Edexcel P3 2022 January — Question 1 4 marks

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2022
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDifferentiating Transcendental Functions
TypeFind stationary points - polynomial/exponential products
DifficultyModerate -0.8 This is a straightforward application of the product rule to find where dy/dx = 0. The differentiation is routine (polynomial times exponential), and solving the resulting linear equation for the stationary point requires minimal algebraic manipulation. Easier than average for A-level.
Spec1.07n Stationary points: find maxima, minima using derivatives1.07q Product and quotient rules: differentiation
  1. Find, using calculus, the \(x\) coordinate of the stationary point on the curve with equation
$$y = ( 2 x + 5 ) e ^ { 3 x }$$
Question 1:
\(y = (2x+5)e^{3x}\)
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\frac{dy}{dx} = 2e^{3x} + (2x+5)3e^{3x}\)M1 A1 M1: Attempts product rule achieving form \(Ae^{3x} + B(2x+5)e^{3x}\) where \(A\), \(B\) are positive constants. Condone missing/poor bracketing. A1: Correct derivative o.e. No requirement to simplify
\(\frac{dy}{dx} = 0 \Rightarrow 2 + 3(2x+5) = 0 \Rightarrow x = -\frac{17}{6}\)dM1 A1 dM1: Dependent on previous M; sets \(\frac{dy}{dx}=0\), cancels/factorises out \(e^{3x}\) term and solves linear equation in \(x\). A1: \(x = -\frac{17}{6}\) o.e. only. Condone awrt \(-2.83\) following correct equation. Ignore any attempt to find \(y\) 
## Question 1:

$y = (2x+5)e^{3x}$

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{dy}{dx} = 2e^{3x} + (2x+5)3e^{3x}$ | M1 A1 | M1: Attempts product rule achieving form $Ae^{3x} + B(2x+5)e^{3x}$ where $A$, $B$ are positive constants. Condone missing/poor bracketing. A1: Correct derivative o.e. No requirement to simplify |
| $\frac{dy}{dx} = 0 \Rightarrow 2 + 3(2x+5) = 0 \Rightarrow x = -\frac{17}{6}$ | dM1 A1 | dM1: Dependent on previous M; sets $\frac{dy}{dx}=0$, cancels/factorises out $e^{3x}$ term and solves linear equation in $x$. A1: $x = -\frac{17}{6}$ o.e. only. Condone awrt $-2.83$ following correct equation. Ignore any attempt to find $y$ |

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\begin{enumerate}
  \item Find, using calculus, the $x$ coordinate of the stationary point on the curve with equation
\end{enumerate}

$$y = ( 2 x + 5 ) e ^ { 3 x }$$

\hfill \mbox{\textit{Edexcel P3 2022 Q1 [4]}}
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Q1 4 Q2 5 Q3 6 Q4 7 Q5 9 Q6 11 Q7 10 Q8 8 Q9 8 Q10 7