Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 523 · 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 circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
2. 2.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 9 (c) 5 (d) 6
3. 3.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 48 (d) 16
4. 4.A bag has 9 white balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 16 (b) 2 (c) 10 (d) 11
5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
6. 6.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2³ × 3² (c) 2² × 3³ (d) 2² × 3²
7. 7.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 120° (c) 60° (d) 240°
8. 8.If a + b = 18 and ab = 80, what is a² + b²? (a) 484 (b) 244 (c) 324 (d) 164
9. 9.What is the smallest prime factor of 247? (a) 2 (b) 19 (c) 1 (d) 13
10. 10.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 600 cu cm (c) 1000 cu cm (d) 30 cu cm
11. 11.What are the roots of x² − 15x + 56 = 0? (a) 2 and 28 (b) 1 and 14 (c) 7 and 8 (d) 1 and 56
12. 12.How many factors does 96 have? (a) 13 (b) 11 (c) 12 (d) 10
13. 13.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
14. 14.In a class of 40 children, 18 like cricket, 21 like football and 2 like both. How many like neither? (a) 2 (b) 5 (c) 1 (d) 3
15. 15.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 66 (d) 144
16. 16.What is the mean of 20, 11, 17 and 8? (a) 15 (b) 16 (c) 14 (d) 13
17. 17.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 332 (c) 381 (d) 391
18. 18.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 100° (c) 40° (d) 80°
19. 19.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 10 (d) 20
20. 20.What is the median of 21, 2, 12, 32, 30, 40 and 15? (a) 32 (b) 15 (c) 21 (d) 30
21. 21.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 21 (c) 10 (d) 24
22. 22.How many factors does 114 have? (a) 7 (b) 6 (c) 9 (d) 8
23. 23.How many factors does 115 have? (a) 3 (b) 5 (c) 4 (d) 2
24. 24.In which quadrant does the point (−5, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
25. 25.In a class of 41 children, 26 like dance, 16 like music and 9 like both. How many like only dance? (a) 25 (b) 17 (c) 7 (d) 26
26. 26.A drawer has lots of blue, red and green 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) 3 (c) 6 (d) 2
27. 27.A drawer has lots of red 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) 4 (b) 2 (c) 5 (d) 3
28. 28.What is the product of the roots of x² − 10x + 24 = 0? (a) 25 (b) 23 (c) 24 (d) 10
29. 29.The mean of 8 numbers is 16. When the number 34 is added to them, what is the new mean? (a) 16 (b) 25 (c) 19 (d) 18
30. 30.A drawer has lots of red, white and yellow 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) 2 (c) 4 (d) 3
31. 31.How many factors does 79 have? (a) 2 (b) 1 (c) 3 (d) 4
32. 32.What is the prime factorisation of 14? (a) 2 × 7 (b) 2 × 7² (c) 2² × 7 (d) 2³ × 7
33. 33.There are 8 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 64 (b) 15 (c) 112 (d) 56
34. 34.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 135° (b) 105° (c) 60° (d) 120°
35. 35.In which quadrant does the point (5, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.How many factors does 49 have? (a) 1 (b) 2 (c) 4 (d) 3
37. 37.A bag has 4 green balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 15 (c) 5 (d) 6
38. 38.Which term of the AP 15, 20, 25, 30, … is 95? (a) 18th (b) 17th (c) 19th (d) 16th
39. 39.What is the median of 21, 14, 39, 26, 3, 35 and 38? (a) 35 (b) 21 (c) 26 (d) 27
40. 40.How many factors does 32 have? (a) 4 (b) 7 (c) 5 (d) 6

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