| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2024 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Find indefinite integral of polynomial/power |
| Difficulty | Easy -1.2 This is a straightforward application of standard integration rules for powers of x. Each term integrates independently using the power rule, requiring only recall of the formula ∫x^n dx = x^(n+1)/(n+1) + C. No problem-solving or conceptual insight needed—purely mechanical execution of a basic technique from early A-level content. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\int\left(10x^4 - \frac{3}{2x^3} - 7\right)dx = 2x^5 + \frac{3}{4}x^{-2} - 7x + c\) | M1A1A1 | M1: Increase one power of \(x\) by 1, e.g. \(x^4 \to x^5\) or \(x^{-3} \to x^{-2}\) or \(7 \to 7x\). First A1: Any two correctly integrated terms, unsimplified or simplified. Allow e.g. \(\frac{10}{4+1}x^{4+1}\), \(-\frac{3}{-4}x^{-3+1}\), \(-7x^1\). Second A1: All correct and simplified in one expression including "\(+c\)". Allow correct simplified equivalents for \(\frac{3}{4}x^{-2}\) e.g. \(0.75x^{-2}\), \(\frac{3}{4x^2}\) but do not allow \(-7x^1\) for \(-7x\) or \(\frac{2}{1}\) for 2. Condone poor notation e.g. spurious integral signs, "d\(x\)", \(\frac{dy}{dx} = \ldots\) |
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\int\left(10x^4 - \frac{3}{2x^3} - 7\right)dx = 2x^5 + \frac{3}{4}x^{-2} - 7x + c$ | M1A1A1 | M1: Increase one power of $x$ by 1, e.g. $x^4 \to x^5$ or $x^{-3} \to x^{-2}$ or $7 \to 7x$. First A1: Any two correctly integrated terms, unsimplified or simplified. Allow e.g. $\frac{10}{4+1}x^{4+1}$, $-\frac{3}{-4}x^{-3+1}$, $-7x^1$. Second A1: All correct and simplified in one expression including "$+c$". Allow correct simplified equivalents for $\frac{3}{4}x^{-2}$ e.g. $0.75x^{-2}$, $\frac{3}{4x^2}$ but do **not** allow $-7x^1$ for $-7x$ or $\frac{2}{1}$ for 2. Condone poor notation e.g. spurious integral signs, "d$x$", $\frac{dy}{dx} = \ldots$ |
---\begin{enumerate}
\item Find
\end{enumerate}
$$\int \left( 10 x ^ { 4 } - \frac { 3 } { 2 x ^ { 3 } } - 7 \right) \mathrm { d } x$$
giving each term in simplest form.
\hfill \mbox{\textit{Edexcel P1 2024 Q1 [3]}}