OCR MEI C2 — Question 1 4 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTangents, normals and gradients
TypeFind derivative of simple polynomial (integer powers)
DifficultyEasy -1.2 This is a straightforward integration question requiring only the reverse power rule and using an initial condition to find the constant of integration. It's simpler than average A-level questions as it involves a basic polynomial with no complications, making it easier than typical multi-step problems.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation
1 The gradient of a curve is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 - 5 x\).
Find the equation of the curve given that it passes through the point \(( 0,1 )\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(\frac{dy}{dx} = 2 - 5x\)M1
\(\Rightarrow y = 2x - \frac{5}{2}x^2 + c\)A1
When \(x = 0, y = 1\)M1
\(\Rightarrow 1 = c \Rightarrow y = 2x - \frac{5}{2}x^2 + 1\)A1 [4] 
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{dy}{dx} = 2 - 5x$ | M1 | |
| $\Rightarrow y = 2x - \frac{5}{2}x^2 + c$ | A1 | |
| When $x = 0, y = 1$ | M1 | |
| $\Rightarrow 1 = c \Rightarrow y = 2x - \frac{5}{2}x^2 + 1$ | A1 | **[4]** |

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1 The gradient of a curve is given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 - 5 x$.\\
Find the equation of the curve given that it passes through the point $( 0,1 )$.

\hfill \mbox{\textit{OCR MEI C2  Q1 [4]}}
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