GCSE Mathematics · Edexcel 1MA1 · Topic A.2

Graphs

Key points

Straight lines: $y = mx + c$ , where $m$ is the gradient and $c$ is the $y$ -intercept. Gradient = $\frac{\text{change in } y}{\text{change in } x}$ .
Parallel lines have equal gradients; perpendicular lines have gradients that multiply to $-1$ (higher).
Quadratic graphs are U-shaped (or ∩ if the $x^2$ term is negative). Roots are where the curve crosses the $x$ -axis; the turning point can be found by completing the square.
Recognise cubic ( $y = x^3$ ), reciprocal ( $y = \frac{1}{x}$ ) and, at higher tier, exponential ( $y = k^x$ ) and trigonometric graphs.
Real-life graphs: on a distance–time graph the gradient is speed; on a velocity–time graph the gradient is acceleration and the area is distance.
Circle centred at the origin (higher): $x^2 + y^2 = r^2$ . The tangent at a point is perpendicular to the radius.
Graph transformations (higher): $y = f(x) + a$ moves up $a$ ; $y = f(x + a)$ moves left $a$ ; $y = -f(x)$ reflects in the $x$ -axis.

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Graphs turn algebra into pictures: a line or curve shows every solution of its equation at once. You need to plot and recognise standard graphs, find equations of straight lines, read real-life graphs and, at Higher tier, work with circles…

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