Exam & Papers · Graphs and sketches
Graph and sketch questions in SPM Additional Mathematics
Graph work turns up as plotting a straight line in a linear-law question, sketching the shape of a curve, shading a region, and reading a value back off a graph you have drawn. Label the axes with units, keep to a sensible scale, plot points accurately, and show your construction lines, with analytic marking, the method marks live in the drawing, not only in the final number.
What this page covers
Across the two written papers, Add Math asks you to work with graphs in several ways: plotting a straight line in a linear-law question, sketching the shape of a curve, shading a region that satisfies inequalities, and reading a value back off a graph you have drawn. These questions reward care as much as knowledge.
Because the papers are marked analytically, with method marks awarded, a graph drawn neatly and labelled correctly earns marks well before you reach the final answer. This page sorts the graph and sketch question types you will meet and shows the drawing habits that keep those marks safe.
Paper 1 runs for 2 hours (80 marks, Sections A and B) and Paper 2 for 2 hours 30 minutes (100 marks, Sections A, B and C); there is no Paper 3, so every graph is drawn by hand on paper.
The kinds of graph work you will meet
It helps to name the job before you start drawing, because each type is marked for different things. Broadly there are four families, and a single question may combine two of them, for instance, drawing a graph and then reading a value from it.
| Question type | What you do | Where the marks sit |
|---|---|---|
| Linear law | Reduce a non-linear relation to the form , plot the points, and draw the line of best fit | Correct axes and plotting, then the gradient and intercept read from your line |
| Curve sketching | Show the shape of a quadratic, reciprocal, exponential or logarithmic function | Intercepts, turning point, asymptote and the correct overall shape |
| Shading a region | Draw straight-line boundaries and shade the region satisfying several inequalities | Correct lines, the correct side shaded, and the vertices identified |
| Reading a graph | Use a graph you have drawn to find a gradient, an area, or a value at a point | Visible construction lines and a value read to the accuracy of your scale |
Notice that a linear-law question is really an algebra question in disguise: the hard step is rewriting the given relation so that it looks like , after which the drawing is straightforward. A sketch question, by contrast, is testing whether you know how a family of functions behaves, so the key features matter far more than neatness.
Plotting and reading a graph for marks
When a question says plot or draw, you are working on the grid to scale, and small habits protect real marks.
- 1
Label the axes
Write the quantity and its unit on each axis, and state the scale you are using.
- 2
Choose a friendly scale
Pick a scale that fills the grid and is easy to read back, such as 2 cm to 1 unit.
- 3
Mark points as crosses
Use a small, sharp cross for each point rather than a heavy dot you cannot see under the line.
- 4
Draw the line or curve
Use a ruler for a straight line of best fit, or a single smooth stroke for a curve.
- 5
Show construction lines
When you read a value, draw the dashed lines across to the axes and leave them on the page.
A readable scale saves marks
A scale like 1 cm to 3 units is hard to read back accurately. Choose 1, 2, 5 or 10 units per large square so that intermediate values are easy to plot and easy to read.
Plot, draw, or sketch, read the instruction
The command word tells you how much accuracy is expected. To plot or draw means work to scale on graph paper from a table of values or given data.
To sketch means show the shape and the key features, intercepts, turning point, and any asymptote, with the parts correctly proportioned; graph paper is not needed and the drawing need not be to scale. Reading the instruction correctly stops you wasting minutes drawing an accurate graph when only a shape was asked for, and it stops you offering a rough sketch when accurate plotting was required.
Two variables and are related by , where and are constants. Written in the linear form , the straight-line graph of against passes through the points and .
Find the values of and .
Show worked solution
Here is plotted against , so the gradient of the line is and the vertical intercept is .
Substitute the point into with :
So and , which gives . The method marks come from writing the relation in linear form and finding the gradient; the accuracy marks come from the correct values.
How we rehearse this one-to-one
In one-to-one lessons our teachers put a sheet of graph paper in front of you early and turn plotting into a routine you can trust: choose the scale aloud, label the axes with units, plot with crosses, draw a ruled line or a smooth curve, and read values back with construction lines left on the page. Because the paper awards method marks, we drill the habits that earn them rather than only the final answer.
We rehearse the difference between plotting and sketching so you spend accuracy where it is asked for and speed where a shape is enough. Teachers at spmaddmath.com.my are experienced, and lessons are online and taught in English.
Message us on WhatsApp to arrange a one-hour paid class from RM50/hr at the teacher's rate.
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Book a Trial ClassFrequently asked questions
Do I earn marks for the graph itself, or only for the final answer?
Both. With analytic marking, method marks are awarded for correct axes, a sensible scale, accurate plotting and a properly drawn line or curve, even before you reach the final value.
A neat, well-labelled graph protects marks that a bare answer cannot.
What is the difference between 'plot' and 'sketch'?
To plot means work accurately to scale on graph paper from data. To sketch means show the shape and key features, intercepts, turning point, asymptote, correctly proportioned, with no grid needed.
Read the command word before you start drawing.
Which scale should I choose for plotting?
Choose a scale that fills the grid and is easy to read back: 1, 2, 5 or 10 units per large square. Avoid awkward scales such as 3 units per square, which make intermediate points hard to plot and to read.
Are graph questions only in one paper?
Graph and sketch work appears across both written papers. Paper 1 is 2 hours and Paper 2 is 2 hours 30 minutes; there is no Paper 3, so every graph is drawn by hand on paper using a non-programmable scientific calculator for any figures.
Source:SRC-FORMAT