Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 257 · 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.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 215° (d) 36°
2. 2.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
3. 3.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 90° (b) 270° (c) 140° (d) 130°
4. 4.How many factors does 76 have? (a) 6 (b) 7 (c) 4 (d) 5
5. 5.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) 24 (b) 25 (c) 12 (d) 13
6. 6.A bag has 2 green, 7 blue and 3 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/12 (b) 1/4 (c) 3/4 (d) 1/3
7. 7.A bag has 9 white, 9 blue and 3 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 3/4 (b) 4/7 (c) 1/3 (d) 3/7
8. 8.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 15 (c) 36 (d) 12
9. 9.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 72 (c) 90 (d) 81
10. 10.A bag has 4 blue, 7 white and 8 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 13/19 (c) 7/19 (d) 12/19
11. 11.A drawer has lots of green, blue 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) 2 (b) 4 (c) 6 (d) 3
12. 12.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
13. 13.A bag has 7 white balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 11 (c) 2 (d) 5
14. 14.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 42 (c) 32 (d) 50
15. 15.What is the mean of 18, 16, 2, 11, 19 and 18? (a) 15 (b) 13 (c) 14 (d) 12
16. 16.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 209 (b) 396 (c) 198 (d) 28
17. 17.What is the midpoint of the line joining (6, 18) and (10, 8)? (a) (13, 8) (b) (8, 13) (c) (16, 26) (d) (2, 5)
18. 18.In which quadrant does the point (7, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
19. 19.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 125° (d) 85°
20. 20.What is the mean of 9, 11, 14 and 10? (a) 11 (b) 12 (c) 13 (d) 10
21. 21.What is the median of 3, 1, 25, 34, 17, 33 and 37? (a) 25 (b) 17 (c) 33 (d) 34
22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
23. 23.In a class of 35 children, 21 like dance, 13 like music and 4 like both. How many like at least one of the two? (a) 30 (b) 35 (c) 26 (d) 34
24. 24.If a + b = 4 and ab = 3, what is (a − b)²? (a) 16 (b) 10 (c) 4 (d) 2
25. 25.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 22 (c) 121 (d) 110
26. 26.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2⁴ × 3 × 7 (c) 2³ × 3 × 7 (d) 2² × 3 × 7
27. 27.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 1/4 (c) 5/8 (d) 3/5
28. 28.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
29. 29.How many factors does 111 have? (a) 5 (b) 4 (c) 2 (d) 3
30. 30.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
31. 31.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1275 (c) 1250 (d) 1225
32. 32.If a + b = 19 and ab = 90, what is a² + b²? (a) 271 (b) 541 (c) 181 (d) 361
33. 33.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 140° (b) 80° (c) 220° (d) 40°
34. 34.A bag has 5 yellow balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 16 (b) 7 (c) 2 (d) 6
35. 35.A bag has 4 white balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 2 (c) 6 (d) 15
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/12 (d) 1/11
37. 37.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 48 (d) 16
38. 38.What is the midpoint of the line joining (3, 5) and (5, 9)? (a) (4, 7) (b) (7, 4) (c) (8, 14) (d) (1, 2)
39. 39.What is the median of 15, 14, 6, 33, 35, 29 and 11? (a) 29 (b) 33 (c) 15 (d) 14
40. 40.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 280° (c) 140° (d) 100°

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