IP AMaths Notes (Upper Sec, Year 3-4): 03) Linear Law
Transform non-linear relationships into straight lines for graph paper work and regression checks in IP AMaths.
Q: What does IP AMaths Notes (Upper Sec, Year 3-4): 03) Linear Law cover?
A: Transform non-linear relationships into straight lines for graph paper work and regression checks in IP AMaths.
Linear-law questions ask you to recast a model so plotting gives a straight line. Identify the transformation, compute plotting coordinates, and interpret the resulting gradient and intercept.
Keep the full topic roadmap handy via our IP Maths tuition hub so you can jump into related drills, quizzes, or diagnostics as you move through these notes.
New to the Integrated Programme? Start with What is IP? | Browse all free IP notes.
These notes align with SEAB GCE O-Level Additional Mathematics (4049) content used in IP programmes (exams from 2025).
Status: SEAB O-Level Additional Mathematics 4049 syllabus (exams from 2025) checked 2025-11-30 - scope unchanged; remains the reference for this note.
The core idea is simple: Linear Law turns a curved model into a straight-line graph.
Use it as a working check: Decide what to plot on each axis before calculating values. The gradient and intercept must translate back to the original constants.
Then go one layer deeper: Example: for a power model y = A x^n, plot log(y) against log(x); the gradient gives n and the intercept gives log(A).
Choosing the plotting axes
Before making a table of values, decide what quantity should become the straight-line vertical axis and what should become the horizontal axis. This prevents the common mistake of plotting the original against the original when the model is not linear.
