Maths · AQA Paper 1
Ratio and Proportion
The ratio and proportion skills tested on AQA Paper 1: ratio, direct and inverse proportion, speed and density, units and scale, and repeated percentage change, all done without a calculator.
Lessons
Ticks are remembered on this device only.
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1
Ratio: Simplifying and Sharing
Writing and simplifying ratios, sharing amounts in a given ratio, and linking ratios to fractions.
9 terms -
2
Direct and Inverse Proportion
Solving proportion problems with the unitary method, best buys and exchange rates, and recognising direct and inverse proportion.
9 terms -
3
Speed, Distance, Time and Density
Using speed, distance and time, reading distance-time graphs, and calculating density and pressure.
9 terms -
4
Units, Conversions and Scale
Converting between metric units, using scales on maps and drawings, and changing units of area and volume.
9 terms -
5
Repeated Percentage Change and Compound Interest
Using multipliers for percentage change, compound interest and depreciation, and working back to the original amount.
9 terms
Key terms in this chapter
All 45, gathered from every lesson.
- Ratio
- A comparison of the sizes of two or more quantities, written with a colon such as \(3 : 5\).
- Part
- One share of a ratio. The parts added together make the whole.
- Simplest form
- A ratio whose parts have no common factor except 1.
- Equivalent ratios
- Ratios with the same relationship between their parts, such as \(1 : 2\) and \(3 : 6\).
- Share in a ratio
- Divide an amount into parts that are in a stated ratio.
- Total parts
- The sum of the numbers in a ratio, which is the number of equal parts the whole is split into.
- One part
- The value of a single part of the ratio, found by dividing the whole by the total parts.
- Proportion
- A part compared with the whole, often written as a fraction, decimal or percentage.
- Scale factor
- The number you multiply by to enlarge or reduce, such as \(\dfrac{3}{2}\) to increase in the ratio \(3 : 2\).
- Direct proportion
- A relationship in which two quantities increase or decrease at the same rate, so their ratio stays the same.
- Inverse proportion
- A relationship in which one quantity increases as the other decreases, so their product stays the same.
- Unitary method
- Finding the value of one unit first, then scaling up to the amount needed.
- Best buy
- The pack or size that costs least for the same amount.
- Unit price
- The cost of one unit, such as the price per gram or per item.
- Exchange rate
- The amount of one currency that you get for one unit of another.
- Constant of proportionality
- The fixed number \(k\) that links two quantities in direct proportion, so that \(y = kx\).
- Rate
- A comparison of two different kinds of quantity, such as pounds per hour.
- Proportional to
- The meaning of \(\propto\): changing in a fixed relationship with another quantity.
- Compound measure
- A measure made by comparing two different quantities, such as speed (distance per time).
- Speed
- How far something travels in a unit of time, found by dividing distance by time.
- Average speed
- Total distance travelled divided by total time taken.
- Distance-time graph
- A graph showing the distance from the start against time, where the gradient is the speed.
- Gradient
- A measure of how steep a line is, found by dividing the change up by the change across.
- Density
- The mass of a material in each unit of volume, found by dividing mass by volume.
- Mass
- The amount of matter in an object, measured in grams or kilograms.
- Volume
- The amount of space an object takes up, measured in cubic units such as cm\(^3\).
- Pressure
- The force on each unit of area, found by dividing force by area.
- Metric units
- Units based on powers of ten, such as millimetres, centimetres, metres and kilometres.
- Conversion factor
- The number you multiply or divide by to change from one unit to another.
- Capacity
- The amount a container can hold, measured in litres or millilitres.
- Tonne
- A unit of mass equal to 1000 kilograms.
- Scale
- The ratio between a length on a drawing or map and the real length.
- Scale factor
- The number you multiply by to turn a drawing length into a real length.
- Map
- A scale drawing of an area, where lengths on the paper represent real distances.
- Area
- The amount of surface a shape covers, measured in square units.
- Volume
- The amount of space a solid takes up, measured in cubic units.
- Multiplier
- The number you multiply by to apply a percentage change in one step.
- Compound interest
- Interest calculated on the original amount plus any interest already added.
- Simple interest
- Interest calculated only on the original amount, giving the same amount each year.
- Depreciation
- The fall in value of an item, such as a car, over time.
- Growth
- An increase over time, with a multiplier greater than 1.
- Decay
- A decrease over time, with a multiplier less than 1.
- Principal
- The amount of money first invested or borrowed.
- Original amount
- The starting value before a percentage change is applied.
- Per annum
- Each year.