Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 160 · 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.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 33 (d) 36
2. 2.A drawer has lots of black, 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) 3 (b) 4 (c) 6 (d) 2
3. 3.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 406 (c) 435 (d) 870
4. 4.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 20° (b) 95° (c) 105° (d) 160°
5. 5.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
6. 6.4 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 6 (c) 8 (d) 12
7. 7.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 75° (c) 150° (d) 105°
8. 8.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 120° (b) 115° (c) 125° (d) 65°
9. 9.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
10. 10.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 270° (d) 135°
11. 11.What is the prime factorisation of 63? (a) 3 × 7 (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7²
12. 12.What is the mean of 6, 11, 20, 4 and 19? (a) 15 (b) 10 (c) 13 (d) 12
13. 13.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
14. 14.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 45 (c) 36 (d) 81
15. 15.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 115° (b) 60° (c) 125° (d) 120°
16. 16.In a class of 50 children, 21 like mangoes, 28 like bananas and 9 like both. How many like at least one of the two? (a) 49 (b) 40 (c) 31 (d) 50
17. 17.A drawer has lots of white 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) 4 (c) 3 (d) 2
18. 18.What is the midpoint of the line joining (7, 10) and (11, 16)? (a) (2, 3) (b) (18, 26) (c) (13, 9) (d) (9, 13)
19. 19.What is the midpoint of the line joining (1, 10) and (3, 2)? (a) (2, 6) (b) (6, 2) (c) (4, 12) (d) (1, 4)
20. 20.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
21. 21.A drawer has lots of yellow, green, blue and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 4 (c) 5 (d) 2
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 7/36 (c) 1/11 (d) 1/6
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
24. 24.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
25. 25.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 36 (c) 24 (d) 25
26. 26.What is the median of 5, 4, 25, 37 and 32? (a) 26 (b) 5 (c) 25 (d) 32
27. 27.A cuboid is 9 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 450 sq cm (b) 185 sq cm (c) 740 sq cm (d) 370 sq cm
28. 28.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
29. 29.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 135° (b) 120° (c) 105° (d) 75°
30. 30.A bag has 5 white, 5 green and 7 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 5/17 (c) 13/17 (d) 12/17
31. 31.What is the smallest prime factor of 155? (a) 31 (b) 5 (c) 2 (d) 1
32. 32.In a class of 40 children, 19 like mangoes, 14 like bananas and 3 like both. How many like at least one of the two? (a) 30 (b) 33 (c) 40 (d) 27
33. 33.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 105° (c) 75° (d) 15°
34. 34.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 35 (c) 11 (d) 60
35. 35.A bag has 5 green balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 6 (c) 7 (d) 2
36. 36.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 15 (c) 20 (d) 10
37. 37.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 12 (c) 15 (d) 36
38. 38.The mean of 8 numbers is 11. When the number 38 is added to them, what is the new mean? (a) 15 (b) 14 (c) 13 (d) 11
39. 39.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
40. 40.How many factors does 24 have? (a) 9 (b) 8 (c) 7 (d) 6

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