Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 199 · 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. 1.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 20 (d) 15
2. 2.In a class of 37 children, 20 like maths, 19 like science and 11 like both. How many like only maths? (a) 20 (b) 9 (c) 8 (d) 18
3. 3.How many factors does 106 have? (a) 3 (b) 5 (c) 2 (d) 4
4. 4.What is the sum of the roots of x² − 17x + 72 = 0? (a) 18 (b) 72 (c) 16 (d) 17
5. 5.What is the distance between the points (1, 12) and (7, 4)? (a) 10 (b) 14 (c) 11 (d) 100
6. 6.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
7. 7.In a class of 36 children, 20 like cricket, 20 like football and 7 like neither. How many like both? (a) 29 (b) 11 (c) 7 (d) 4
8. 8.What is the 26th term of the AP 18, 26, 34, 42, …? (a) 226 (b) 200 (c) 208 (d) 218
9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 7 (b) 16 (c) 17 (d) 18
10. 10.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
11. 11.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 145° (b) 215° (c) 35° (d) 70°
12. 12.The mean of 8 numbers is 39. When the number 30 is added to them, what is the new mean? (a) 38 (b) 37 (c) 40 (d) 39
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/18 (c) 1/36 (d) 1/12
14. 14.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 170° (c) 11° (d) 190°
15. 15.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 145° (b) 105° (c) 75° (d) 140°
16. 16.The mean of 5 numbers is 22. When the number 28 is added to them, what is the new mean? (a) 22 (b) 24 (c) 25 (d) 23
17. 17.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 145° (b) 70° (c) 105° (d) 110°
18. 18.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3³
19. 19.Using (a + b)² = a² + 2ab + b², what is 103²? (a) 10009 (b) 9409 (c) 10619 (d) 10609
20. 20.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 48 (d) 12
21. 21.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 150° (c) 330° (d) 30°
22. 22.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 80° (b) 130° (c) 150° (d) 100°
23. 23.In a class of 28 children, 19 like cricket, 11 like football and 3 like both. How many like at least one of the two? (a) 24 (b) 28 (c) 27 (d) 30
24. 24.6 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 36 (c) 12 (d) 72
25. 25.What is the 35th term of the AP 8, 14, 20, 26, …? (a) 204 (b) 218 (c) 210 (d) 212
26. 26.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
27. 27.In a class of 43 children, 28 like dance, 19 like music and 10 like both. How many like neither? (a) 6 (b) 7 (c) 16 (d) 10
28. 28.A bag has 5 green balls and 6 red 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) 7 (d) 2
29. 29.A bag has 2 red, 4 blue and 3 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 8/9 (c) 7/9 (d) 2/9
30. 30.In a class of 40 children, 32 like maths, 16 like science and 12 like both. How many like only maths? (a) 4 (b) 32 (c) 24 (d) 20
31. 31.How many factors does 13 have? (a) 2 (b) 3 (c) 4 (d) 1
32. 32.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 134 (c) 125 (d) 126
33. 33.A bag has 6 blue, 2 red and 4 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/2 (b) 1/12 (c) 7/12 (d) 1/3
34. 34.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 81 (c) 18 (d) 36
35. 35.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)
36. 36.6 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 18 (b) 24 (c) 9 (d) 36
37. 37.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 25 (d) 120
38. 38.What is the median of 26, 18, 9, 16, 24, 2 and 6? (a) 18 (b) 17 (c) 9 (d) 16
39. 39.In which quadrant does the point (4, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
40. 40.In a class of 39 children, 15 like dance, 24 like music and 8 like both. How many like neither? (a) 16 (b) 0 (c) 9 (d) 8

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