OCR MEI C2 2012 June — Question 7 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2012
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeFind curve equation from derivative (straightforward integration + point)
DifficultyModerate -0.8 This is a straightforward integration question requiring only basic power rule application and using an initial condition to find the constant. It's simpler than average A-level questions as it involves no chain rule, substitution, or problem-solving—just direct integration of two standard terms and one algebraic step to find C.
Spec1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums
7 The gradient of a curve is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x ^ { \frac { 1 } { 2 } } - 5\). Given also that the curve passes through the point (4, 20), find the equation of the curve.
Question 7:
AnswerMarks Guidance
AnswerMarks Guidance
\(\frac{6x^{\frac{3}{2}}}{\frac{3}{2}}\)M1*
\(4x^{\frac{3}{2}}\)A1 may appear later
\(-5x + c\)B1 B0 if from \(y = (6x^{\frac{1}{2}} - 5)x + c\); condone "\(+ c\)" not appearing until substitution
substitution of \((4, 20)\)M1dep*
\([y =]\ 4x^{1.5} - 5x + 8\) or \(c = 8\) iswA1 
## Question 7:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{6x^{\frac{3}{2}}}{\frac{3}{2}}$ | M1* | |
| $4x^{\frac{3}{2}}$ | A1 | may appear later |
| $-5x + c$ | B1 | B0 if from $y = (6x^{\frac{1}{2}} - 5)x + c$; condone "$+ c$" not appearing until substitution |
| substitution of $(4, 20)$ | M1dep* | |
| $[y =]\ 4x^{1.5} - 5x + 8$ or $c = 8$ isw | A1 | |

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7 The gradient of a curve is given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x ^ { \frac { 1 } { 2 } } - 5$. Given also that the curve passes through the point (4, 20), find the equation of the curve.

\hfill \mbox{\textit{OCR MEI C2 2012 Q7 [5]}}
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