CSEC PHYSICS · SECTION A · LESSON A2

Graphs, the Line of Best Fit, Gradient and Significant Figures

How to plot a graph that earns full marks, draw a line of best fit, calculate a gradient with its unit, interpret what it means, and express answers to a suitable number of significant figures.

MechanicsA 1.4A 1.5A 1.6≈ 40 min🎮 3 games
Before you start

By the end of this lesson you can…

Step 1 · Watch

Explainer video

5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.

LESSON A2 · EXPLAINER

Graphs, the Line of Best Fit, Gradient and Significant Figures

Graph plotting and gradient questions are among the most reliable marks in Paper 2 — and among the most often lost through missing units.

Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.

Step 2 · Read

Key notes

Copy these into your notebook in your own words — that is how they stick.

Axes

Quantity and unit on each; independent variable on the x-axis.

Scale

Simple even steps; points fill more than half of the grid.

Best fit

Smooth line or straight ruled line; roughly equal points either side.

Gradient

Δy ÷ Δx with a large triangle (more than half the line).

Gradient unit

unit of y ÷ unit of x.

Meaning

d–t: speed. v–t: acceleration (area = distance). weight–mass: g. force–extension: spring constant.

Proportional

Straight line through the origin.

Significant figures

Same s.f. as the least precise data; round at the end.

EXAM TIPS & COMMON MISTAKES

  • Show the triangle on your graph and the values used — gradient marks need the working.
  • Always write the unit with your gradient; the examiners’ most common loss in graph questions is a missing or wrong unit.
  • Do not choose an awkward scale such as 3 or 7 squares per unit.
  • State what the gradient represents if the question asks — use the relationship between the variables on the axes.
Play & practise

Games

3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Physics Arcade.

Step 3 · Practise

Paper 1 practice — multiple choice

8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.

Syllabus A 1.3

1. The independent variable in an experiment is usually plotted on the

Answer: A. The variable you change is plotted on the horizontal axis.
Syllabus A 1.4

2. A line of best fit should be drawn so that it

Answer: B. The best-fit line is the best average of the data.
Syllabus A 1.5

3. The gradient of a straight line graph is calculated as

Answer: C. Gradient is the change in y over the change in x.
Syllabus A 1.5

4. The gradient of a distance (m) against time (s) graph has unit

Answer: D. unit of y ÷ unit of x = m ÷ s.
Syllabus A 4.2

5. The gradient of a velocity–time graph represents

Answer: A. Gradient of v–t is Δv ÷ Δt = acceleration.
Syllabus A 1.6

6. How many significant figures are in 0.0450?

Answer: B. 4 and 5 are significant, and the trailing zero after the decimal point is significant; the leading zeros are not.
Syllabus A 1.6

7. A student calculates speed = 5.2 m ÷ 3.1 s on a calculator and gets 1.677419… The best answer is

Answer: B. Two significant figures, the same as the data.
Syllabus A 1.3

8. A straight-line graph through the origin shows that y is

Answer: C. y = mx is direct proportion.
Step 4 · Apply

Paper 2 practice — structured questions

Write full answers, then reveal the mark scheme and tick the points you earned (12 marks in total). Show all your working — method marks count. Your answers are saved on this device.

Paper 2 style · Graph analysis

Question 1 [12 marks]

A trolley moves along a straight track. Its distance d from a starting mark is measured at different times t. The graph of d against t is a straight line through (0, 0) and (5.0 s, 10.0 m). A calculator may be used.

(a) (a) State which variable should be plotted on the x-axis, and why. [2]

MARK SCHEME — (a) (max 2)

(b) (b) State two features of a good scale for the axes. [2]

MARK SCHEME — (b) (max 2)

(c) (c) Calculate the gradient of the line. [3]

MARK SCHEME — (c) (max 3)

(d) (d) State the physical quantity represented by the gradient. [1]

MARK SCHEME — (d) (max 1)

(e) (e) What does the line passing through the origin tell you about d and t? [1]

MARK SCHEME — (e) (max 1)

(f) (f) The data: d = 4.0 m when t = 2.0 s. Calculate 4.0 ÷ 2.0 and write the answer to a suitable number of significant figures, explaining your choice. [3]

MARK SCHEME — (f) (max 3)

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Sources

Where this topic appears in CSEC papers

Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.