| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2024 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Integrate after expanding or multiplying out |
| Difficulty | Moderate -0.3 This requires expanding three linear factors and integrating the resulting polynomial term-by-term using the standard power rule. While algebraically lengthy, it's a straightforward mechanical process with no conceptual difficulty beyond basic integration rules, making it slightly easier than average for A-level. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.08b Integrate x^n: where n != -1 and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \((2x-5)(3x+2)(2x+5) = (6x^2-11x-10)(2x+5) = \ldots\) | M1 | Attempt to multiply two brackets to form a quadratic, then combine with third. Must lead to \(ax^3+bx^2+cx+d\) where \(a,b,c,d \neq 0\). Condone slips. |
| \(= 12x^3+8x^2-75x-50\) | A1 | Allow unsimplified with terms uncollected. |
| \(\int(2x-5)(3x+2)(2x+5)\,dx = 3x^4+\frac{8}{3}x^3-\frac{75}{2}x^2-50x+c\) | M1, A1ft, A1 | M1: \(\int x^n\,dx \to x^{n+1}\), \(n\neq 0\). A1ft: correct follow through on any two terms of \(ax^3+bx^2+cx+d\). A1: fully correct including \(+c\). Do not ISW if candidates multiply through by 6. |
## Question 1:
$\int (2x-5)(3x+2)(2x+5)\,dx$
| Working/Answer | Mark | Guidance |
|---|---|---|
| $(2x-5)(3x+2)(2x+5) = (6x^2-11x-10)(2x+5) = \ldots$ | M1 | Attempt to multiply two brackets to form a quadratic, then combine with third. Must lead to $ax^3+bx^2+cx+d$ where $a,b,c,d \neq 0$. Condone slips. |
| $= 12x^3+8x^2-75x-50$ | A1 | Allow unsimplified with terms uncollected. |
| $\int(2x-5)(3x+2)(2x+5)\,dx = 3x^4+\frac{8}{3}x^3-\frac{75}{2}x^2-50x+c$ | M1, A1ft, A1 | M1: $\int x^n\,dx \to x^{n+1}$, $n\neq 0$. A1ft: correct follow through on any **two terms** of $ax^3+bx^2+cx+d$. A1: fully correct including $+c$. Do not ISW if candidates multiply through by 6. |
---\begin{enumerate}
\item Find
\end{enumerate}
$$\int ( 2 x - 5 ) ( 3 x + 2 ) ( 2 x + 5 ) \mathrm { d } x$$
writing your answer in simplest form.
\hfill \mbox{\textit{Edexcel P1 2024 Q1 [5]}}