Question 5 - A-Level Maths

AQA C4 2010 January — Question 5 5 marks

Exam Board	AQA
Module	C4 (Core Mathematics 4)
Year	2010
Session	January
Marks	5
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Implicit equations and differentiation
Type	Find dy/dx at a point
Difficulty	Moderate -0.3 This is a straightforward implicit differentiation question requiring product rule and chain rule application, followed by simple substitution. The algebra is clean with convenient coordinates (-1,0) making e^0=1, and it's a standard single-step problem worth modest marks.
Spec	1.07s Parametric and implicit differentiation

5 A curve is defined by the equation $$x ^ { 2 } + x y = \mathrm { e } ^ { y }$$ Find the gradient at the point $( - 1,0 )$ on this curve.

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Question 5:

Answer	Marks	Guidance
$x^2+xy=e^y$
$2x+y+x\frac{dy}{dx}=e^y\frac{dy}{dx}$	B1	$2x$
M1	Use product rule
A1
B1	RHS
$(-1,0)\quad\frac{dy}{dx}=-1$	A1 (5 marks)	CSO

Total: 5 marks

## Question 5:
| $x^2+xy=e^y$ | | |
| $2x+y+x\frac{dy}{dx}=e^y\frac{dy}{dx}$ | B1 | $2x$ |
| | M1 | Use product rule |
| | A1 | |
| | B1 | RHS |
| $(-1,0)\quad\frac{dy}{dx}=-1$ | A1 (5 marks) | CSO |

**Total: 5 marks**

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5 A curve is defined by the equation

$$x ^ { 2 } + x y = \mathrm { e } ^ { y }$$

Find the gradient at the point $( - 1,0 )$ on this curve.

\hfill \mbox{\textit{AQA C4 2010 Q5 [5]}}

This paper (9 questions)

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Q1 8 Q2 10 Q3 7 Q4 8 Q5 5 Q6 10 Q7 6 Q8 11 Q9 10

Answer	Marks	Guidance
\(x^2+xy=e^y\)
\(2x+y+x\frac{dy}{dx}=e^y\frac{dy}{dx}\)	B1	\(2x\)
M1	Use product rule
A1
B1	RHS
\((-1,0)\quad\frac{dy}{dx}=-1\)	A1 (5 marks)	CSO