| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Topic | Tangents, normals and gradients |
| Type | Find normal line equation at given point |
| Difficulty | Standard +0.3 This is a straightforward calculus application requiring finding where y=0, computing the derivative, finding the normal gradient, and writing the line equation. All steps are routine A-level techniques with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.07l Derivative of ln(x): and related functions1.07m Tangents and normals: gradient and equations |
Find the equation of the normal to the curve $y = 4 \ln(2x - 3)$ at the point where the curve crosses the $x$ axis. Give your answer in the form $ax + by + k = 0$ where $a > 0$.
[5]
\hfill \mbox{\textit{SPS SPS SM 2021 Q4 [5]}}