OCR MEI C2 2010 June — Question 6 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2010
SessionJune
Marks5
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Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeFind curve from gradient
DifficultyModerate -0.5 This is a straightforward integration question requiring students to integrate a polynomial and square root term, then use the given point to find the constant of integration. While it involves multiple steps (integrate, substitute point, solve for c), the techniques are routine C2 material with no conceptual challenges or problem-solving required beyond standard procedure.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08b Integrate x^n: where n != -1 and sums
The gradient of a curve is \(6x^2 + 12x^{\frac{1}{2}}\). The curve passes through the point \((4, 10)\). Find the equation of the curve. [5]
AnswerMarks Guidance
Attempt to integrate \(6x^2 + 12x^{\frac{1}{2}}\)M1
\([y=] 2x^3 + 8x^{1.5} + c\)A2 Accept un-simplified; A1 for 2 terms correct
Substitution of \((4, 10)\)M1 Dependent on attempted integral with \(+ c\) term
\([y=] 2x^3 + 8x^{1.5} - 182\) or \(c = -182\)A1 
Attempt to integrate $6x^2 + 12x^{\frac{1}{2}}$ | M1 | 
$[y=] 2x^3 + 8x^{1.5} + c$ | A2 | Accept un-simplified; A1 for 2 terms correct
Substitution of $(4, 10)$ | M1 | Dependent on attempted integral with $+ c$ term
$[y=] 2x^3 + 8x^{1.5} - 182$ or $c = -182$ | A1 |
The gradient of a curve is $6x^2 + 12x^{\frac{1}{2}}$. The curve passes through the point $(4, 10)$. Find the equation of the curve. [5]

\hfill \mbox{\textit{OCR MEI C2 2010 Q6 [5]}}
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Q1 2 Q2 4 Q3 5 Q4 4 Q5 4 Q6 5 Q7 2 Q8 5 Q9 5 Q10 13 Q11 13 Q12 10