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Welcome to GCSE Edexcel Maths revision.

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Topic M 25: Units, rates and scale.

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This video covers Foundation and Higher tiers.

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Convert length using 10 millimetres equals 1 centimetre, 100 centimetres equals 1 metre and 1000 metres equals 1 kilometre.

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Convert mass using 1000 grams equals 1 kilogram and 1000 kilograms equals 1 tonne.

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For area, square the length conversion: 1 square metres equals 10,000 square centimetres .

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For volume, cube it: 1 cubic metres equals 1,000,000 cubic centimetres .

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Capacity conversions include 1 litre equals 1000 ml and 1 ml equals 1 cubic centimetres .

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Therefore 1 litre equals 1000 cubic centimetres .

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Time uses 60 seconds per minute and 60 minutes per hour. 1 hour 30 min equals 1.5 hours, not 1.30 hours.

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A map scale 1 to 50,000 means 1 centimetre represents 50,000 centimetres equals 500 metres.

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A 6 centimetres map distance represents 3 kilometres.

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Measure in matching units before applying the scale.

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Worked example: A drawing uses scale 1 : 20.

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A real length of 2.4 metres is 240 centimetres, so the drawn length is 240 divided by 20 equals 12 centimetres.

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Average speed equals the fraction with numerator open bracket distance close bracket and denominator open bracket time close bracket ,

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end fraction ,

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distance equals speed multiplied by time,

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and time equals the fraction with numerator open bracket distance close bracket and denominator open bracket speed close bracket ,

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end fraction .

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Use consistent units.

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Converting kilometres per hour to metres per second

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Worked example: 150 kilometres in 2.5 hours gives an average speed of 60 kilometres per hour.

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This does not mean the speed was 60 kilometres per hour throughout.

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To convert kilometres per hour to metres per second,

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divide by 3.6: 72 kilometres per hour equals the fraction with numerator open bracket 72,000 close bracket and denominator open bracket 3600 close bracket ,

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end fraction equals 20 metres per second.

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Reverse by multiplying by 3.6.

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Density equals the fraction with numerator open bracket mass close bracket and denominator open bracket volume close bracket , end fraction .

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A 540 grams object with volume 200 cubic centimetres has density 2.7 grams over cubic centimetres .

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Rearrange to mass equals density multiplied by volume.

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Pressure equals the fraction with numerator open bracket force close bracket and denominator open bracket area close bracket ,

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end fraction . 120 newtons spread over 0.03 square metres gives 4000 newtons per square metre ,

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or 4000 pascals.

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The same force on a smaller area gives greater pressure.

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Rates of pay and unit prices compare amount per unit. 18 pounds for 12 kilograms costs 1 pound and 50 pence per kilogram;

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14 pounds for 8 kilograms costs 1 pound and 75 pence per kilogram,

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so the first is cheaper per kilogram.

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Worked example: A journey covers 60 kilometres in 1 hour and 120 kilometres in 3 hours.

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Overall average speed equals 180 over 4 equals 45 kilometres per hour.

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It is not the arithmetic mean of 60 and 40 kilometres per hour because the time intervals differ.

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For exchange rates, identify the direction: if 1 pound buys 1.20 euros, 50 pounds buys 60, euros while 60 euros converts to 60 pounds divided by 1.20 equals 50 pounds.

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Include any stated fees separately.

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Check units by cancelling them: open bracket g over cubic centimetres close bracket multiplied by cubic centimetres gives g.

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Dimensional checks can reveal an inverted formula.

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That completes Units, rates and scale.

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Revisit the notes and test yourself on the revision website.