Speed, Density and Pressure Revision Notes for AQA GCSE Maths

Speed, density and pressure

Understanding speed, density and pressure is all about learning the right formulas and knowing how to use them properly. These three concepts follow similar patterns - they all involve dividing one quantity by another to find a rate or relationship.

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Notice the pattern: all three concepts involve division to find a relationship between quantities. This makes them easier to remember and work with once you understand the underlying structure.

Speed

Speed tells us how fast something is moving by measuring the distance travelled per unit of time. Common units include kilometres per hour (km/h) and metres per second (m/s).

The formula for speed is:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

This relationship can be rearranged to find any of the three quantities:

Time = Distance ÷ Speed
Distance = Speed × Time

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Units are crucial: Make sure your distance and time units match what you want for speed. If distance is in metres and time is in seconds, speed will be in m/s.

Formula triangle for speed

Formula triangles are incredibly useful tools for remembering these relationships. For speed calculations, the triangle shows:

D (Distance) at the top
S (Speed) and T (Time) at the bottom, separated by a multiplication sign

To use a formula triangle:

Cover up the quantity you want to find
What remains shows you the calculation needed
Put in your values and calculate, checking your units are correct

Worked example

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Worked Example: Calculating Time from Speed and Distance

When a car travels 9 miles at 36 miles per hour, we can calculate the time taken:

Step 1: Write down the formula $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

Step 2: Substitute the values $\text{Time} = \frac{9 \text{ miles}}{36 \text{ mph}} = 0.25 \text{ hours}$

Step 3: Convert to minutes $0.25 \text{ hours} = 0.25 \times 60 = 15 \text{ minutes}$

Density

Density measures how much mass is packed into a given volume of a substance. It's typically measured in kilogrammes per cubic metre (kg/m³) or grammes per cubic centimetre (g/cm³).

The formula for density is:

$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

This can be rearranged to find:

Volume = Mass ÷ Density
Mass = Density × Volume

Formula triangle for density

The density triangle shows:

M (Mass) at the top
D (Density) and V (Volume) at the bottom, separated by a multiplication sign

Worked example

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Worked Example: Finding Mass from Density and Volume

For a chocolate bar with density 1.3 g/cm³ and volume 1800 cm³:

Step 1: Write down the formula $\text{Mass} = \text{Density} \times \text{Volume}$

Step 2: Substitute the values $\text{Mass} = 1.3 \text{ g/cm³} \times 1800 \text{ cm³} = 2340 \text{ g}$

Step 3: Convert to kilogrammes $2340 \text{ g} = 2.34 \text{ kg}$

chatImportant

Always check that your units match - if density is in g/cm³, volume must be in cm³ to get mass in grammes. Mismatched units are a common source of errors in density calculations.

Pressure

Pressure measures the amount of force acting per unit area. It's usually measured in Newtons per square metre (N/m²) or pascals (Pa), where 1 Pa = 1 N/m².

The formula for pressure is:

$\text{Pressure} = \frac{\text{Force}}{\text{Area}}$

This can be rearranged to find:

Area = Force ÷ Pressure
Force = Pressure × Area

Formula triangle for pressure

The pressure triangle shows:

F (Force) at the top
P (Pressure) and A (Area) at the bottom, separated by a multiplication sign

Worked example

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Worked Example: Calculating Pressure from Force and Area

A cylindrical barrel weighing 200 N rests on the ground. The circular base has a radius of 0.4 m:

Step 1: Calculate the area of the circular base $\text{Area} = \pi \times r^2 = \pi \times (0.4)^2 = 0.5026 \text{ m²}$

Step 2: Write down the formula $\text{Pressure} = \frac{\text{Force}}{\text{Area}}$

Step 3: Substitute the values $\text{Pressure} = \frac{200 \text{ N}}{0.5026 \text{ m²}} = 397.9 \text{ N/m²}$

Using formula triangles effectively

Formula triangles provide a simple method for remembering these relationships. They work by using the visual layout to show mathematical relationships clearly.

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The key steps for using formula triangles:

Cover up what you want to find
The remaining parts show you the calculation
Substitute your values carefully
Check your units make sense in the final answer

Whether you're calculating speed, density, or pressure, the same triangular approach works every time.

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Key Points to Remember:

Speed = Distance ÷ Time, measuring how fast something moves
Density = Mass ÷ Volume, measuring how much matter is in a given space
Pressure = Force ÷ Area, measuring how much force is spread over a surface
Formula triangles help you remember and rearrange these relationships quickly
Always check your units match throughout the calculation and make sense in your final answer
All three concepts follow the same pattern: dividing one quantity by another to find a rate or relationship

Speed, Density and Pressure (AQA GCSE Maths): Revision Notes