AVU Revision

Table of ContentsPercentages of Amounts 3

Fractions of Amounts 4

Decimal Word Problems 5

Enlargement and Reduction 7

Reading Pie Charts 10

Solving Equations 11

1

Area of Compound Shapes Including Circles 12

Sequences and Number Patterns 13

Speed, Distance and Time 15

Pythagoras 16

Using Trigonometry 18

Scattergraphs 20

Probability 23

Answers 24

Percentages of an Amount

1. Find: (a) 25% of 40 (b) 10% of 780 (c) 20% of 55(d) 50% of £11 (e) 70% of 250 m (f) 75% of 140 kg

2. In a quiz there were 60 questions altogether:

Team A answered 20% of the questions correctlyTeam B answered 25% of the questions correctly Team C answered 50% of the questions correctly

How many questions did each team answer correctly?

3. During a period of 60 minutes a pupil spent 15% of the time day dreaming. How many minutes is this?

2

4. A packet of crisps weighs 30g. Special offer packs give 40% extra free. What weight of crisps do you get in a packet now?

5. Susan was buying a new computer. She had to pay a deposit of 30%. How much deposit would have to pay if her computer was going to cost £900?

6. In a group of 240 pupils 70% of them said they enjoyed Maths.How many pupils was this?

7. Miss Moore just loves nail varnish! She has 60 nail varnishes; 30% are blue.How many blue nail varnishes does Miss Moore have?

8. There are 820 spectators at the rounders tournament. 55% are children. How many children are there?

Fractions of an Amount

1. Calculate:

(a)

13 of £96 (b)

15 of 65kg (c)

17 of £36.40

(d)

34 of 48cm (e)

58 of £136 (f)

78 of 58·4g

(g)

23 of £15.96 (h)

910 of 45kg (i)

37 of £10.92

(j)

56 of £5.10 (k)

38 of 984mm (l)

34 of £1.08

2. A piece of wood is 8·4m long. 13 of it is used.

How many metres are used?

3. On board a ship there has to be someone 'on watch' all the time. Each person is

on duty for 14 of a day. How many hours is this?

3

4. In the cinema there are 230 people. 1

10 of them are children. How many adults are there?

5. There are 8 people in a rowing team. 14 of them are girls? How many boys are

there in the team?

6. There are 48 sweets in a packet. 34 of them are citrus flavours.

How many citrus sweets are there in the packet?

7. In a class of 24 pupils 78 of them are present.

(a) How many pupils are present?(b) How many are absent?

8. In a school there are 1450 pupils. 45 of them bring a mobile phone to school.

(a) How many pupils bring a mobile phone?(b) How many do not bring a phone with them?

9.57 of the cars in a car park were grey. If there were 560 cars altogether, how many of them were grey?

Decimal Word Problems

1. Peter cuts a piece of string into three lengths. One is 4.26cm long, one is 7.54cm long and the third is 3.90cm long. How long was the string before it was cut?

2. The local DIY store was charging £15.50 for a 2-litre can of paint. In a sale they were selling it for £12.95.How much discount was this?

3. A pair of shoes cost £42.70 in a sale after £12.30 had been given as a discount.How much were the shoes before the sale?

4. A school bought some calculators which cost £74.20. This included £10.20 VAT. How much will the calculators actually cost the school if there was no VAT charged?

4

5. Mary joins four lengths of wood together. One is 17.41cm long, one is 23.29cm long, one is 16.07cm long. Altogether they are 80 cm long. How long is the fourth piece of wood?

6. I have three bags of sweets. One weighs 64.17g, one weighs 58.29g and the third weighs 68.47g. How much do they weigh altogether?

7. Sarah has four friends. Lauren is 1.54m tall, Sophie is 1.50m tall, Kristy is 1.52m tall and Natalie is 1.49m tall. If they all stood on top of each other how high would they be?

8. Bill, Sarah and Joshua each have bottles of juice. Bill bottle contains 33ml and Joshua’s bottle contains ¼ of a litre. They have 338 ml of juice altogether. How much was in Sarah’s bottle?

9. a) Allan runs 7.7km on Monday, 6.5km on Tuesday and 9.35km on Wednesday. Find the total of his runs.

b) He goes for a run on Thursday too and his total of the four days is now 32.05km. How far did he run on Thursday?

10. At four shops Fiona spends the following amounts: £14.78, £7.45, £5.10 and £10.54.How much did Fiona spend altogether?How much did she have left from £50?

11. If it costs £8.60 to hire a bike for a day, how much would it cost to hire it for the whole of the month of June?

12. Find the total cost of :3 tee shirts at £12.755 jumpers at £27.504 tops at £22.401 coat at £87.40

13. Claire bought 12 large bottles of "Loca" for a party. They cost £1.19 each . How much did she pay altogether?

14. It cost Elsie £34.80 to buy 8 Easter eggs for her friends. How much was this for each one?

5

15. 35 people were going ten-pin bowling. It cost each person £5.50 for 2 games.

How much did it cost altogether for the 35 people?

16. For her birthday, Naaila took her 4 best friends to the cinema and then to Le Hut de Pizza. The total cost of the outing was £44.75. How much was this for each person? {CAREFUL!}

17. 6 friends had a day out to the seaside. They all had ice cream which cost £1.45 each. Two had a pizza costing £8.25 each, three had a fish supper costing £6.30 each and the sixth one had a burger costing £5.49.

a) Calculate the total cost of the day out.b) They decided to each put £8 in a "kitty". Was this enough to pay for

everything they had?c) How much over or under were they?

Enlargement and Reduction

1. Copy each of the following and carry out the enlargement or reduction.

Scale factor ¼ Scale factor ⅓

Scale factor ½ Scale factor ¾

6

Scale factor 2½ Scale factor ⅔

2 a. From the diagram below, state the scale factor that has been used to:

(i) create shape C from shape B

(ii) create shape B from shape C

(iii) create shape B from shape A

(iv) create shape C from shape A

b. James claims that the scale factor for enlargement from B to A is 3/2.Is he correct? Explain your answer.

7A

B

A B C

3. From the diagram below, state the scale factor that has been used to:

(a) create shape B from A

(b) Sam states that Shape A is a reduction of Shape C by a scale factor of ⅔.

Is he correct? Explain your answer.

8

C

Reading Pie Charts

1. In a survey, some students were asked what their favourite leisure activity was. Their answers were used to draw this pie chart.

a) Write down the fraction of the students who answered“Television”. Give your answer in its simplest form.

72 pupils took part in the survey. b) Work out how many liked Television.

2.a.

i.1.

a.1.

9

2. Here is a pie chart showing the eye colour of 180 S3 pupils. How many pupils had:a. Blue eyesb. Green eyesc. Grey eyes d. Hazel eyes e. Brown eyes?

3. Here is a pie chart showing favourite types of music for music teachers.

56 teachers took part in the survey. How many teachers liked Jazz?

Solving Equations

Solve the following equations:

1. 3x = 12 – x 2. 5m = 24 – 3m 3. y = 21 – 2y

4. 5t = 42 – t 5. 2a = 20 – 2a 6. 6x = 40 – 4x

7. 2x + 1 = x + 3 8. 2y + 1 = y + 9 9. 5m + 3 = 4m + 9

10. 8a + 6 = 7a + 14 11. 2p - 1 = p + 5 12. 2q - 3 = q + 7

13. 4b - 3 = 3b + 3 14. 2w + 1 = w + 3 15. 2k + 1 = k + 9

16. 5p + 3 = 4p + 9 17. 3c + 1 =c + 7 18. 3d + 4 = d + 6

19. 5g - 1 = g + 3 20. 6f + 1 = 4f + 9 21. 5x - 1 = x + 19

22. 8y - 8 = 5y + 7 23. 5n + 2 = n + 22 24. 7m - 3 = 2m + 32

10

60o

40o

50o

70o

60o

125o

60o

25. 10q - 40 = 3q + 9 26. 4y + 1 = y + 10 27. 2y + 1 = 21 – 3y

28. p – 3 = 21 – 5p 29. 8r – 5 = 45 – 2r 30. 2 + 6d = 24 – 5d

31. 6 + x = 12 – 2x 32. 14 + 4a = 26 – 2a 33. 9 + x = 27 – 5x

34. 1 + 3c = 13 – c 35. 6 + 4x = –2x + 12 36. 3x + 5 = –4x + 19

37. 5v – 1 = –3v + 15 38. 8 + 7x = –2x + 35 39. 5x – 7 = –2

40. 3x – 12 = –3 41. 7y – 15 = –1 42. 8v – 8 = 6v – 2

43. 4h – 1 = 2h – 5 44. 6a – 16 = a – 6 45. 5m – 18 = m – 6

46. 8e – 30 = 2e – 6 47. 3x – 11 = x – 5 48. 2x – 12 = –3x – 2

49. 5y – 20 = –2y – 6 50. 3a – 9 = –2a – 4 51. 7x – 13 = –x – 5

52. 4k – 24 = –2k – 12 53. 3c – 18 = –c – 2 54. 10 – 2x = 6 + 2x

55. 33 – w = 8 + 4w 56. 58 – y = 6y + 2 57. 4a – 2 = 13 – a

58. 17 + 8m = 89 – m 59. 5k + 3 = 45 – k 60. 5y – 2 = 28 – 5y

61. 3(a + 2) = a + 12 62. 4(x + 3) = 2x + 30 63. 5(d – 1) = 3d + 7

64. 7(x + 2) = 4(x + 5) 65. 7(x – 2) = 4(x + 1) 66. 8(w – 1) = 6(w + 4

Compound Shapes with Circles

Give all answers to 1 decimal place.

1. Find the area of these circles

a) b) c) d)

e) f) g) h)

11

3cm 7cm 4.5cm6.5cm

10cm 6cm

5cm

12.2 cm

Find the area of the glass in this stained glass window.

2. Work out the area of these shapes made from circles and rectangles.

a) b) c) d)

4. Find the area of the shaded regions

Sequences and Patterns

1. The squares in the diagram represent tables and the dots represent people sitting at them.

(a) Copy and complete this table for the number of tables and the number of people.

Number of tables

1 2 3 4 5 10 14

12

6cm

2cm 5cm

1cm

6cm

5cm4cm

4cm

4cm

18 cm

18 cm

Number of people

(b) Write down a rule in words for the finding the number of people if you know how many tables there are.

(c) Write the formula in symbols using T for the number of tables and P for the number of people.

(d) Use your formula to find how many people would be able to sit at 20 tables.

(e) There are 44 people at a gathering. How many tables would be needed to seat them?

2. Plain and patterned tiles are laid in a strip. Copy and complete the table for the following pattern

Number of patterned tiles

2 3 4 5 6 7 8 10

Number of plain tiles

(a) Write down a formula for finding the number of plain tiles (P) when you know the number of patterned tiles (R).

(b) If there are 152 plain tiles, how many patterned tiles would there be?

3. (a) Complete the table below for this tile pattern made from coloured and white tiles.

Number of coloured tiles

1 2 3 4 10 20 50

13

Number of white tiles

(b) Write down a formula for finding the number of white tiles (W) when you know the number of coloured tiles (C).

(c) If there are 86 white tiles, how many coloured tiles would there be?

4. (i) Find a formula for each of the following.

(a)

(b)

(c)

(d)

(ii) Use your formulae to complete the missing entries in the tables.

Speed, Distance and Time

1. Calculate the distance covered by a car travelling at(a) 50 km /h for 3 hrs (b) 40 km/h for 4 hrs (c) 60 km/h for 2 hrs(d) 60 mph for 3·5 hrs (e) 70 mph for 1·25 hrs (f) 42 mph for 23

4 hrs

2. Calculate the speed of a car travelling:(a) 480 km in 8 hrs (b) 350 km in 7 hrs (c) 240 km in 3 hrs(d) 125 miles in 2.5 hrs (e) 96 miles in 1 1

4 hrs(f) 30 miles in 3 34

hrs

3. Calculate the time taken, in hours, by a car travelling: (a) 480 km at 80 km/h (b) 720 km at 60 km/h (c) 640 km at 64 km/h(d) 150 miles at 60 mph (e) 50 miles at 40 mph(f) 27 miles at 4 mph

14

P 1 2 3 4 5 6 12

Q 3 6 9 12 15 18 48 90R 1 2 3 4 5 6 14

T 2 5 8 11 14 17 26 47

D 5 6 7 8 9 10 20

K 4 5 6 7 8 9 31 68

V 2 3 4 5 6 7 15

A 3 6 9 12 15 18 57 72

24 mm7 mm

x8 m

15 m

x

89m 15 m

x

5 cm

9 cm

x

83 m 121 m

x

4. Calculate the number of hours and minutes between:

(a) 10 p.m. and 3 a.m. (b) 0100 and 1300(c) 8 p.m. and 11 a.m. (d) 10.30 p.m. and 1.30 a.m.

(e) 7.30 p.m. and 2.45 a.m (f) 9.30 p.m. and 12.15 a.m.(g) 1845 and 2030 (h) 0845 and 0900

5. Write the answers to Question 4(e), (f), (g) and (h) in decimal hours.

6. The distance between Heysham and the Isle of Man is 80 km.A hovercraft travels at 40 km per hour. How long does the journey take?

7. Selina takes 112 hours to cycle 12 miles. What is her average cycling speed?

8. Darren travels 70 miles from Ashington to Newcastle by bus.He leaves Ashington at 10.00 and arrives in Newcastle at 11.45. How fast was the bus travelling?

9. A train left Dublin at 11.30 and travelled at an average speed of 96 km/h. It arrived in Cork at 1400. a. What distance did the train travel?b. A lorry took four hours to travel the same distance. What was the average

speed in km/h for the lorry?

10.Superman flies at a speed of 400 m/s. How long does it take superman to fly 1800 m.

11.Dara left Lucan by car at 0925 and arrived in Sligo at 1155 and drove at a speed of 78 miles per hour. Calculate the distance he travelled.

Pythagoras

1. Find the length of the hypotenuse, marked x, in each of the following triangles. Where necessary, round your answers to one decimal place.

15

(e)

6 cm

8 cm

x

(a) (b)(c)

(d) (f)

8 m15 m

x

5 cm8 cm

x

24 mm

7 mm x

79 cm4 cm

x

63 m

121 m

x

6 cm

10 cm

x

25. 7 cm

x

4. 3 cm

14 mm

x

16 mm

3 m

7.5 m

x

32o

30 mh

27 m

65 cm

52 cm

6 m

3 m

2. Find the length of the side, marked x, in each of the following triangles. Where necessary, round your answers to two decimal places.

3.Find the length of the side, marked x, in each of the following triangles. Where necessary, round your answers to two decimal places.

4. Eddie is flying his kite. He lets out 30 metres of string and moves 27 metres from his starting point.

How high is the kite above the ground?

5. A rectangular jigsaw measures 65 cm by 52 cm.

What length is its diagonal?

6. The room shown opposite has two parallel sides.16

(a) (b) (c)

(d) (e) (f)

Use the given dimensions to calculate the perimeter of the room.

7. A square envelope has a decorative trim around the outside and the folds as shown.

Calculate the total length of decorative trim required for the envelope.

8cm

Trigonometry1. Calculate the length of the side marked x in these right-angled triangles.

You will have to choose which ratio to use.

2. Calculate the size of the angle marked xo in these right-angled triangles. You will have to choose which ratio to use.

17

48o

A

20 cm20 cm

M

12 m

xo

10 m

940 mm

5048 mmxo

17m

h m

25o

3. In triangle ABC, angle BAC is 48o.Calculate the length of BC.

4. A fire-fighter has a 12 metre ladder and needs to reach a window 10 metres from the ground.

What angle, xo, will the ladder make with the building?

5. A manufacturer of concrete roof tiles states that to be suitable for concrete tiles the angle of a roof(pitch) must be greater than 21o.

This roof is symmetrical. Is this roof suitable for concrete tiles?

Give a reason for your answer.

6. A skateboard ramp has been designed to have the dimensions shown in the diagram.

To be safe the height of the ramp cannot be more than 7.5 metres.

Is this ramp safe?

Give a reason for your answer

7. Below is an equilateral triangle.

18

B C

x

y

x

y

x

y

Umbrella sales

rainfall Hair colour

Pocket money time

speed

Calculate the height of the triangle.

Scattergraphs

1. Using the words positive, negative or no relation, describe the correlation in each of the diagrams below.

(a) (b) (c)

2. What do the diagrams tell you about the correlation between the two variables involved?

3. Copy these graphs and use your ruler to draw what you think is the line of best fit.

19

(a) (b) (c)

6

7

8

9

10

11

12

13

14

Temperature in oC

4. For the following sets of data, draw a scatter diagram and draw a line of best fit.

(a) (b)

5. The following table gives the temperature of a bottle of water as it cools.

(a) Plot the points and draw the best fitting straight line through them.

(b) Use your graph to estimate the temperature after 2½ minutes.

6. The graph shows the height above sea-level, in metres, of eight places in Scotland and the corresponding temperatures.

20

x 1 2 3 4 5

y 5 7 8 10 12

x 1 2 3 4 5

y 8 6 5 4 2

Time, min (T) 1 3 5 7 9

Temperature (oC) 66 61 57 53 50

90 100

10

Intelligence (IQ)

Reading Speed(w

ords per minute)

120110 130 140 150

20

30

40

50

(a) Draw a line of best fit through the points on the graph.

(b) The weather forecast had predicted a temperature of 6oC in a town that is 1250 metres above sea level. Was the forecast correct?

7. The table below shows the results of an experiment to test the relationship between intelligence and reading speed (words per minute) in a group of 8 year olds.

Intelligence(IQ) 95 105 115 125 135 140 150

Reading Speed 10 20 25 25 40 35 50

(a) Complete the scatter graph below to illustrate this.

21

(b) Draw the line of best fit on your graph.

(c) An 8 year old can read 30 words per minute. Their teacher thinks that the child is likely to have an IQ of 130.

Do you agree with the teacher?

Probability

1. A bag has 3 red sweets, 6 green sweets and 9 blue sweets.

If a sweet is picked at random, what is the probability that the sweet will be:-

(a) red (b) green (c) blue (d) orange ?

2. A garage forecourt has the following colours of cars :–

12 blue, 8 green, 6 silver, 4 white, 3 black, 2 red, 1 yellow

Find the following probabilities:-

(a) P (blue) (b) P (green) (c) P (silver) (d) P (white)

(e) P (black) (f) P (red) (g) P (yellow)

3. Sue buys tickets for two different prize draws. In the first prize draw there are 20 entries and Sue buys 4 tickets. In the second prize draw there are 60 entries and she buys 24 tickets. She thinks she has a better chance of winning the first prize draw. Is she correct?Justify your answer by calculation.

4. A small bag of 34 sweets contains 16 blue sweets. A medium bag of 48 sweets contains 28 blue sweets. From which bag is there a better chance of picking a blue sweet?

22

Justify your answer by calculation.

5. Two piggy banks are filled with copper coins. Piggy bank 1 has 500 coins of which 107 are 1p coins. Piggy bank two has 660 coins of which 140 are 1p coins. John claims that he has a better chance of picking a 1p coin from Piggy bank 1. Is he correct? Justify your answer by calculation.

Answers

Percentages of amounts

1. a) 10 b) 78 c) 11 d) £5.50 e) 175m f) 1052. Team A = 12, Team B = 15, Team C = 303. 9 minutes4. 42g5. £2706. 168 pupils7. 188. 451

Fractions of amounts

1. a) £32 b)13kg c) £5.20 d) 36cm e) £85 f) 51.1g g) £10.64 h) 40.5kg i) £4.68 j) £4.25 k) 369mm l) 81p

2. 2.8m3. 6 hours4. 207 adults 5. 6 boys6. 367. a) 21 b) 38. a) 1160 b) 2909. 400 cars

Decimal word problems

1. 15.7cm2. £2.553. £554. £645. 23.23cm6. 190.93g

23

7. 4.51m8. 55ml9. a) 23.55 b) 8.5 km10. a) £37.87 b) £12.1311. £25812. £38.25 + £137.50 + £89.60 + 87.40 = £352.7513. £14.2814. £4.3515. £192.5016. £8.9517. a) £8.70 + £16.50 + £18.90 + £5.49 = £49.59 b) No c) Under by £1.59

Enlargements and reductions

1.

2. a) i) 2 ii) 12 iii) 2

3 iv) 43

b) Yes

3. No, the scale factor should be 23

Reading Pie Charts

1. a) 518 b) 20 pupils

2. a) 45 pupils b) 25 pupils c) 20 pupils d) 30 pupils e) 60 pupils 24

3. 7 teachers

Solving Equations

1. x = 3 2. m = 3 3. y = 7 4. t = 7 5. a = 5 6. x = 4 7. x = 2 8. y = 89. m = 6 10. a = 8 11. p = 6 12. q =

1013. b = 6 14. w = 2 15. k = 8 16. p = 6

17. c = 3 18. d = 1 19. g = 1 20. f = 4 21. x = 5 22. y = 5 23. n = 5 24. m = 525. q = 7 26. y = 3 27. y = 4 28. p = 4 29. r = 4 30. d = 2 31. x = 2 32. a = 233. x = 3 34. c = 3 35. x = 2 36. x = 2 37. v = 2 38. x = 3 39. x = 1 40. x = 341. y = 2 42. v = 3 43. h = 2 44. a = 2 45. m = 3 46. e = 4 47. x = 3 48. x = 249. y = 2 50. a = 1 51. x = 1 52. k = 2 53. c = 4 54. x = 1 55. w = 5 56. y = 857. a = 3 58. m = 8 59. k = 7 60. y = 3 61. a = 3 62. x = 9 63. d = 6 64. x = 265. x = 6 66. w = 16

Area of compound shapes

1a. 28.2 cm2 b. 38.5 cm2 c. 132.7 cm2 d. 15.9 cm2

e. 39.3 cm2 f. 28.3 cm2 g. 58.9 cm2 h. 58.4 cm2

2a. 26.1 cm2 b. 24.6 cm2 c. 58.3 cm2 d. 41.1 cm2

3. 5481.7 cm2

4a. 85.8 cm2 b. 69.5 cm2

Sequences and Number Patterns

1. a)

Number of tables

1 2 3 4 5 10 14

Number of people

4 6 8 10 12 22 30

b) The number of people equals twice the number of tables plus twoc) P = 2T + 2d) 42 peoplee) 21 tables

Number of patterned tiles

2 3 4 5 6 7 8 10

Number of 10 12 14 16 18 20 22 2625

plain tiles2. a)

b) P = 2R + 6c) 73

3. a)

Number of coloured tiles

1 3 4 5 10 20 50

Number of white tiles

6 10 14 18 38 78 198

b)W = 4C – 2c) 22

4 a) i) Q = 3Pii)

P 1 2 3 4 5 6 12 16 30Q 3 6 9 12 15 18 36 48 90

b) i) T= 3R - 1ii)

R 1 2 3 4 5 6 14 9 16T 2 5 8 11 14 17 41 26 47

c) i) K = D - 1ii)

D 5 6 7 8 9 10 20 32 69K 4 5 6 7 8 9 19 31 68

d) i) A = 3V – 3ii)

V 2 3 4 5 6 7 15 20 25A 3 6 9 12 15 18 42 57 72

Speed Distance and Time

1a. 150 km b. 160 km c. 120 km d. 210 miles e. 87.5 miles f.115.5 miles

2a. 60 km/h b. 50km/h c. 80 km/h d. 50 mph e. 76.8 mph f. 8mph

3a. 12 hours b. 12 hours c. 16 hours d. 2.5 hours e. 1.25 hours f. 6.75 hours.

26

4a. 5 hours b. 12 hours c. 15 hours d. 3 hours e. 7 hours and 15 minutes

f. 3 hours and 45 minutes g. 1 hour and 30 minutes h. 15 minutes

5. e. 7.25 hours f. 3.75 hours g. 1.5 hours h. 0.25 hours

6. 2 hours

7. 8 mph

8. 40 mph

9a. 240 km b. 60 km/h

10. 4.5 seconds

11. 195 miles

Pythagoras

1a) 10 cm b) 17 m c) 25 mm d) 10.3 cm e) 14.7 m f) 17.4 m

2a) 6.24 cm b) 12.69 m c) 22.96 mm d) 8 cm e) 10.33 m f) 6.81 cm

3a) 6.87 m b) 21.26 mm c) 25.34 cm

4) 13.08 metres

5) 83.24 centimetres

6) 3.31 + 6 + 3 + 4.6 = 16.91 metres

7) 54.62 centimetres

Using Trigonometry

1a. 64.9 cm b. 12.96 m c. 3.9 cm

2a. 58° b. 48° c. 38°

3. BM = 8.1 cm BC = 16.2 cm

4. 34°

5. x° = 20° to the nearest degree. No it is not suitable as 20° < 21°.

6. h = 7.9 m. No it is not safe as 7.9m > 7.5 m.

7. h = 8.7 cm

Scattergraphs

1a) no relation b) positive correlation c) negative correlation

27

2a) As rainfall increases, umbrella sales increase (positive correlation) b) Amount of pocket money and hair colour have no relation c) As the speed increases, the time decreases (negative correlation)

3. Appropriate line of best fit

4. a) b)

5a)

b) 62 oC

6a) Appropriate line of best fit b) Yes

7a) , b)

28

0 1 2 3 4 5 60123456789

0 1 2 3 4 5 60

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

70

Time (minutes)

Temperature (oC)

c) No, we would expect the child to have an IQ of 125.

Probability

1a. 16 b. 1

3 c. 12 d. 0

2a. 13 b. 29 c. 1

6 d. 19 e. 112 f. 1

13 g. 136

3. 1st prize draw = 4

20 = 0.2

2nd prize draw = 2460 = 0.4

No she is not correct as 0.2 < 0.4

4. Small bag = 1634

=0.47

Medium bag = 2848

=0.58

There is a better chance of picking a sweet from medium tin as 0.58 > 0.47.

5. Piggy Bank 1 = 107500

=0.214

Piggy Bank 2 = 140660

=0.212

Yes he is correct as 0.214 > 0.212.

29

90 100 110 120 130 140 150 1600

10

20

30

40

50

60

30