Are these Units, Rates and Conversions notes free?

Yes. The full 3-page Units, Rates and Conversions sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Units, Rates and Conversions revision sheet cover?

A unit is part of the answer, The shapes that keep coming back, speed, distance and time, density of a material, population density, people per unit area, a conversion factor, worth 1, Worked: a rate across a unit boundary, Four rates, one idea, Speed, Density, Population density, Unit price.

Is this for Digital SAT SAT Math?

Yes, it is written for the Digital SAT SAT Math syllabus.

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Units, Rates and Conversions — Digital SAT SAT Math revision notes

A 3-page visual revision sheet for Units, Rates and Conversions, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Units, Rates and Conversions revision notes, page 1 of 3 — A preview of page 1 — all 3 pages open full size in the app.

Units, Rates and Conversions in one look

multiply by one, written as a fraction, until the units you do not want cancel

A unit is part of the answer

every conversion factor is a fraction worth exactly 1, because its top and bottom are the same amount written two ways: 60 minutes over 1 hour
multiplying by 1 changes the number and never the quantity, which is why a conversion chain can be as long as it needs to be
write each factor so the unit you want to LOSE sits diagonally opposite itself, once on top and once underneath. It then cancels
a rate carries two units, one over the other. Reading kilometres per hour as a single fraction is what makes it convertible at all

The shapes that keep coming back

speed, distance and time v=d/t
density of a material ρ=m/V
population density, people per unit area D=N/A
a conversion factor, worth 1 1=60 minutes/1 hour

Worked: a rate across a unit boundary

Q. a tap runs at 18 litres per minute. How many litres does it deliver in 2.5 hours?

the rate is per MINUTE and the time is in HOURS, so one of them has to move
convert the time: 2.5×60=150 minutes
now the units match: 150×18=2700
check the unit of the answer: minutes times litres per minute leaves litres, which is what was asked for

Answer: 2700 litres

Four rates, one idea

Speed: distance per unit time, so kilometres per hour or metres per second
Density: mass per unit volume, so grams per cubic centimetre
Population density: people per unit area, so people per square kilometre
Unit price: cost per unit amount, so rupees per litre or per kilogram

Page 1 of 3. The full sheet, all 3 pages, opens free in the app.

What this Units, Rates and Conversions sheet covers

A unit is part of the answer
The shapes that keep coming back
speed, distance and time
density of a material
population density, people per unit area
a conversion factor, worth 1
Worked: a rate across a unit boundary
Four rates, one idea
Speed
Density
Population density
Unit price
Worked: a two-part conversion
Worked: density with mismatched units
One constant rate, two pictures
Conversions worth knowing cold
Where does the conversion belong
Pacing, the calculator, and typed answers
Symbols and terms
Traps that cost points
Tricks that save time

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