Practical investigation: a non-linear relationship (internal)
Internal 4 credits Linearising Independent variable Graphing Gradient DiscussionAS 91168, 4 credits. Achieved names exactly three requirements: collect data over a reasonable range and number of values, draw a graph showing the relationship, and write a conclusion describing the TYPE of mathematical relationship. Excellence requires a DISCUSSION addressing five specific named critical issues — not a general evaluation.
1 Reading the notation
The Excellence discussion has five specific named issues — not a general evaluation paragraph.📖 Terms the schedule grades you on
4 terms- Carry out (Achieved)
- Collect over a reasonable range/number; graph the relationship; conclude the TYPE.
- In-depth (Merit)
- Control significant variables; increase measurement accuracy; conclude the relationship OBTAINED from data.
- Comprehensive (Excellence)
- A discussion addressing FIVE named critical issues.
- The five critical issues
- Range limits at both ends; justifying a controlled variable; measurement difficulties overcome; findings vs physics ideas; unexpected results and validity.
2 Linearising the relationship
A straight line is the only shape you can confidently extract a gradient from.| If the relationship is | Plot | Gradient gives |
|---|---|---|
| y ∝ x² | y against x² | The constant k in y = kx² |
| y ∝ √x | y against √x | The constant in y = k√x |
| y ∝ 1/x | y against 1/x | The constant in y = k/x |
| T = 2π√(L/g) | T² against L | 4π²/g, so g = 4π²/gradient |
All of these produce a line through the origin. A significant non-zero intercept means either the theory does not fit or there is a systematic error — both worth saying.
3 Graphing and the gradient
The axis label is where the transformation is communicated. ✕Using raw data points for the gradient
Reading the gradient from two adjacent raw data points defeats the purpose of the line of best fit, which exists to average out scatter. Always pick two widely-separated points ON the fitted line itself.4 The Excellence-level discussion
Five specific, named issues — controlling vs justifying, and the two ends of the range.The five issues, restated as checklist items
- Why the range has a limit at BOTH the low and high end.
- Why a specific variable NEEDED to be controlled (not just that it was).
- A specific measurement difficulty, and how it was overcome.
- The findings connected explicitly to physics ideas.
- Any unexpected result, its likely cause, and its effect on validity.
Practice
Recall it first, then use it — testing yourself builds the memory, where rereading the notes above only feels easier.
Recall and application shuffled together — you have to work out what each item wants before you can answer it, which is the part the exam actually tests. Both kinds feed the same spacing schedule, so anything you miss comes back sooner.
Say the answer out loud before flipping — that attempt is where the learning happens, even when you get it wrong.
Exam-style only. Instant feedback, shuffled each attempt, best score saved on this device.