Speed, Density & Pressure (Edexcel IGCSE Maths B): Revision Note

• Look out for a mixture of units

  • Time can be given as minutes but common phrases like 'half an hour' (30 minutes) could also be used in the same question

  • Any mixed units should be those in common use and easy to convert, e.g., g to kg or m to km etc

A box exerts a force of 140 newtons on a table.
The pressure on the table is 35 newtons/m².

$p=\frac{F}{A}$        $$\begin{gathered} p=\mathrm{pressure} \\ F=\mathrm{force} \\ A=\mathrm{area} \end{gathered}$$

Calculate the area of the box that is in contact with the table.

Answer:

Method 1

Substitute the numbers you know into the formula

$35=\frac{140}{A}$      

Solve the equation for A
First multiply both sides by A to get A out of the denominator

$35A=140$

Then divide by 35 to find the value of A

$\begin{array}{rcl}A& =& \frac{140}{35}\end{array}$

The units will be m², matching the units seen in newtons/m²

4 m² 

Method 2

Use the given formula to create a formula triangle for pressure, force and area

$$\begin{gathered} F \\ pA \end{gathered}$$      

A is on the bottom of the triangle, so this tells us to divide F by P

$A=\frac{F}{p}=\frac{140}{35}=4$      

4 m²

The density of pure gold is 19.3 g/cm³.

What is the volume of a gold bar that has a mass of 0.454 kg? 

Answer:

Begin by checking that all of the units are consistent
Density is given in g/cm³
Convert the mass of the gold bar into grams to match the units for density

0.454 kg = (0.454 × 1000) g = 454 g

The units of density are g/cm³, so divide the mass (g) by the volume (cm³)

Or, write out the formula triangle

Write out the formula that you will need

$\mathrm{Volume}=\frac{\mathrm{mass}}{\mathrm{density}}$

Substitute the given values for the mass and the density

$\mathrm{Volume}=\frac{454}{19.3}=23.5233...$

Make sure you give the correct units with your final answer
The density is given in g/cm³, so the volume should be cm³

Volume = 23.5 cm³ (1 d.p.)