How to Answer 'Sketch a Graph' Questions

Use this guide to draw sketch graphs that show the correct physics in Cambridge IGCSE Physics 0625 exams.

What the examiner expects

A sketch graph must show:

1. Labelled axes (quantity and unit on each axis).
2. Correct shape (straight, curve, exponential, step).
3. Key features (starting point, end point, intercepts, gradient changes, flat sections).
4. Correct proportionality where relevant (through the origin for directly proportional).

Common graph shapes in IGCSE Physics

Straight line through the origin

$y \propto x$ (directly proportional). Examples: $F = kx$ (Hooke’s law), $V = IR$ (Ohm’s law at constant $R$), $W = Fd$.

Straight line not through the origin

$y = mx + c$ (linear but not proportional). Example: Celsius to kelvin conversion.

Curve (inverse proportion)

$y \propto 1/x$. Example: $p$ vs $V$ (Boyle’s law). The curve never touches the axes.

Exponential decay

Halving pattern. Example: activity vs time for radioactive decay. The curve approaches but never reaches zero.

Step graph (constant during state change)

Temperature vs time during melting or boiling. Flat sections at the melting and boiling points.

Process for drawing a sketch graph

1. Read the question to identify the two variables and the relationship.
2. Label the axes (quantity, unit).
3. Mark the origin and any known points.
4. Draw the correct shape.
5. Mark key features (flat sections, gradient changes, intercepts).

Common errors and how to correct them

1. Unlabelled axes. Always write the quantity and unit on each axis.
2. Wrong starting point. If the object starts from rest, the velocity-time graph starts at $(0, 0)$.
3. Straight line instead of curve. An inverse proportion is a smooth curve, not a straight line joining two points.
4. Curve touching the axis. Exponential decay and inverse proportions approach but never reach zero.

How to apply this in an exam

Label axes first. Think about the equation or physics to determine the shape. Draw the key features. Check: does the graph match the physics?