Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 595 · 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 which quadrant does the point (4, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
2. 2.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
3. 3.If a + b = 11 and ab = 18, what is a² + b²? (a) 157 (b) 85 (c) 103 (d) 121
4. 4.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7² (d) 2 × 5 × 7
5. 5.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 50° (c) 310° (d) 130°
6. 6.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
7. 7.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
8. 8.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
9. 9.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 115° (b) 90° (c) 155° (d) 65°
10. 10.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 5 (d) 3
11. 11.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
12. 12.There are 5 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) 10 (b) 20 (c) 15 (d) 7
13. 13.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 110° (c) 35° (d) 290°
14. 14.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
15. 15.What is the midpoint of the line joining (9, 14) and (15, 4)? (a) (9, 12) (b) (24, 18) (c) (12, 9) (d) (3, 5)
16. 16.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
17. 17.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2 × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
19. 19.A bag has 12 green balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 13 (c) 2 (d) 5
20. 20.What is the mean of 4, 14, 18, 19, 13 and 22? (a) 18 (b) 15 (c) 14 (d) 16
21. 21.A bag has 10 black balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 22 (b) 11 (c) 2 (d) 12
22. 22.In a class of 26 children, 19 like cricket, 8 like football and 3 like neither. How many like both? (a) 3 (b) 1 (c) 4 (d) 23
23. 23.A drawer has lots of red 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) 3 (b) 5 (c) 2 (d) 4
24. 24.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
25. 25.How many prime numbers are there between 20 and 50? (a) 8 (b) 9 (c) 6 (d) 7
26. 26.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 78 (d) 66
27. 27.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 3/8 (c) 5/8 (d) 1/4
28. 28.A bag has 5 blue balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 7 (b) 6 (c) 15 (d) 2
29. 29.What is the smallest prime factor of 115? (a) 23 (b) 2 (c) 1 (d) 5
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/11 (c) 1/6 (d) 5/11
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 1/6 (c) 5/11 (d) 1/11
32. 32.In which quadrant does the point (−6, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
33. 33.7 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) 28 (b) 21 (c) 42 (d) 10
34. 34.What are the roots of x² − 13x + 36 = 0? (a) 2 and 18 (b) 1 and 12 (c) 1 and 36 (d) 4 and 9
35. 35.The mean of 4 numbers is 21. When the number 16 is added to them, what is the new mean? (a) 19 (b) 22 (c) 20 (d) 21
36. 36.What is the distance between the points (6, 9) and (18, 0)? (a) 225 (b) 15 (c) 16 (d) 21
37. 37.In a class of 53 children, 23 like tea, 23 like coffee and 10 like neither. How many like both? (a) 10 (b) 43 (c) 4 (d) 3
38. 38.A bag has 8 red, 7 blue and 9 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 3/5 (c) 5/8 (d) 3/8
39. 39.What is the mean of 19, 12, 8, 10, 7 and 22? (a) 14 (b) 13 (c) 12 (d) 15
40. 40.What is the midpoint of the line joining (6, 11) and (16, 9)? (a) (11, 10) (b) (5, 1) (c) (10, 11) (d) (22, 20)

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