AQA Paper 2 2018 June — Question 6 7 marks

Exam BoardAQA
ModulePaper 2 (Paper 2)
Year2018
SessionJune
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicImplicit equations and differentiation
TypeFind stationary points
DifficultyChallenging +1.2 This question requires implicit differentiation of a composite function involving an exponential, then solving the resulting system to find stationary points. While it combines several techniques (chain rule, implicit differentiation, exponential functions), the approach is methodical and the algebra, though careful, follows standard patterns. It's moderately harder than average due to the implicit nature and multi-step solving required, but doesn't demand unusual insight.
Spec1.07n Stationary points: find maxima, minima using derivatives1.07s Parametric and implicit differentiation
Find the coordinates of the stationary point of the curve with equation \((x + y - 2)^2 = e^y - 1\) [7 marks]
Question 6:
AnswerMarks Guidance
6Selects appropriate technique to
differentiateAO3.1a M1
2x y2 1 ey
 
 dx dx
dy
0 x y20
dx
0ey 1
y 0
x2
Differentiates term involving ey
AnswerMarks Guidance
correctlyAO1.1b B1
Differentiates fully correctlyAO1.1b A1
dy
Uses 0
AnswerMarks Guidance
dxAO1.1a M1
Eliminates x or y from the equation
AnswerMarks Guidance
of the curveAO1.1a M1
Obtains correct y CAOAO1.1b A1
Obtains correct x CAOAO1.1b A1
Total7
QMarking Instructions AO 
Question 6:
6 | Selects appropriate technique to
differentiate | AO3.1a | M1 |  dy dy
2x y2 1 ey
 
 dx dx
dy
0 x y20
dx
0ey 1
y 0
x2
Differentiates term involving ey
correctly | AO1.1b | B1
Differentiates fully correctly | AO1.1b | A1
dy
Uses 0
dx | AO1.1a | M1
Eliminates x or y from the equation
of the curve | AO1.1a | M1
Obtains correct y CAO | AO1.1b | A1
Obtains correct x CAO | AO1.1b | A1
Total | 7
Q | Marking Instructions | AO | Marks | Typical Solution
Find the coordinates of the stationary point of the curve with equation

$(x + y - 2)^2 = e^y - 1$
[7 marks]

\hfill \mbox{\textit{AQA Paper 2 2018 Q6 [7]}}
This paper (17 questions)
View full paper
Q1 1 Q2 1 Q3 1 Q4 6 Q5 2 Q6 7 Q7 8 Q8 10 Q9 14 Q10 1 Q11 1 Q12 5 Q13 8 Q14 6 Q15 9 Q16 6 Q17 14