OCR MEI C3 — Question 4 5 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicImplicit equations and differentiation
TypeFind dy/dx at a point
DifficultyModerate -0.8 This is a straightforward implicit differentiation question requiring only one differentiation step (2y dy/dx = 5), solving for dy/dx, then substituting x=8 to find y-values and evaluating the gradient. It's simpler than average as it involves a basic implicit equation with minimal algebraic manipulation and is a standard textbook exercise.
Spec1.07s Parametric and implicit differentiation
4 A curve has equation \(y ^ { 2 } = 5 x - 4\).
Find the gradient of the curve at the points where \(x = 8\).
AnswerMarks
\(y^2 = 5x-4 \Rightarrow 2y\frac{dy}{dx} = 5 \Rightarrow \frac{dy}{dx} = \frac{5}{2y}\)M1 A1
When \(x = 8\), \(y^2 = 36 \Rightarrow y = \pm 6\)A1
\(\Rightarrow\) gradients \(= \frac{5}{12}\) and \(-\frac{5}{12}\)A1 A1
5 
$y^2 = 5x-4 \Rightarrow 2y\frac{dy}{dx} = 5 \Rightarrow \frac{dy}{dx} = \frac{5}{2y}$ | M1 A1 | 

When $x = 8$, $y^2 = 36 \Rightarrow y = \pm 6$ | A1 | 

$\Rightarrow$ gradients $= \frac{5}{12}$ and $-\frac{5}{12}$ | A1 A1 | 
| 5 |
4 A curve has equation $y ^ { 2 } = 5 x - 4$.\\
Find the gradient of the curve at the points where $x = 8$.

\hfill \mbox{\textit{OCR MEI C3  Q4 [5]}}
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Q1 4 Q2 4 Q3 6 Q4 5 Q5 4 Q6 8 Q7 5 Q8 18 Q9 18