| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2003 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Basic power rule differentiation |
| Difficulty | Easy -1.3 This is a straightforward application of basic differentiation and integration rules requiring only recall of power rule mechanics. Both parts are routine textbook exercises with no problem-solving element—students simply apply standard formulas to each term independently. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\frac{dy}{dx} = 4 - 12x^{-3}\) | B2, 1 [2] | One off for each error (4, -, 12, -3) |
| (b) \(\int 2x^2 - 6x^{-1} + c\) | 3 × B1 [3] | One for each term – only give +c if obvious attempt at integration. (a) (quotient OK M1 correct formula, A1 co) |
**(a)** $\frac{dy}{dx} = 4 - 12x^{-3}$ | B2, 1 [2] | One off for each error (4, -, 12, -3)
**(b)** $\int 2x^2 - 6x^{-1} + c$ | 3 × B1 [3] | One for each term – only give +c if obvious attempt at integration. (a) (quotient OK M1 correct formula, A1 co)3
\begin{enumerate}[label=(\alph*)]
\item Differentiate $4 x + \frac { 6 } { x ^ { 2 } }$ with respect to $x$.
\item Find $\int \left( 4 x + \frac { 6 } { x ^ { 2 } } \right) \mathrm { d } x$.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2003 Q3 [5]}}