AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Determine the uncertainties in the gradient and intercept of a…
Full specification wording
Limitation of physical measurements: Determine the uncertainties in the gradient and intercept of a straight-line graph.
The gradient and intercept of a straight-line graph are found from a line of best fit, but that line is not unique.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 6 of 7
- 2 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The gradient and intercept of a straight-line graph are found from a line of best fit, but that line is not unique. Draw the steepest and shallowest lines that remain consistent with the error bars, then calculate the gradient of each. Half the difference between the steepest and shallowest gradients gives the uncertainty in the gradient. Repeat for the intercept: read the intercept of each extreme line and halve the difference. For example, if gradients are 2.4 and 2.0, the best gradient is 2.2 ± 0.2 in the stated units. This method links graphical work to the uncertainty in a derived quantity.
What earns the marks
- Draw a line of best fit through the data, taking account of error bars.
- Draw a steepest and a shallowest acceptable line that still pass through the error bars.
- Calculate the gradient of the best, steepest and shallowest lines using well-separated points on each line.
- Find the uncertainty as half the difference between the steepest and shallowest values.
- Read the intercept of each extreme line and halve the difference to find the intercept uncertainty.
- State the final result with correct units and a sensible number of significant figures.
Common mistakes and how to put them right
Using the difference between the steepest and shallowest values directly as the uncertainty instead of halving it.
Put it right by dividing by two.
Choosing extreme lines that miss the error bars entirely.
Put it right by ensuring each extreme line still passes through the bars.
Reading gradient points too close together, which magnifies reading error.
Put it right by using points near opposite ends of the line.
Exam tips
- Show the coordinates you used for each gradient calculation so your method is clear.
- Keep units consistent and quote the gradient and intercept with their uncertainties and units.
- If error bars are small, say so and explain that the uncertainty is correspondingly small.
Try the lesson
The start of the Limitation of physical measurements: Determine the uncertainties in the gradient and intercept of a straight-line graph. lesson, made from checked teaching notes for this specification point.
Have a go first
A student plots a graph and draws a line of best fit, a line of maximum gradient, and a line of minimum gradient. The gradient of the line of maximum gradient is 5.2 and the gradient of the line of minimum gradient is 4.4. What is the uncertainty in the gradient of the line of best fit?
Listen
The gradient and intercept of a straight-line graph are found from a line of best fit, but that line is not unique. Draw the steepest and shallowest lines that remain consistent with the error bars, then calculate the gradient of each. Half the difference between the steepest and shallowest gradients gives the uncertainty in the gradient. Repeat for the intercept: read the intercept of each extreme line and halve the difference. For example, if gradients are 2.4 and 2.0, the best gradient is 2.2 ± 0.2 in the stated units. This method links graphical work to the uncertainty in a derived quantity. A strong answer earns marks for these points. Draw a line of best fit through the data, taking account of error bars. Draw a steepest and a shallowest acceptable line that still pass through the error bars. Calculate the gradient of the best, steepest and shallowest lines using well-separated points on each line. Find the uncertainty as half the difference between the steepest and shallowest values. A common slip: Using the difference between the steepest and shallowest values directly as the uncertainty instead of halving it. Instead, dividing by two. Exam tip: Show the coordinates you used for each gradient calculation so your method is clear.
Key words
Say what each word means before you turn the card.
Lines of best fit
Try answering aloud or in your head before turning the card.
Gradient and intercept
Try answering aloud or in your head before turning the card.
See every definition
- Lines of best fit
- A line drawn through the data taking account of error bars, from which the gradient and intercept are found.
- Gradient and intercept
- Values found from a line of best fit, whose uncertainties are obtained by halving the difference between the steepest and shallowest values.
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