OCR MEI C2 — Question 8 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeFind curve from gradient
DifficultyModerate -0.8 This is a straightforward integration question requiring students to integrate a polynomial expression (applying the power rule to two terms) and then use a given point to find the constant of integration. It's a standard C2 exercise with routine techniques and no problem-solving insight required, making it easier than average but not trivial since it involves fractional powers.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08b Integrate x^n: where n != -1 and sums
8 The gradient of a curve is \(6 x ^ { 2 } + 12 x ^ { \frac { 1 } { 2 } }\). The curve passes through the point \(( 4,10 )\). Find the equation of the curve.
Question 8:
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
\([y =]\ 2x^3 + 8a^{1.5} - 182\) or \(c = -182\)A1 
## Question 8:

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
$[y =]\ 2x^3 + 8a^{1.5} - 182$ or $c = -182$ | A1 |

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8 The gradient of a curve is $6 x ^ { 2 } + 12 x ^ { \frac { 1 } { 2 } }$. The curve passes through the point $( 4,10 )$. Find the equation of the curve.

\hfill \mbox{\textit{OCR MEI C2  Q8 [5]}}
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