Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 347 · 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.What is the smallest prime factor of 403? (a) 2 (b) 1 (c) 13 (d) 31
2. 2.5 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) 50 (b) 10 (c) 25 (d) 30
3. 3.In a class of 34 children, 12 like mangoes, 22 like bananas and 3 like both. How many like neither? (a) 4 (b) 0 (c) 3 (d) 6
4. 4.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 85° (c) 275° (d) 95°
5. 5.What is the product of the roots of x² − 7x + 12 = 0? (a) 11 (b) 13 (c) 12 (d) 7
6. 6.How many factors does 44 have? (a) 5 (b) 7 (c) 4 (d) 6
7. 7.What is the mean of 17, 5, 2, 19, 11 and 12? (a) 11 (b) 13 (c) 12 (d) 10
8. 8.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 9 (b) 10 (c) 4 (d) 11
10. 10.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) 25 (b) 36 (c) 24 (d) 37
11. 11.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 125° (d) 150°
12. 12.A bag has 4 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 2 (c) 5 (d) 6
13. 13.What is the mean of 9, 19, 5, 20 and 12? (a) 12 (b) 14 (c) 13 (d) 15
14. 14.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 110° (b) 235° (c) 125° (d) 55°
15. 15.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2 × 3² (c) 2² × 3² (d) 2² × 3³
16. 16.A drawer has lots of black, white, red 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) 4 (b) 2 (c) 5 (d) 8
17. 17.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 22 (d) 15
18. 18.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
19. 19.What is the midpoint of the line joining (0, 6) and (2, 14)? (a) (1, 10) (b) (1, 4) (c) (10, 1) (d) (2, 20)
20. 20.What is the distance between the points (3, 0) and (15, 9)? (a) 225 (b) 21 (c) 16 (d) 15
21. 21.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7
22. 22.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 12 (d) 24
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 1/11 (c) 5/36 (d) 1/9
24. 24.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 12 (d) 30
25. 25.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
26. 26.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 265° (c) 95° (d) 86°
27. 27.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 15 (c) 14 (d) 7
28. 28.In which quadrant does the point (−7, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
29. 29.A drawer has lots of black 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) 4 (b) 3 (c) 5 (d) 2
30. 30.The mean of 9 numbers is 13. When the number 3 is added to them, what is the new mean? (a) 13 (b) 12 (c) 8 (d) 11
31. 31.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 45 (d) 55
32. 32.What is the distance between the points (0, 0) and (8, 6)? (a) 10 (b) 100 (c) 11 (d) 14
33. 33.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 32 (c) 48 (d) 11
34. 34.A bag has 10 red balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 11 (b) 12 (c) 17 (d) 2
35. 35.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 50° (b) 20° (c) 150° (d) 160°
36. 36.The mean of 6 numbers is 15. When the number 1 is added to them, what is the new mean? (a) 14 (b) 13 (c) 15 (d) 8
37. 37.What is the 18th term of the AP 8, 12, 16, 20, …? (a) 80 (b) 72 (c) 68 (d) 76
38. 38.A bag has 8 green, 3 yellow and 3 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 3/11 (b) 11/14 (c) 3/14 (d) 1/3
39. 39.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
40. 40.What is the distance between the points (7, 9) and (22, 1)? (a) 23 (b) 17 (c) 289 (d) 18

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