OCR MEI C2 — Question 5 4 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeFind curve from gradient
DifficultyEasy -1.2 This is a straightforward integration question requiring students to integrate a simple linear function and use a given point to find the constant of integration. It involves only basic polynomial integration (a standard C2 skill) with no problem-solving complexity—purely routine application of technique.
Spec1.07a Derivative as gradient: of tangent to curve1.08a Fundamental theorem of calculus: integration as reverse of differentiation
5 The gradient of a curve is given by the function \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 - x\).
The curve passes through the point \(( 1,2 )\).
Find the equation of the curve.
Question 5:
AnswerMarks Guidance
\(\frac{dy}{dx} = 2-x \Rightarrow y = 2x - \frac{x^2}{2} + c\)M1 A1
Through \((1,2) \Rightarrow 2 = 2 - \frac{1}{2} + c \Rightarrow c = \frac{1}{2}\)M1
\(\Rightarrow y = 2x - \frac{x^2}{2} + \frac{1}{2}\)A1 Total: 4 
## Question 5:

$\frac{dy}{dx} = 2-x \Rightarrow y = 2x - \frac{x^2}{2} + c$ | M1 A1 |

Through $(1,2) \Rightarrow 2 = 2 - \frac{1}{2} + c \Rightarrow c = \frac{1}{2}$ | M1 |

$\Rightarrow y = 2x - \frac{x^2}{2} + \frac{1}{2}$ | A1 | **Total: 4**

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

\hfill \mbox{\textit{OCR MEI C2  Q5 [4]}}
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Q1 3 Q2 3 Q3 3 Q4 5 Q5 4 Q6 5 Q7 5 Q8 4 Q9 4 Q10 12 Q11 12 Q12 12