S1.3.1—General mathematics

Choose the mathematics from the relationship

First identify what changes, what is held constant and whether the model is additive, proportional, exponential or geometric. Rearrange symbols before substituting numbers; this exposes the dependence and reduces calculator-entry errors.

Signal in the problem	Useful move	Check
$y\propto x^n$	Write $y=kx^n$ and compare scale factors	Multiplying $x$ by $a$ multiplies $y$ by $a^n$
Exponential law	Use powers or logarithms to isolate the exponent	Equal intervals give a constant factor, not a constant difference
Rate	Divide the change in a quantity by the corresponding time or other interval	State the rate unit
Geometry/components	Draw the shape, mark angles and use Pythagoras or trigonometry	Result is consistent with the diagram

\text{percentage change}=\frac{\text{new}-\text{original}}{\text{original}}\times100%\text{percentage difference}=\frac{|A-B|}{(A+B)/2}\times100%

Worked check — rearrangement and proportion

From $E=\tfrac12mv^2$ , $v=\sqrt{2E/m}$ . If $m$ is unchanged and $E$ becomes four times larger, $v$ becomes $\sqrt4=2$ times larger. This scale check should agree with the calculated value.

Estimate before accepting a result

Keep guard digits until the end, compare the answer with the nearest order of magnitude and neglect an effect only when you can explain why it is small. A proportionality is not an equation until its constant is included.

How it is assessed

Questions show an algebraic equivalence or convert a decimal number to binary.

Command terms

Show / Identify

What earns marks

Show the algebraic step or use the correct base conversion, keeping constants and powers explicit.

Watch for

Substituting too early and losing a factor, or confusing binary place values.

Calculate carefully

Rearrange symbolically, resolve vectors, convert units and use proportional reasoning before substituting.

Report evidence

Propagate uncertainty with the correct operation, then use labelled graphs, error bars, gradients, intercepts and areas to test the model.

S1.3.1—General mathematics

Use Mathematical Tools

S1.3.1 Exam Analysis

Assessment in practice

Retrieve Mathematical Practice