Graphs of Motion · Form 4
Graphs of Motion: Paper 2 Answering Guide
How Graphs of Motion appears in Mathematics Paper 2 (Subjective), and how to lay out your working so you earn every method mark.
How it is examined
A Paper 2 favourite: a speed–time graph where you find acceleration from a gradient and total distance from the area, often across several stages of a journey. Real-life contexts run throughout, so read the units carefully.
Showing your working
Mathematics Paper 2 (Subjective) is worth 100 marks and gives marks for the steps, not only the answer. Write each line clearly: state the formula or rule, substitute the numbers, then simplify.
If the question carries units, carry them through to the final line.
A worked speed-time graph question, laid out for marks
Question: A motorcyclist starts from rest and accelerates uniformly to 24 m/s in 6 seconds. She then travels at a constant 24 m/s for the next 10 seconds, and finally decelerates uniformly to 12 m/s in a further 4 seconds.
(a) Find the acceleration during the first stage. (b) Find the total distance travelled in the 20 seconds.
(c) Find the average speed for the whole journey. (d) Find the acceleration during the last stage.
- (a) State the rule: acceleration = gradient = change in speed divided by time.
- Substitute: (24 minus 0) divided by 6 = 4 m/s squared.
- (b) State the rule: distance = area under the speed-time graph, split into three parts.
- Stage 1 (triangle): one half multiplied by 6 multiplied by 24 = 72 m.
- Stage 2 (rectangle): 24 multiplied by 10 = 240 m.
- Stage 3 (trapezium): one half multiplied by (24 plus 12) multiplied by 4 = 72 m.
- Total distance = 72 + 240 + 72 = 384 m.
- (c) State the rule: average speed = total distance divided by total time = 384 divided by 20 = 19.2 m/s.
- (d) Acceleration = (12 minus 24) divided by 4 = negative 3 m/s squared, a deceleration of 3 m/s squared.
Where the marks sit in this answer
A Paper 2 question like this is typically worth about 7 to 8 marks, spread across the parts rather than saved for the final line. Part (a) usually carries one method mark for gradient = change in speed divided by time and one accuracy mark for 4 m/s squared.
Part (b) rewards each correctly computed area, so the triangle, the rectangle and the trapezium can each score even before the total 384 m appears. Part (c) gives a mark for the correct method total distance divided by total time and a mark for 19.2 m/s.
Part (d) needs the negative sign to gain full credit. Because marks are attached to method lines, a fully written-out solution protects you: an arithmetic slip in one area costs that area alone, not the whole question.
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Do I have to draw the graph if the question only describes the journey in words?
Sketch it even when not asked. A quick speed-time sketch turns each stage into a shape you can see, which makes the triangle, rectangle and trapezium obvious and stops you missing a stage.
It costs under a minute and often earns a method mark for a correct diagram.
In part (b), can I use a single trapezium for the whole journey instead of three shapes?
Only if the whole outline is genuinely one trapezium, which needs the top to be a single straight line. Here the speed rises, stays flat, then falls, so the outline is not one clean trapezium.
Splitting into a triangle, a rectangle and a trapezium is the safe method and keeps your working easy to mark.
How should I round the average speed?
Follow the instruction in the question. If it asks for a set number of decimal places or significant figures, round only at the very end, keeping full accuracy in the working.
Here 384 divided by 20 = 19.2 m/s is exact, so no rounding is needed, but always carry the unit m/s into the final line.