Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 23 · 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.In a class of 31 children, 5 like cricket, 20 like football and 2 like both. How many like at least one of the two? (a) 21 (b) 31 (c) 23 (d) 25
2. 2.In a class of 45 children, 28 like dance, 28 like music and 12 like both. How many like only dance? (a) 12 (b) 16 (c) 17 (d) 28
3. 3.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 90° (b) 130° (c) 140° (d) 40°
4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 9 (b) 17 (c) 15 (d) 18
5. 5.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 28 (c) 11 (d) 32
6. 6.A cuboid is 10 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 95 sq cm (b) 190 sq cm (c) 380 sq cm (d) 150 sq cm
7. 7.How many prime numbers are there between 40 and 50? (a) 2 (b) 5 (c) 4 (d) 3
8. 8.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 100 sq cm (d) 150 sq cm
9. 9.A bag has 3 yellow balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 15 (b) 5 (c) 2 (d) 4
10. 10.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 48 (d) 24
11. 11.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 162 (c) 57 (d) 18
12. 12.In a class of 32 children, 9 like dance, 20 like music and 4 like both. How many like at least one of the two? (a) 29 (b) 25 (c) 21 (d) 32
13. 13.What is the 18th term of the AP 3, 6, 9, 12, …? (a) 51 (b) 57 (c) 55 (d) 54
14. 14.What is the smallest prime factor of 85? (a) 17 (b) 2 (c) 1 (d) 5
15. 15.What is the median of 28, 9, 23, 18 and 21? (a) 23 (b) 22 (c) 18 (d) 21
16. 16.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 16 sq cm (d) 96 sq cm
17. 17.There are 6 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) 18 (b) 9 (c) 36 (d) 24
18. 18.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 85° (d) 160°
19. 19.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 130° (b) 50° (c) 155° (d) 310°
20. 20.In a class of 38 children, 25 like tea, 13 like coffee and 7 like both. How many like only tea? (a) 25 (b) 18 (c) 7 (d) 6
21. 21.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 340° (c) 160° (d) 70°
22. 22.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 8 (b) 11 (c) 10 (d) 9
23. 23.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
24. 24.In a class of 33 children, 12 like cricket, 20 like football and 8 like both. How many like only cricket? (a) 12 (b) 4 (c) 8 (d) 13
25. 25.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
26. 26.Which term of the AP 3, 12, 21, 30, … is 336? (a) 37th (b) 38th (c) 40th (d) 39th
27. 27.What is the mode of 20, 20, 2, 13, 13, 7 and 13? (a) 13 (b) 20 (c) 2 (d) 7
28. 28.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 64 (c) 16 (d) 28
29. 29.A drawer has lots of black and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 5 (c) 4 (d) 2
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
31. 31.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 100 cu cm (d) 15 cu cm
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 16 (b) 18 (c) 17 (d) 6
33. 33.What is the mode of 17, 4, 5, 17, 4, 16 and 17? (a) 5 (b) 17 (c) 16 (d) 4
34. 34.If a + b = 17 and ab = 66, what is (a − b)²? (a) 25 (b) 157 (c) 289 (d) 5
35. 35.A drawer has lots of red, green 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) 6 (c) 3 (d) 2
36. 36.If a + b = 7 and ab = 12, what is a² + b²? (a) 73 (b) 49 (c) 37 (d) 25
37. 37.A bag has 7 green balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 15 (b) 8 (c) 2 (d) 9
38. 38.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
39. 39.Which is the correct factorisation of x² + 5x + 6? (a) (x + 1)(x + 6) (b) (x + 1)(x + 4) (c) (x + 2)(x + 3) (d) (x − 2)(x − 3)
40. 40.A bag has 5 red, 2 blue and 2 green balls. One ball is taken out without looking. What is the probability that it is red? (a) 2/3 (b) 5/9 (c) 4/9 (d) 1/3

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