Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 129 · 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. 1.4 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) 28 (b) 24 (c) 10 (d) 48
2. 2.What is the median of 39, 7, 17, 38 and 6? (a) 17 (b) 18 (c) 38 (d) 7
3. 3.What is the prime factorisation of 20? (a) 2 × 5 (b) 2³ × 5 (c) 2 × 5² (d) 2² × 5
4. 4.In a class of 43 children, 22 like dance, 25 like music and 11 like both. How many like only dance? (a) 11 (b) 14 (c) 22 (d) 18
5. 5.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 80° (c) 40° (d) 50°
6. 6.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 3/8 (c) 1/4 (d) 1/8
7. 7.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 160° (c) 45° (d) 155°
8. 8.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 25° (d) 35°
9. 9.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1849 (b) 1591 (c) 1379 (d) 1369
10. 10.If a + b = 12 and ab = 20, what is (a − b)²? (a) 64 (b) 144 (c) 8 (d) 104
11. 11.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 240 (c) 243 (d) 253
12. 12.What is the distance between the points (4, 6) and (20, 18)? (a) 400 (b) 20 (c) 21 (d) 28
13. 13.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 1/9 (d) 4/11
15. 15.There are 7 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 42 (b) 21 (c) 10 (d) 28
16. 16.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 20 (c) 8 (d) 30
17. 17.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 100° (b) 155° (c) 80° (d) 125°
18. 18.What is the distance between the points (4, 5) and (13, 17)? (a) 225 (b) 15 (c) 16 (d) 21
19. 19.How many prime numbers are there between 60 and 80? (a) 4 (b) 5 (c) 7 (d) 6
20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 3 (b) 14 (c) 15 (d) 13
21. 21.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 25 (b) 26 (c) 32 (d) 24
22. 22.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 2/3 (d) 1/2
23. 23.In which quadrant does the point (−7, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
24. 24.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) 25 (c) 24 (d) 12
25. 25.A bag has 9 blue, 7 green and 3 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 11/19 (c) 10/19 (d) 9/19
26. 26.What is the mean of 9, 15, 2 and 14? (a) 9 (b) 8 (c) 11 (d) 10
27. 27.What is the midpoint of the line joining (4, 5) and (8, 3)? (a) (6, 4) (b) (2, 1) (c) (4, 6) (d) (12, 8)
28. 28.A bag has 11 red balls and 7 white 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) 12 (c) 2 (d) 18
29. 29.A bag has 9 black balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 2 (c) 10 (d) 6
30. 30.What is the 15th term of the AP 20, 23, 26, 29, …? (a) 45 (b) 42 (c) 62 (d) 65
31. 31.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
32. 32.There are 5 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 25 (b) 20 (c) 9 (d) 40
33. 33.In a class of 47 children, 19 like maths, 26 like science and 8 like both. How many like only maths? (a) 18 (b) 11 (c) 21 (d) 19
34. 34.5 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 25 (b) 40 (c) 20 (d) 9
35. 35.A bag has 8 white balls and 5 black 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) 13 (c) 9 (d) 2
36. 36.There are 8 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) 24 (b) 10 (c) 32 (d) 16
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 6/11 (c) 7/36 (d) 1/6
38. 38.In a class of 31 children, 16 like tea, 9 like coffee and 2 like both. How many like at least one of the two? (a) 23 (b) 25 (c) 21 (d) 31
39. 39.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 15 (c) 21 (d) 30
40. 40.A bag has 3 yellow, 9 red and 5 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 12/17 (b) 5/12 (c) 1/3 (d) 5/17

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