Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 341 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/9 (c) 1/12 (d) 1/11
2. 2.A bag has 6 red balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 8 (b) 15 (c) 2 (d) 7
3. 3.What is the midpoint of the line joining (2, 3) and (14, 1)? (a) (6, 1) (b) (2, 8) (c) (8, 2) (d) (16, 4)
4. 4.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 25 (c) 240 (d) 20
5. 5.A bag has 5 yellow balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 6 (c) 11 (d) 7
6. 6.A bag has 5 white balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 7 (b) 6 (c) 2 (d) 10
7. 7.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 60° (c) 70° (d) 120°
8. 8.In a class of 35 children, 28 like cricket, 16 like football and 10 like both. How many like at least one of the two? (a) 24 (b) 34 (c) 44 (d) 35
9. 9.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 14 (d) 42
10. 10.What is the missing term in the AP 1, 6, 11, ?, 21? (a) 17 (b) 21 (c) 16 (d) 15
11. 11.4 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) 24 (b) 7 (c) 16 (d) 12
12. 12.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 25 (c) 12 (d) 24
13. 13.A drawer has lots of black, 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) 8 (b) 4 (c) 2 (d) 5
14. 14.A bag has 3 green balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 12 (b) 4 (c) 5 (d) 2
15. 15.A bag has 12 green balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 15 (c) 13 (d) 14
16. 16.What is the median of 13, 11, 35, 21 and 25? (a) 25 (b) 21 (c) 13 (d) 35
17. 17.Which is the correct factorisation of x² + 5x + 6? (a) (x + 2)(x + 3) (b) (x + 1)(x + 6) (c) (x + 1)(x + 4) (d) (x − 2)(x − 3)
18. 18.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 8 times (d) 6 times
19. 19.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 40° (c) 50° (d) 130°
20. 20.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 100 cu cm (d) 150 cu cm
21. 21.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
22. 22.What is the product of the roots of x² − 8x + 15 = 0? (a) 8 (b) 16 (c) 15 (d) 14
23. 23.What is the midpoint of the line joining (0, 4) and (4, 16)? (a) (2, 6) (b) (4, 20) (c) (10, 2) (d) (2, 10)
24. 24.What is the smallest prime factor of 119? (a) 7 (b) 1 (c) 2 (d) 17
25. 25.How many factors does 108 have? (a) 11 (b) 13 (c) 12 (d) 10
26. 26.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 196 (d) 91
27. 27.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/18 (c) 1/36 (d) 1/11
29. 29.A drawer has lots of red, white, blue, 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) 5 (b) 2 (c) 10 (d) 6
30. 30.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 51 (c) 48 (d) 144
31. 31.What is the 34th term of the AP 1, 10, 19, 28, …? (a) 306 (b) 307 (c) 298 (d) 297
32. 32.In which quadrant does the point (−1, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
33. 33.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 120 (d) 240
34. 34.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 24 (d) 12
35. 35.What is the 13th term of the AP 8, 11, 14, 17, …? (a) 47 (b) 44 (c) 39 (d) 36
36. 36.If a + b = 9 and ab = 18, what is a² + b²? (a) 63 (b) 81 (c) 117 (d) 45
37. 37.A bag has 2 blue, 6 red and 4 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/12 (b) 1/12 (c) 1/2 (d) 1/3
38. 38.What is the midpoint of the line joining (5, 3) and (13, 15)? (a) (9, 9) (b) (18, 18) (c) (10, 9) (d) (4, 6)
39. 39.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 3/8 (c) 1/8 (d) 1/4
40. 40.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) 7 (b) 14 (c) 15 (d) 8

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