Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 474 · 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 mean of 13, 3, 14, 17, 13 and 12? (a) 13 (b) 14 (c) 11 (d) 12
2. 2.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
3. 3.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
4. 4.How many factors does 75 have? (a) 6 (b) 5 (c) 7 (d) 4
5. 5.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 384 cu cm (c) 512 cu cm (d) 24 cu cm
6. 6.How many factors does 66 have? (a) 7 (b) 9 (c) 6 (d) 8
7. 7.What is the mean of 19, 5, 15 and 13? (a) 13 (b) 12 (c) 14 (d) 15
8. 8.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 16 (d) 12
9. 9.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 70° (d) 110°
10. 10.How many prime numbers are there between 40 and 70? (a) 6 (b) 7 (c) 8 (d) 9
11. 11.A bag has 6 red balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 8 (c) 7 (d) 2
12. 12.What is the midpoint of the line joining (0, 14) and (2, 8)? (a) (11, 1) (b) (1, 3) (c) (2, 22) (d) (1, 11)
13. 13.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 24 (d) 16
14. 14.What is the sum of the roots of x² − 7x + 10 = 0? (a) 6 (b) 10 (c) 8 (d) 7
15. 15.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 30 (d) 12
16. 16.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 130° (b) 160° (c) 50° (d) 70°
17. 17.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 120 (d) 240
18. 18.In a class of 56 children, 30 like tea, 27 like coffee and 11 like both. How many like only tea? (a) 29 (b) 19 (c) 30 (d) 16
19. 19.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 15 (c) 48 (d) 135
20. 20.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 72 (c) 24 (d) 8
21. 21.What is the mode of 20, 15, 6, 20, 10, 20 and 15? (a) 10 (b) 6 (c) 15 (d) 20
22. 22.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
23. 23.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
24. 24.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 20 (d) 10
25. 25.What is the mean of 12, 9, 3, 8 and 23? (a) 13 (b) 12 (c) 10 (d) 11
26. 26.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 265 (b) 264 (c) 248 (d) 255
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
28. 28.What is the midpoint of the line joining (9, 6) and (13, 10)? (a) (8, 11) (b) (11, 8) (c) (22, 16) (d) (2, 2)
29. 29.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2³ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2 × 3 × 7⁴
30. 30.A bag has 10 black balls and 7 blue 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) 11 (c) 8 (d) 17
31. 31.12 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
32. 32.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 56 (c) 64 (d) 28
33. 33.The mean of 4 numbers is 32. When the number 42 is added to them, what is the new mean? (a) 37 (b) 34 (c) 35 (d) 32
34. 34.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/3 (c) 1/4 (d) 1/2
35. 35.A bag has 12 blue balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 22 (b) 2 (c) 11 (d) 13
36. 36.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 24 (c) 8 (d) 12
37. 37.In which quadrant does the point (8, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
38. 38.A bag has 7 blue, 9 white and 4 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/4 (b) 1/3 (c) 1/5 (d) 4/5
39. 39.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 240 (c) 252 (d) 243
40. 40.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 484 cu cm (d) 726 cu cm

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