AQA C4 2009 June — Question 5 5 marks

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2009
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicImplicit equations and differentiation
TypeFind dy/dx at a point
DifficultyStandard +0.3 This is a straightforward implicit differentiation question requiring students to differentiate both sides with respect to x, apply the product rule to 3xy, then substitute the given point to find the gradient. While implicit differentiation is a C4 topic, this is a standard single-step application with no algebraic complications, making it slightly easier than average.
Spec1.07s Parametric and implicit differentiation
5 A curve is defined by the equation \(4 x ^ { 2 } + y ^ { 2 } = 4 + 3 x y\).
Find the gradient at the point ( 1,3 ) on this curve.
Question 5:
\(8x + 2y\frac{dy}{dx} = 3y + 3x\frac{dy}{dx}\)
AnswerMarks Guidance
\(8x\) and \(4 \to 0\)B1
\(2y\frac{dy}{dx}\)B1
\(3y + 3x\frac{dy}{dx}\)M1 A1 Two terms with one \(\frac{dy}{dx}\)
At \((1,3)\): \(\frac{dy}{dx} = \frac{1}{3}\)A1 (5 marks) CSO 
# Question 5:

$8x + 2y\frac{dy}{dx} = 3y + 3x\frac{dy}{dx}$

$8x$ and $4 \to 0$ | B1 |

$2y\frac{dy}{dx}$ | B1 |

$3y + 3x\frac{dy}{dx}$ | M1 A1 | Two terms with one $\frac{dy}{dx}$

At $(1,3)$: $\frac{dy}{dx} = \frac{1}{3}$ | A1 (5 marks) | CSO

---
5 A curve is defined by the equation $4 x ^ { 2 } + y ^ { 2 } = 4 + 3 x y$.\\
Find the gradient at the point ( 1,3 ) on this curve.

\hfill \mbox{\textit{AQA C4 2009 Q5 [5]}}
This paper (8 questions)
View full paper
Q1 5 Q2 11 Q3 13 Q4 6 Q5 5 Q6 15 Q7 10 Q8 10