| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Basic power rule differentiation |
| Difficulty | Easy -1.2 This is a straightforward P1 question testing basic differentiation and integration of power functions. Both parts require only direct application of standard rules (power rule) with no chain rule actually needed despite the topic label. The algebraic manipulation is minimal, making this easier than average A-level questions. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
| Answer | Marks |
|---|---|
| 1(a) | 5 |
| Answer | Marks |
|---|---|
| x3 | M1 |
| 3 × 4x2 or −5 × −2x−3 (o.e.) (Ignore + c for this mark) | A1 |
| Answer | Marks |
|---|---|
| all on one line and no + c | A1 |
| Answer | Marks |
|---|---|
| (b) | xn (cid:111)xn(cid:14)1 |
| Answer | Marks |
|---|---|
| x1 | M1 |
| Answer | Marks |
|---|---|
| 4 (cid:16)1 | A1 |
| Answer | Marks |
|---|---|
| (cid:159) Allow 1x4 for x4 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Scheme | Marks |
Question 1:
--- 1(a) ---
1(a) | 5
y = 4x3 −
x2
xn (cid:111)xn(cid:16)1
1
e.g. sight of x2 or x−3 or
x3 | M1
3 × 4x2 or −5 × −2x−3 (o.e.) (Ignore + c for this mark) | A1
10
12x2 + or 12x2 + 10x−3
x3
all on one line and no + c | A1
(3)
(b) | xn (cid:111)xn(cid:14)1
1
e.g. sight of x4 or x−1 or
x1 | M1
Do not award for integrating their answer to part (a)
x4 x(cid:16)1
4 or −5 ×
4 (cid:16)1 | A1
For fully correct and simplified answer with + c all on one line. Allow
1
(cid:159)Allow x4 + 5 × + c
x
(cid:159) Allow 1x4 for x4 | A1
(3)
(6 marks)
Question | Scheme | MarksGiven that $y = 4x^3 - \frac{5}{x^2}$, $x \neq 0$, find in their simplest form
\begin{enumerate}[label=(\alph*)]
\item $\frac{dy}{dx}$. [3]
\item $\int y \, dx$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2018 Q1 [6]}}