94 Practise the maths 95

LEVEL 2

Formulae

Practise the mathsYou can use letters to represent unknown numbers in formulae. Scientists use a formula for radioactive decay to work out the age of fossilised bones.

Formulae20

1 Work out a 4 7 1 b 9 12 3 c 10 2 6 3 d 200 10 3 4

2 You can use this formula to calculate the distance you have travelled.a Calculate the value of D if S 30 and T 4.b Matt travels at an average speed of 40 km/h for

3.5 hours. How far has he travelled?

3 A phone company uses this formula to calculate the total cost of a bill.

C 5T 15M C is the total cost of the bill in penceT is the number of text messages sentM is the number of minutes of call time

Calculate the total cost of each of these bills.a

Texts sent: 20Minutes of call time: 50

b Texts sent: 91

Minutes of call time: 18

c Texts sent: 35

Minutes of call time: 106

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20.1 Using letters in formulae

Worked example: A courier company calculates the cost of sending a parcel using this formula.Use this formula to calculate the cost of a parcel weighing 4 kg.

Answer

C = 5W + 8

= 5 × 4 + 8

= 20 + 8

= 28

The cost is £28. (2 marks)

5W means 5 W

Remember BIDMAS (or BODMAS): you do division and multiplication before addition and subtraction.

Substitute the value for W into the formula. The parcel weighs 4 kg, so W 4.

1 A swimming pool manufacturer uses this formula to work out how much chlorine to add to a swimming pool.

C N L3 _______

100

C is the amount of chlorine in mlN is the number of people using the swimming poolL is the length of the swimming pool in metres

Calculate the amount of chlorine needed ifa 3 people use a 15 m swimming pool b 5 people use an 18 m swimming pool.

1 Alison is working out how much it will cost a group of her friends to go bowling.She uses this formula

C N(D 2G 5).C is the total cost in poundsN is the number of friendsD is the cost of dinner per personG is the cost of one game of bowling per person.

Calculate the value of C ifa N 5, D 12 and G 6 b N 4, D 15 and G 7.5 c N 7, D 10.5 and G 8

20.2 Using formulae with division

Worked example: Jake uses this formula to estimate how much paint he needs for a room.Estimate the amount of paint needed for a room which is 4 m wide.

20.3 Using formulae with brackets

Worked example: The total cost of a school theatre trip is calculated using this formula 36 students go on the theatre trip. The cost of one theatre ticket is £8.Calculate the total cost of the theatre trip.Answer

C = N(12 + T)

= 36(12 + 8)

= 36 × 20

= 720

The total cost is £720. (3 marks)

Remember BIDMAS (or BODMAS) you work out the brackets fi rst.

Answer

V = W 2 ____ 10

= 42 ___ 10

= 16 ___ 10

= 1.6

He needs 1.6 litres of paint. (2 marks)

42 means ‘4 squared’. You can use the x2 button on your calculator.

16 __ 10 means 16 10

V W2 ___

10

V is the amount of paint (in litres)W is the width of the room (in metres).

C 5W 8C is the cost of sending the parcel in poundsW is the weight of the parcel in kg

D ST D is the distance travelled in kmS is your average speed in km/hT is the time taken in hours

PTM_CH20_EX14

C N(12 T).C is the total cost in poundsN is the number of students T is the cost of one theatre ticket in pounds

96 97FormulaeWind power

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1 The UK produces about 45 000 MW of electrical power.a What percentage of the UK’s electrical power comes from wind power?b Calculate how many MW of electrical power come from wind power.

2 The table opposite shows four planned wind farm projects.a Use the formula given to calculate the cost of building the Camster

wind farm.b How much more will it cost to build the Whitelee project than the

Drone Hill project?c The Bradwell-on-Sea wind farm project has a budget of £7 million.

Will it go over budget? Show all of your working.

3 A newspaper prints a report on wind power.

Do you agree with the headline? You must show your working.

4 The world’s largest wind turbine is the Enercon E-126. It has a diameter of 126 m. Use the formula given to work out the amount of power produced by the Enercon E-126 if the wind speed is 18 mph. Round your answer to the nearest 100 000 W.

5 Chloe wants to buy a wind turbine for her house. She compares three different products.

a How much more does the Tempest cost than the Squirrel 150?b Calculate the power output of the Tempest if the wind speed

is 12.5 mph. Round your answer to the nerarest watt.c Calculate the power output of the Squirrel 150 if the wind speed

is 15 mph. Round your answer to the nerarest watt.

6 The average wind speed at Chloe’s school is 9.5 mph. The manufacturer of the Apollo 1200 claims that it will produce 1200 W of electrical power. Do you agree with this claim? Show all of your working.

Wind power - Formulae20 Questions LEVEL 2

Data sheetWind turbines create electricity using the power of the wind. Sources of energy like wind and solar power are called renewable sources of energy because they don‘t use up natural resources like oil or gas.

Around 2% of the electricity generated in the UK comes from wind turbines. This is enough to supply half a million homes.

Wind farm projects

Project Bradwell-on-Sea Whitelee Camster Drone HillNumber of turbines 10 39 25 22

Cost of manufacturing each turbine

£360 000 £620 000 £400 000 £230 000

Cost of transporting each turbine

£80 000 £195 000 £110 000 £65 000

Power output (megawatts) 5 42 15 9

Cost of project 5 N(M 1 T 1 £10 000)N is the number of wind turbines in the projectM is the cost of manufacturing each wind turbineT is the cost of transporting each wind turbine

Tempest

Diameter: 3.7 m

Price: £5875

Squirrel 150

Diameter: 1.5 m

Price: £755

Apollo 1200

Diameter: 2.7 m

Price £2450

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Power facts

Power output is measured in watts (W). One kilowatt (kW) is 1000 W, and 1 megawatt (MW) is 1 000 000 W.The power generated by a wind turbine depends on the diameter of the blades and the speed of the wind. You can use this formula to estimate the power of a turbine.P 5 D

2 × W3 ________ 60

P is the power generated in wattsD is the diameter of the blades in metresW is the wind speed in mph

Produces 1200 W of

power!

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Daily ★ Record

A REPORT ON THE COST OF NEW WIND FARMS

£1 million per MW