Functions and graphs usually include a small set of patterns.
If you master these, you can pick up marks quickly.
Core question types
| Question type | Typical marks | What examiners want |
|---|---|---|
| Reading values from a graph | $1$–$2$ | Accurate readings with correct units |
| Plotting points and drawing curves | $2$–$4$ | Smooth curve through all points, not dot-to-dot |
| Gradient and intercept | $2$–$3$ | Correct formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ |
| Composite functions $fg(x)$ | $2$–$3$ | Substitute inner function first |
| Inverse functions $f^{-1}(x)$ | $3$–$4$ | Swap $x$ and $y$, then rearrange |
| Real-life graph interpretation | $2$–$4$ | Describe what each section means in context |
Fast improvement tips
Tip 1: Use a clear scale. If the scale is wrong, the whole question collapses. Count grid squares before you start plotting.
Tip 2: Plot points first, draw later. Always mark points before drawing the line or curve. Use a sharp pencil and small crosses, not blobs.
Tip 3: Check for reasonableness. If a value is outside the graph, you misread the axis. Substitute your answer back into the equation to verify.
Tip 4: Know the shape before you plot. Quadratics are U-shaped (or n-shaped). Cubics have an S-curve. Reciprocals have two branches. If your graph doesn’t match the expected shape, recheck your table of values.
Practice strategy
Do $5$–$8$ short questions daily instead of one long worksheet. Consistency beats volume. Focus on one sub-type per session (e.g., only inverse functions, only gradient questions).
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