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Pressure

FoundationHigherAQAEdexcelOCR

This free Foundation and Higher GCSE Maths worksheet on pressure helps you revise pressure, force and area calculations. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. Pressure = force ÷ area.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

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Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Pressure is the force applied per unit of area, calculated as \(\text{pressure} = \frac{\text{force}}{\text{area}}\). It is measured in newtons per square metre, also called pascals.

The relationship explains why a drawing pin pushes into a wall easily while your thumb does not. The same force spread over a tiny area produces a much greater pressure.

Because area is on the bottom, increasing the area reduces the pressure. That is why skis stop you sinking into snow and why heavy vehicles have wide tyres — the load is spread over a larger area.

Revision notes

The formula

\(P = \frac{F}{A}\), where \(P\) is pressure, \(F\) is force and \(A\) is area.

A force of \(200\)N on an area of \(4\)m² gives a pressure of \(50\)N/m².

Rearranging

Force equals pressure times area, and area equals force divided by pressure.

So a pressure of \(30\)N/m² acting on \(5\)m² produces a force of \(150\)N.

Why area matters

For a fixed force, a smaller area gives a greater pressure.

This is why sharp objects cut easily and why wide tyres reduce ground pressure. Questions often ask you to explain this rather than just calculate.

Key points

  • Pressure is force divided by area.
  • Force equals pressure times area.
  • Area equals force divided by pressure.
  • Units are N/m², also called pascals.
  • A smaller area gives a greater pressure.
  • Convert to consistent units before calculating.

Worked examples

Example 1

A force of \(600\)N acts on an area of \(3\)m². Find the pressure.

Working

\[\frac{600}{3}\]divide force by area
\[= 200\text{N/m}^2\]state the pressure with units

Example 2

A pressure of \(45\)N/m² acts on an area of \(8\)m². Find the force.

Working

\[F = PA = 45 \times 8\]force equals pressure times area
\[= 360\text{N}\]state the force

Example 3

Explain why a drawing pin pushes into a wall more easily than a thumb.

Working

\[\text{The point has a very small area}\]identify the key difference
\[\text{The same force gives a much greater pressure}\]explain using the formula

Common mistakes

  • Multiplying force by area to find pressure.

    Pressure is force divided by area, not the product.

  • Mixing units of area.

    Convert cm² to m² before calculating, remembering the factor is squared.

  • Omitting units.

    Pressure is measured in N/m² or pascals.

  • Thinking a larger area gives more pressure.

    Area is on the bottom, so a larger area reduces the pressure.

Exam tips

  • Write the formula down before substituting.
  • Convert areas carefully, squaring the length factor.
  • Include N/m² or pascals in the answer.
  • Explain the area effect in context when asked.

Key terms

Pressure
Force per unit area.
Force
A push or pull, measured in newtons.
Pascal
A unit of pressure equal to one newton per square metre.
Newton
The unit of force.

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Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.