| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| Topic | Differentiation from First Principles |
| Type | First principles: polynomial with multiple terms |
| Difficulty | Standard +0.3 This is a straightforward application of differentiation from first principles to a simple polynomial. While the method requires careful algebraic manipulation of the limit definition, it's a standard textbook exercise with no conceptual difficulty beyond executing the formula correctly. The 4-mark allocation reflects the working required rather than genuine difficulty. |
| Spec | 1.07a Derivative as gradient: of tangent to curve1.07g Differentiation from first principles: for small positive integer powers of x |
A curve has equation
$$y = 4x^2 - 5x$$
The curve passes through the point $P(2, 6)$
Use differentiation from first principles to find the value of the gradient of the curve at $P$. [4]
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q9 [4]}}