OCR MEI C2 — Question 4 4 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTangents, normals and gradients
TypeFind tangent at given point (polynomial/algebraic)
DifficultyModerate -0.8 This is a straightforward application of differentiation requiring students to find where the curve cuts the y-axis (x=0), differentiate to find the gradient, and write the tangent equation. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial since it requires multiple standard techniques.
Spec1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations
4 Find the equation of the tangent to the curve \(y = x ^ { 3 } + 2 x - 7\) at the point where it cuts the \(y\) axis.
Question 4:
AnswerMarks Guidance
AnswerMarks Guidance
\(\frac{dy}{dx} = 3x^2 + 2\)B1
When \(x = 0, \frac{dy}{dx} = 2 \Rightarrow y - 7 = 2(x - 0)\)B1, M1, A1
\(\Rightarrow y = 2x + 7\) [4] 
## Question 4:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{dy}{dx} = 3x^2 + 2$ | B1 | |
| When $x = 0, \frac{dy}{dx} = 2 \Rightarrow y - 7 = 2(x - 0)$ | B1, M1, A1 | |
| $\Rightarrow y = 2x + 7$ | | **[4]** |

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4 Find the equation of the tangent to the curve $y = x ^ { 3 } + 2 x - 7$ at the point where it cuts the $y$ axis.

\hfill \mbox{\textit{OCR MEI C2  Q4 [4]}}
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