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 211 (c) 212 (d) 210
11. 11.The mean of 3 numbers is 36. When the number 48 is added to them, what is the new mean? (a) 36 (b) 42 (c) 39 (d) 40
12. 12.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
13. 13.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
14. 14.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
15. 15.What is the mode of 2, 3, 3, 8, 8, 11 and 8? (a) 8 (b) 2 (c) 3 (d) 11
16. 16.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) 12 (d) 25
17. 17.In a class of 36 children, 16 like dance, 25 like music and 6 like neither. How many like both? (a) 30 (b) 6 (c) 11 (d) 5
18. 18.A bag has 5 white, 4 yellow and 9 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 5/18 (c) 7/9 (d) 13/18
19. 19.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 6 (d) 12
20. 20.How many prime numbers are there between 60 and 70? (a) 3 (b) 2 (c) 1 (d) 4
21. 21.A bag has 10 green balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 20 (c) 11 (d) 12
22. 22.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
23. 23.A drawer has lots of yellow, 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) 6 (b) 3 (c) 2 (d) 4
24. 24.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
25. 25.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 66 (c) 55 (d) 121
26. 26.How many factors does 45 have? (a) 6 (b) 7 (c) 5 (d) 4
27. 27.How many factors does 40 have? (a) 7 (b) 6 (c) 9 (d) 8
28. 28.In a class of 32 children, 19 like dance, 5 like music and 10 like neither. How many like both? (a) 2 (b) 3 (c) 22 (d) 10
29. 29.What is the 12th term of the AP 15, 21, 27, 33, …? (a) 81 (b) 72 (c) 87 (d) 66
30. 30.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
31. 31.A bag has 5 white balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 11 (c) 15 (d) 2
32. 32.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 90 (d) 100
33. 33.A bag has 7 green balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 9 (c) 14 (d) 2
34. 34.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 160° (b) 115° (c) 135° (d) 65°
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
36. 36.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6734 (b) 6404 (c) 6724 (d) 6084
37. 37.What is the mode of 7, 5, 8, 12, 12, 12 and 5? (a) 5 (b) 7 (c) 8 (d) 12
38. 38.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 240 (d) 25
39. 39.A bag has 10 red balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 14 (b) 2 (c) 12 (d) 11
40. 40.What is the median of 20, 28, 31, 22, 27, 40 and 32? (a) 22 (b) 27 (c) 28 (d) 31

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