OCR MEI C2 2006 June — Question 5 4 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2006
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeFind curve from gradient
DifficultyModerate -0.8 This is a straightforward integration question requiring only the power rule and finding a constant using given coordinates. It's a standard C2 exercise with minimal steps (integrate, substitute point, solve for c) and no conceptual challenges, making it easier than the average A-level question.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation
The gradient of a curve is given by \(\frac{dy}{dx} = 3 - x^2\). The curve passes through the point \((6, 1)\). Find the equation of the curve. [4]
AnswerMarks Guidance
\([y =] 3x - x^3/3 + c\)B1
subst of \((6, 1)\) in their eqn with cB1 Dep't on integration attempt
\(y = 3x - x^3/3 + 55\) c.a.oM1 A1 Dep't on BoB1; Allow \(c = 55\) isw 
$[y =] 3x - x^3/3 + c$ | B1 |  | 
subst of $(6, 1)$ in their eqn with c | B1 | Dep't on integration attempt | 
$y = 3x - x^3/3 + 55$ c.a.o | M1 A1 | Dep't on BoB1; Allow $c = 55$ isw | $4$ | $17$ |
The gradient of a curve is given by $\frac{dy}{dx} = 3 - x^2$. The curve passes through the point $(6, 1)$. Find the equation of the curve. [4]

\hfill \mbox{\textit{OCR MEI C2 2006 Q5 [4]}}
This paper (12 questions)
View full paper
Q1 2 Q2 3 Q3 3 Q4 5 Q5 4 Q6 5 Q7 5 Q8 5 Q9 4 Q10 11 Q11 13 Q12 12