AQA GCSE Engineering: Maths and science for engineers, a complete overview of calculations, forces and electrical work

What the maths and science topic demands

Engineering decisions rest on numbers: how big, how strong, how much current, how efficient. This topic gives you the calculation toolkit that runs through the whole qualification, from tolerances in manufacture to gear ratios in systems. AQA rewards fluent, accurate calculation with correct units and clear working. This overview ties together the three dot-point pages in the topic.

Calculations for engineering

Engineers work with SI units (metre, kilogram, second, newton, watt) and prefixes (kilo $\times 1000$, milli $\div 1000$, mega $\times 1000000$). You must rearrange formulae to make any term the subject, use ratio and proportion for gear ratios and scale drawings, calculate area (length times width, remembering $1 \text{ cm}^2 = 100 \text{ mm}^2$) and volume, and use standard form such as $4.7 \times 10^{3}$ for very large or small numbers. The recurring exam habit is stating the correct unit on every answer.

Forces and mechanical advantage

A moment is a turning effect: $\text{moment} = F \times d$ in newton metres. The principle of moments says a balanced body has equal clockwise and anticlockwise moments, which finds unknown forces or distances. Mechanical advantage is load divided by effort, and velocity ratio is the distance moved by the effort divided by the distance moved by the load. Efficiency is useful output divided by total input, always below 100 percent because friction wastes energy.

Electrical calculations

Ohm's law links voltage, current and resistance: $V = I \times R$, with units volts, amperes and ohms. Electrical power is $P = V \times I$ in watts, and can also be found from $P = I^2 R$ or $P = V^2 / R$. Resistors in series add; resistors in parallel give a total smaller than the smallest single resistor. As always, rearrange to find the unknown and state the unit.

Check your knowledge

A mix of calculation and recall questions covering the maths and science topic. Attempt them under timed conditions, then check against the solutions.

1. Convert $2200 \text{ }\Omega$ to kilo-ohms. (1 mark)
2. A plate is $200 \text{ mm}$ by $150 \text{ mm}$. Calculate its area in $\text{mm}^2$. (2 marks)
3. Calculate the moment of a $40 \text{ N}$ force acting $0.25 \text{ m}$ from a pivot. (2 marks)
4. State the formula for mechanical advantage. (1 mark)
5. A $12 \text{ V}$ supply drives $0.5 \text{ A}$ through a heater. Calculate its resistance. (2 marks)
6. Calculate the power dissipated by that heater. (2 marks)
7. Two $10 \text{ }\Omega$ resistors are connected in series. State the total resistance. (1 mark)