Eduqas A-Level Product Design mathematics for design and technology: a complete overview

What this theme demands

The mathematics is woven through Component 1, and it is where careful, accurate candidates pick up marks others drop. The paper tests percentages and costing, scale and tolerancing, structural and mechanical calculations, and electronic calculations, with a calculator allowed but working and units carrying the marks. Marks are lost when units are wrong (area not in square metres, current in milliamps, a moment without newton metres), when a ratio is inverted, or when the square and cube scaling of area and volume is missed, and gained by showing method and units throughout. This overview ties the four dot-point pages together.

Costing, scale and tolerancing

Costing finds the material cost per part from the yield (parts per sheet, set by nesting), adds labour and overheads, and works out profit, selling price and break-even; percentage waste is the wasted area over the total. Scale relates drawing to real (reduction multiplies, enlargement divides), and the key rule is that a linear scale factor $k$ scales area by $k^2$ and volume by $k^3$, so size, weight and cost grow fast. Tolerances give upper and lower limits (size plus or minus the tolerance). See costing and quantities and scale, ratio and tolerancing maths.

Structural and mechanical calculations

The moment of a force is $M = F \times d$ in newton metres, with equilibrium when moments balance. Stress is $\sigma = \frac{F}{A}$ in pascals, strain $\varepsilon = \frac{\Delta L}{L}$ (no units), and Young's modulus $E = \frac{\sigma}{\varepsilon}$. Mechanical advantage is load over effort (or effort arm over load arm), and the gear (velocity) ratio is driven teeth over driver teeth, a reduction slowing the output and raising torque. See structural and mechanical calculations.

Electronic and systems calculations

Ohm's law is $V = IR$; power is $P = VI$ (also $I^2 R$ and $\frac{V^2}{R}$) in watts; energy is $E = Pt$. The potential divider output is $V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2}$, series resistors add and parallel resistors combine reciprocally, and an LED's series resistor is $\frac{V_{supply} - V_{LED}}{I}$. Convert milliamps to amps and keep the units. See electronic and systems calculations.

How to revise this theme

1. Drill costing. Material cost per part from the yield, plus labour, profit and break-even, and percentage waste over the total.
2. Master scale factors. Area scales by the square and volume by the cube of the linear factor; reductions multiply and enlargements divide.
3. Learn the structural and mechanical formulae. Moments, stress, strain, Young's modulus, mechanical advantage and gear ratios, with units.
4. Practise the electronics. Ohm's law, power, energy, the potential divider and the LED resistor, converting milliamps to amps.
5. Always show working and units. They carry the marks, so convert to consistent units first, then attempt the quiz.