Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 506 · 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.A bag has 5 white balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 7 (c) 6 (d) 16
2. 2.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 444 (b) 222 (c) 240 (d) 35
3. 3.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 392 (c) 812 (d) 406
4. 4.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 150° (d) 30°
5. 5.4 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) 12 (b) 16 (c) 7 (d) 24
6. 6.If a + b = 16 and ab = 60, what is (a − b)²? (a) 256 (b) 136 (c) 16 (d) 4
7. 7.What is the smallest prime factor of 143? (a) 2 (b) 11 (c) 13 (d) 1
8. 8.What is the distance between the points (5, 1) and (17, 17)? (a) 21 (b) 20 (c) 28 (d) 400
9. 9.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
10. 10.How many prime numbers are there between 60 and 90? (a) 9 (b) 6 (c) 7 (d) 8
11. 11.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
12. 12.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
13. 13.There are 8 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) 24 (b) 32 (c) 11 (d) 48
14. 14.What is the 14th term of the AP 8, 14, 20, 26, …? (a) 78 (b) 84 (c) 92 (d) 86
15. 15.A bag has 4 red, 8 blue and 5 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 9/17 (b) 8/17 (c) 10/17 (d) 1/3
16. 16.The mean of 3 numbers is 25. When the number 13 is added to them, what is the new mean? (a) 25 (b) 22 (c) 19 (d) 23
17. 17.A drawer has lots of green, black 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) 4 (b) 6 (c) 2 (d) 3
18. 18.In a class of 47 children, 19 like mangoes, 27 like bananas and 7 like both. How many like neither? (a) 7 (b) 15 (c) 1 (d) 8
19. 19.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 75° (c) 145° (d) 105°
20. 20.3 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 15 (b) 8 (c) 18 (d) 30
21. 21.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 11) (b) (x + 1)(x + 32) (c) (x + 4)(x + 8) (d) (x − 4)(x − 8)
22. 22.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
23. 23.In a class of 39 children, 21 like tea, 20 like coffee and 7 like both. How many like at least one of the two? (a) 27 (b) 34 (c) 39 (d) 41
24. 24.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
25. 25.What is the smallest prime factor of 65? (a) 1 (b) 2 (c) 13 (d) 5
26. 26.How many factors does 23 have? (a) 1 (b) 2 (c) 3 (d) 4
27. 27.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 85° (c) 95° (d) 110°
28. 28.Using (a + b)² = a² + 2ab + b², what is 71²? (a) 4901 (b) 5051 (c) 5041 (d) 4761
29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 18 (d) 8
30. 30.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 90 (c) 100 (d) 45
31. 31.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 189 (c) 66 (d) 63
32. 32.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 70° (b) 150° (c) 100° (d) 110°
33. 33.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 29 (d) 120
34. 34.Two angles of a triangle are 55° and 75°. What is the third angle? (a) 130° (b) 50° (c) 125° (d) 105°
35. 35.In which quadrant does the point (−8, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
36. 36.A drawer has lots of black, blue, white, yellow 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) 5 (b) 2 (c) 6 (d) 10
37. 37.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 14 (c) 49 (d) 42
38. 38.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 2/3 (c) 1/4 (d) 1/2
39. 39.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 100 (d) 45
40. 40.In a class of 27 children, 21 like mangoes, 15 like bananas and 12 like both. How many like at least one of the two? (a) 27 (b) 36 (c) 24 (d) 12

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