Calderglen Mathematics DepartmentBlue CourseRevision Sheets

Block D

BD1 Ratio and Proportion

BD2 Graphs and Charts.

BD3 Sequences and Straight Line

BD4 Time

BD5 Percentages

BD6 Money

BD1 Ratio and Proportion

BD1.1 I understand how to express a ratio and can simplify ratios.

1. Simplify each of the following ratios

(a) 3 : 6 (b) 10 : 5 (c) 8 : 2 (d) 9 : 12 (e) 2 : 6

(f) 6 : 2 (g) 3 : 9 (h) 5 : 20 (i) 8 : 6 (j) 12 : 15

(k) 18 : 8 (l) 20 : 24 (m) 30 : 25 (n) 30 : 40 (o

) 25 : 75

(p) 10 : 15 (q) 10 :

150 (r) 16 : 4 (s) 35 : 25 (t) 15 : 60

2. Simplify each of the following ratios.Make sure that both quantities are in the same unit.

(a) £5 : £10 (b) 10 p : 25 p (c) 9 kg : 15

kg (d) 8 cm : 6 cm

(e) 24 p : 32 p (f) 25 p : £1 (g) £2 : 50 p (h) 70 p : £2

(i) 5 mm : 1 cm (j) 2 kg :

500 g(k)

1 hr : 20 mins (l) 45 mins : 1

hr

(m)

0.2 cm : 2 cm (n) 0.3 m : 4

m(o)

0.7 m : 3 m (p) 2 cm : 4 m

BD1.2 I can distribute a total amount in a given ratio.

Split each of the following quantities in the given ratio

Ratio Quantity

(a) 2 : 3 £300

(b) 5 : 2 245 tonnes

(c) 3 : 4 84 mm

(d) 7 : 3 650 kg

(e) 1 : 2 : 3 210 kg

(f) 3 : 2 : 4 £216

(g) 5 : 1: 3 477 g

(h) 4 : 3 : 2 585 tonnes

BD1.3 I can solve problems that involve ratio.

1. A cake contains sultanas and flour. A mixture of these ingredients weighs 320 g.

If the sultanas and flour are mixed in the ratio 3 : 5, what is the weight of each of the ingredients used?

2. 2 litres of paint is made by mixing red and yellow paint. These are mixed in the ratio 7 : 9.

What quantity, in cm3, of red and yellow paint is used?

3. At a school assembly there are 432 pupils. The ratio of boys to girls is 5 : 7.

(a) How many boys are at the assembly?

(b) How many girls are at the assembly?

4. A box contains 1350 beads. The beads are blue and red, and mixed in the ratio of 4 : 5.

(a) How many red beads are there in the box?

(b) How many blue beads are there in the box?

5. Concrete is a mixture of cement powder, sand and gravel, which are mixed with water. The water dries out later as the concrete sets.

When cement powder, sand and gravel are mixed they weigh 280 kg.

If they are mixed in the ratio 2 : 5 : 7, what weight of each is used?

6. Four people are to share an inheritance of £5250.

If the money is to be shared in the ratio 3 : 5 : 4 : 3, how much should each person receive?

7. John and David set up a business.

John puts in £28000 and David puts in £44800. They agree to split the profits in the ratio of their investment

(a) What fraction of the profits will each partner get?

(b) If the profits amount to £8190, how much will each receive?

BD1.4 I can solve problems using Direct Proportion.

1. The cost of 8 cakes is £6.80

How much will it cost for 12 similar cakes?

2. When you exchange £100 into Indian Rupees, you receive 8580 Rupees.

How many Rupees will you receive for £30?

3. A car travels 198 miles on 30 litres of petrol.

How far can it travel on 48 litres of petrol?

4. When you exchange 200 Canadian Dollars into Euros you receive 154 Euros.

How many Euros will you receive for 430 Canadian Dollars?

5. It takes 40 lorry loads to shift 92 tonnes of earth from a building site.

How many lorry loads will it take to shift 162.5 tonnes of earth?

BD1.5 I can solve problems using Inverse Proportion.

1. A painting contractor estimates that it will take 9 men 45 hours to complete a painting job.

If the contractor uses 15 men, how long will it take to complete the job?

2. When a textbook costs £12, a school can afford to buy 400 books.

If the cost of each textbook rises to £16, how may textbooks can the school now buy?

3. A woman can read at various speeds.

At 300 words per minute, she takes 8 hours to read a book.If she reads fast, she can read at 400 words per minute.

How long would it take her to read the book at this speed?

4. A car covers a journey in 7 hours travelling at an average speed of 63 km/hr.

Another car takes 2 hours longer to complete the same journey.

What was the second car’s average speed?

5. A farmer has enough silage to feed a herd of 80 cows for 12 weeks.

If he buys another 40 cows, how many weeks will the silage now last?

BD1.6 I have investigated graphs of two quantities which are in direct proportion.

1. The cost of a number of cans of juice is shown in the table below.

Number of cans 1 2 3 4 5 6

Cost (p) 30 60

(a) Copy and complete the above table.

(b)

Using a scale of Horizontal axis (Number of cans) : 2 boxes = 1 can

Vertical axis (Cost) : 1 box = 10 p

Plot the points from the table.

(c) (i) Join the points with a straight line.

(ii) Does the line pass through the Origin?

(iii) Why must the line pass through the Origin?

2. The distances travelled, by a traction engine, in specific times is shown in the table below

Time (Hrs) 1 2 3 4 5 6

Distance travelled (km) 4 8

(a) Copy and complete the table above.

(b)

Using a scale of Horizontal axis (Time) : 2 boxes = 1 hour

Vertical axis(Kilometres) : 1 box = 1

kilometre

Plot the points from the table.

(c) (i) Join the points with a straight line.

(ii) Does the line pass through the Origin?

(iii) Why must the line pass through the Origin?

BD2 Graphs and ChartsI can construct, interpret and extract data from:

1. A boy ran in an 800 metre race. The times he took to run a given distance in the race is shown in the graph below.

(a) How long did it take him to run each of the following distances?(i) 100 m (ii) 500 m (iii) 550 m (iv) 450 m(v) 150 m (vi) 50 m

(b) Which of the 200 metre stretches does he run the quickest and how many seconds does it take him?

(c) Which of the 200 metre stretches does he run the slowest and how many seconds does it take him?

0 200 400 600 8000

20406080

100120140160

Running times

Distance run in metres

Tim

e (s

econ

ds)

BD2.1 a line graph,

2. A crowd of ten thousand people attended a football match which started at 3 pm. The graph below shows the number of people who had entered the ground at various times.

(a) How many people had entered the ground by the following times?

(i) 1.15 pm (ii) 2.15 pm (iii) 12.45 pm (iv) 1.45 pm

(v) 2.45 pm

(b) (i) During which half-hour period did most people enter the ground.

(ii) How many people entered the ground between these times?

12 NOON 12.30 PM 1.00 PM 1.30 PM 2.00 PM 2.30 PM 3.00 PM0

100020003000400050006000700080009000

10000

Attendance at football match

Time

Num

ber

of p

eopl

e in

the

grou

nd

3. The driver of a car recorded the number of litres of petrol in the tank at the end of every hour.The results are shown in the table below.

Time 8 am

9 am

10 am

11 am

12 noon

1 pm

2 pm

3 pm

4 pm

Number of litres of petrol in tank

60 55 45 40 40 40 30 20 5

(a) Construct a line graph to represent the above data.

Use the following scalesHorizontal axis (Time) : 1 cm = I hourVertical axis (Number of litres in petrol tank) : 1 cm = 10 litres

(b) Using your graph :

(i) Between which two times does the driver use most petrol?How do you know?

(ii) Why does the amount of petrol in the tank between 11 am and 1 pm remain the same?

BD2.2 a pie chart,

1. In a statistical survey, 1200 people were asked which of five countries they would like to visit on holiday. The results are shown below.

Country America France Greece Italy SpainPercentage 24 18 36 10 12

(a) Represent the above data in a pie chart.(b) How many people would like to visit France?

2. In a survey, 8000 people were asked which football team they supported. The results are shown below.

Football Team Celtic Hearts Hibernian Partick

Thistle RangersNumber of people 1840 1360 1520 1280 2000

(a) Represent the above data in a pie chart(b) What percentage of the people supported Rangers?(c) What percentage of the people supported Partick Thistle?

3. A sample of people was asked which type of food they preferred. The results are shown below.

Type of food British Chinese Indian Italian MacDonald’s

Number of people 6 12 35 7 12

(a) Represent the above data in a pie chart.(b) What percentage of people preferred MacDonald’s?

Give your answer correct to one decimal place.

BD2.3 a stem and leaf diagram,

1. A busy filling station records the number of motorists who buy diesel fuel for their cars each day.

The number on each of 50 consecutive days is shown below.

28 19 17 30 45 37 43 36 36 1213 17 12 27 10 17 23 23 9 109 14 15 8 26 30 26 22 19 2028 19 32 21 23 26 34 16 17 1833 26 28 31 30 22 21 21 15 19

(a) Construct a stem and leaf diagram to represent this data.

(b) Comment on your results.

2. A gardener is making a fence for his garden. He purchases a large number of pieces of wood, all of them longer than 100 cm. Each piece is then cut so that it is 100 cm long. The lengths of the off-cuts, in cm, resulting from cutting the lengths to size are given below.

5.2 6.6 4.3 8.3 5.1 7.5 8.6 7.1 7.8 2.26.6 5.8 3.5 7.5 6.1 3.8 2.5 2.7 8.8 4.83.5 4.3 6.1 5.6 5.2 8.8 6.4 6.4 3.8 8.18.9 3.5 7.6 3.1 7.2 3.4 7.8 8.4 4.7 7.77.5 6.8 7.5 8.3 6.2 6.7 5.2 3.7 8.6 5.27.3 2.5 4.7 7.6 2.7 5.1 5.2 3.2 3.2 6.4

(a) Construct a stem and leaf diagram to represent this data.

(b) Comment on your results.

3. Over a period of 40 school days, the school canteen recorded the number of packets of crisps bought, each day, by boys and girls at the school.

The results are shown below.

Girls 10 13 27 24 48 16 33 2539 36 34 35 13 18 44 2128 29 10 38 29 16 11 3032 43 11 31 27 11 18 4025 26 44 23 19 32 41 11

Boys 17 40 49 42 24 46 32 2547 22 44 26 37 10 17 1934 28 42 32 14 42 20 4220 39 26 38 41 22 41 1134 31 36 29 20 28 28 48

(a) Construct a back to back stem and leaf diagram to represent the above data.

(b) Comment on your results i.e. When it comes to buying crisps, is there any difference between boys and girls?

BD2.4 a scattergraph,

1. The English and History marks of eight pupils are shown below.

English mark (%)

26 34 48 58 63 65 72 80

History mark (%)

30 49 45 63 72 74 80 75

(a) Construct a scatter graph for this data.

(b) Comment on the relationship between the pupils’ English and History marks.

(c) Draw the line of best fit.

(d) Using your line of best fit, if a pupil has an English mark of 50, what would you predict their History mark to be?

2. The height above sea level, in metres, and the temperature, in °C, of nine towns are shown below.

Height above sea level (m) 200 300 350 450 500 600 700 1100 130

0Temperature (°C) 18 16 15 13 14 13 10 7 6

(a) Construct a scatter graph for this data.

(b) Comment on the relationship between the height above sea level and the temperature.

(c) Draw the line of best fit.

(d) Using your line of best fit, if a town is 400 metres above sea level, what would you predict the temperature to be?

3. The weight of salt, in grammes, which will dissolve in a beaker of water at different temperatures, measured in °C, is given below.

Temperature (°C) 0 10 20 30 40 50Weight of salt (g) 52 57 60 73 79 87

(a) Construct a scatter graph for this data.

(b) Comment on the relationship between the temperature and the weight of salt.

(c) Draw the line of best fit.

(d) Using your line of best fit, if the water temperature is 25 °C, what weight of salt would you predict could be dissolved in the water?

Time for 100m (seconds) (Seconds)

12 131110

BD2.5 and a dot plot

1. A group of athletes are timed in a 100 m sprint. The results are shown below in the ‘dot plot’.

(a) What was the time of the fastest athlete?

(b) What was the time of the slowest athlete?

(c) What time occurred most often?

2. An observer notes the last digit on the registration plates of passing cars.

0 4 5 6 6 6 1 8 4 3 0 2 2 1 78 7 5 7 0 3 2 9 7 9 3 1 8 9 5

(a) Represent the above data in a dot plot.

(b) Which digit occurred most often?

(c) Which digit occurred least often?

BD3 Sequences and Straight LineBD3.1 I can continue and describe more complex sequences

including a sequence of square, triangular, and Fibonacci numbers

1. Describe the rule used to obtain the next term in these sequences and list the next three terms

a) 5, 10, 15, 20, ………. b) 40, 37, 34, 31, ……….

c) 1, 2, 4, 8, 16, ………. d) 4, 9, 16, 25, ……….

e) 1, 3, 6, 10, ………. f) 0, 1, 1, 2, 3, 5, ……….

BD3.2 I can find a rule (formula) for linear Patterns in problems which involve modelling real life contexts.

2. (a) How many dots are in the next I-shape in the sequence ?

(b) Complete this table for the sequence of I-shapes

(c) Write down a formula for the number of dots (d) when you know the shape number (s)

Shape Number (s) 1 2 3 4 5 16Number of dots (d) 7 12 17

BD3.3 I can use a formula of the form un=an ± b to find any term in an arithmetic sequence.

1. Given Un = 4n, find the first 3 terms in the sequence

2. Given Un = 3n – 2, find the first 3 terms in the sequence

3. Given Un = 5n + 1, find U10

4. Given Un = 2n – 3, find U20 and U50

5. If Un = 6n + 3, find the seventh term

6. Given Un = 10 – n, find U6

7. Given Un = 20 – 2n, find the first 3 terms

8. Given Un = 10 – 3n, find the fifth term

BD3.4 I can find a formula of the form un=an ± b to describe the nth term of a sequence.

Find a formula, of the form Un = an + b, to describe the nth term of these sequences, and find the tenth term in each

1. 4, 8, 12, 16, ……….

2. 4, 7, 10, 13, ……….

3. 1, 3, 5, 7, ……….

4. 5, 8, 11, 14, ……….

5. 3, 8, 13, 18, ……….

6. 9, 8, 7, 6, ……….

7. 17, 14, 11, 8 ……

BD3.5 I can complete a table of values for a straight line given the equation of the straight line in the form y=2x+1 etc.

In each example use the equation to complete the table

1. y = 2x + 1

x -2 0 2 4y

2. y = 3x – 2

x -1 0 1 2y

3. y = 5 – x

x -5 -1 0 2y

4. y = 10 – 2x

x -1 0 2 4y

5. y = ¼ x + 1

x -8 -4 8 12y

BD3.6 I can plot a straight line from a table of values.

1. For each example in BD3.5

a) Draw a Cartesian Diagram. Before drawing the axes decide on the minimum and maximum values of both x and y

b) Use the table to list 4 points, then plot the points on the Cartesian diagram

Draw a straight line through the 4 points and label the line

BD3.7 Given a drawn line I can set up a table of values and deduce the equation of the line in the form y=2 x+1 etc.

For each straight line shown on the graphs below

a) Copy out a table of values from x = -2 to 2

b) Fill in the corresponding y values into the table

c) State the equation of the straight line. Check that the equation works for every pair of values in your table

Graph 1

Graph 2

Graph 3

Graph 4

BD4 TimeBD4.1 I have revised using 24 hour times and equating them with

12 hour time and vice versa.

1. Change the following 12 hour clock times to 24 hour clock times

a) 5.45 am b) 2.40 pm c) 9.15 pm d) 10.35 am

2. Change the following 24 hour clock times to 12 hour clock times

a) 1715 b) 0705 c) 2145 d) 1045

BD4.2 I can calculate duration in hours and minutes including over midnight.

1. Calculate how long it is from

a) 3.15pm to 6.05pm b) 7.35am to 2.15pm

b) 1735 to1910 d) 0845 to 1515

2. A flight leaves London at 2135 and arrives in Arizona at 0805 the next day. How long did the flight take?

3. A cruise ship left port at 2.30pm on 28th June and returned on 9th July at 7.45am. How long did the journey take, in days, hours and minutes?

BD4.3 I can carry out calculations involving tenths and hundredths of a second.

1. Here are the results for the S2 60m sprint

Jack 6.9sec Tom 7.4sec Mark 7.1secs Jim 7.3secs Ali 7.0secs

a) Who was 3rd in the sprint

b) How much quicker was Jack than Tom

2. The table shows the result of the 2008 Olympic men’s 100m final

Rank Lane Name Nationality Reaction Time Result

4 Usain Bolt Jamaica 0.165 9.69

5Richard Thompson

Trinidad and Tobago 0.133 9.89

6 Walter Dix United States 0.133 9.91

4 9Churandy Martina

Netherlands Antilles 0.169 9.93

5 7 Asafa Powell Jamaica 0.134 9.95

6 2 Michael Frater Jamaica 0.147 9.97

7 8 Marc Burns Trinidad and Tobago 0.145 10.01

8 3 Darvis Patton United States 0.142 10.03

a) How much faster was Usain Bolt than

i) Richard Thompson ii) Darvis Patton

b) How much slower was Darvis Patton than

i) Richard Thompson ii) Asafa PowellBD4.4 I can convert minutes to hours and vice versa.

1. Convert the following hours into hours

a) 30mins b) 12mins c) 54mins d) 96mins

2. Convert the following into minutes

a) 0.25hrs b) 0.3hrs c) 1.6hrs d) 2.125hrs

BD5 Percentages

Do questions 1, 2 and 3 without a calculator.

1. a) 25% of £64 b) 50% of 990 kg c) 75% of 720 cm

d) 33⅓ % of 5796 e) 66⅔ % of £252 f)15% of 26 g

2. a) 7% of £25 b) 3% of 125 c) 8% of 2500 m

d) 40% of 68m e) 70% of 165 f) 30% of £5400

3. a) There are 318 pupils in S1. 50% of them are girls. How many are girls?

b) 10% of the 650 people attending a football match are female. How many are male?

c) 75% of the 600 goals scored in the Scottish Premier League last season were right footed shots.

How many is this?

Use a calculator to answer questions 4 and 5

4. a) 23% of £170 b) 2.5 % of £6450

c) 17.5 % of £580 d) 45% of 2 kg

5. a) In the school car park 24% of the 125 cars are silver. How many are silver?

b) 35% of the 320 pupils surveyed said they read the Daily Record.

How many pupils is this?

c) 52% of the 1900 babies born in the UK one day were girls.

How many were girls?

BD5.1 I can find a percentage of a quantity.

1. A maths tutor charges £30 per hour. He decides to increase his charge by 5%. What will his new charge be?

2. The average attendance at Fir Park last season was 6800. This season it dropped by 8.5%. What is the average attendance this season?

3. Mary normally runs a total of 28 miles per week. She decides to increase her distance by 10% a week for the next four weeks. How many miles will she run in the fourth week?

4. It is estimated that an iceberg weighs 84000 tonnes. As the iceberg moves into warmer waters, its weight decreases by 25% each day. What will the iceberg weigh after 3 days in the water?

5. A cottage, bought for £90000 in 2005, was put on the market last week. Its value had appreciated by 15% since 2005. What is the cottage now worth?

6. Mrs King bought a new car for £17000. In the first year its value depreciated by 20% and in the second year its value fell by a further 15%. What was her car worth at the end of year 2?

BD5.2 I can calculate percentage increase and decrease

1. Alan scored 28 out of 40 in a Maths test. What was his percentage score?

2. There are 300 pupils in S1. 160 of them are girls. What percentage are boys?

3. In the 2011-2012 season Lionel Messi scored 73 of the 190 goals scored by Barcelona. What percentage of the total goals did he score ( to 1 d.p. )

4. Last year Sally was paid £20 per hour. This year she gets £22.50 per hour. Calculate her percentage increase in pay.

5. Jamie bought a car for £18000 in 2009 and sold it for £8000 three years later. Calculate the depreciation, and express it as a percentage of the cost when new, giving your answer to 1 decimal place.

1. Kerry bought a car in 2006. When she sold it four years later, she found that it had reduced in value by 60% and she received only £4640. How much had Kerry paid for the car in 2006?

2. Tony’s train fare has just gone up by 10%. His new fare is £3.85. What was Tony’s train fare before the price increase?

3. A computer is sold for £632.50. This price includes VAT at 15%. Calculate the price of the computer without VAT.

4. James bought a car last year. It has lost 12.5% of its value since then. It is now valued at £14875. How much did James pay for his car?

BD6 Money

BD5.3 I can express one quantity as a percentage of another and work out a percentage increase or decrease using the original value and final value.

BD5.4 I can calculate the initial value after a percentage increase or decrease

BD6.1 I can convert between currencies and in both directions.

The tables below shows the exchange rates to the pound on May 1st 2012

1. Use the exchange rates in the table to answer these questions

(a) Change £100 into Japanese Yen (b) Change £80 into Euros

(c) Change £250 into Australian Dollars (d) Change £50 into Thai Baht

2. Use the exchange rates in the table to change each currency into British pounds

(a) 6265 South African Rands (b) 7140 Russian Rubles

(c) 4182 Mexican Pesos (d) 5032 Hong Kong Dollars

3. Gavin and Hannah have booked a trip to New York.

(a) If they took £250 with them, how many dollars would they get?

(b) They spend 324 dollars, and change the remainder back into pounds. How many pounds did they get?

4. The cost of an Android ‘phone in India is 10305 rupees. The same ‘phone costs £122 in the UK and 1094 Kroner in Norway.

In which country is the ‘phone cheapest?

Basic Pay

BD6.2 I can calculate wages

American Dollar 1.62Australian Dollar 1.57Euro 1.23Hong Kong Dollar 12.58Indian Rupee 85.17Japanese Yen 130.07

Mexican Peso 20.91Norwegian Kroner 9.27Russian Ruble 47.6South African Rand 12.53Thai Baht 49.81

1 (a) Bibiani works on a production line. She gets paid £6·40 an hour for a 6 hour day.

What is Bibiani’s basic pay?

(b) What is Bibiani’s weekly wage if she works 5 days a week?

2. (a) John gets paid £284 for working a 40 hour week. What is John’s hourly rate?

(b) Calculate John’s annual wage.

3. (a) Sam’s hourly rate for a part-time job is £7.50. Last week his basic pay was £120.

How many hours did he work?

(b) Calculate Sam’s annual wage.

(c) Hence calculate Sam’s monthly wage.

4. Katie’s annual salary is £23920.

If she works a 40 hour week, calculate Katie’s hourly rate.

Overtime Pay

5. Copy and complete the table, calculating the overtime rates for each basic rate of pay.

Basic RateDouble

Time

Time and ahalf

Time and a

quarter(a) £16(b) £8.60

6. Terry is a car mechanic. Her basic rate is £10.80 per hour, for a 40 hour week. Overtime is paid at time-and-a-half. Last week, Terry worked 3 hours overtime.

Calculate her total weekly pay.

7. Joe’s basic hourly rate is £12. Overtime is paid at double time.

How many hours of overtime did Joe work to earn £108?

Commission

8. Pauline sells electrical goods. She earns a basic wage of £1750 per month, plus 15% commission on sales over £4000.

This month, Pauline’s sales were £6280.

Calculate her gross pay.

Wage Rise

9. Aamir earns an annual salary of £31500. He has asked to be paid £32200 next year.

If Aamir’s employer offers a 2.5% rise, should he accept the offer?

1. Catherine works in an optician.

Copy her wage slip and calculate her gross pay, deductions and Net pay.

NAME: C Good

MONTH:9

TAX CODE:810L

NI NUMBER:MK 43 51 22 A

BASIC:£1605

OVERTIME:£210

BONUS: COMMISSION:£150

GROSS PAY:£

INCOME TAX:£176.22

NATIONAL INSURANCE:£120.32

PENSION:£48.15

OTHER:TOTAL DEDUCTIONS:£NET PAY:£

Profit & Loss

1. Steven spent £350 buying the parts to build a PC. He sold it to a friend for £413.

Calculate his percentage profit.

Hire Purchase

1. The cash price of a new car is £14000. The car can be bought on hire purchase for a deposit of 5% followed by 36 monthly payments of £430.

How much more does the car cost using this method of payment?

2. The total cost of a flat screen TV bought on HP is £960. The deposit is £150, and is followed by 12 equal monthly instalments.

Calculate the cost of these payments.

BD6.3 I can interpret a payslip

BD6.4 I can calculate Net Pay

BD6.6 I have experience of solving problems that include profit and loss and Hire Purchase