OCR MEI C2 — Question 7 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
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 polynomial integration and using a boundary condition to find the constant. It's simpler than average A-level questions as it involves routine application of a single technique with no problem-solving or conceptual challenges.
Spec1.07a Derivative as gradient: of tangent to curve1.08a Fundamental theorem of calculus: integration as reverse of differentiation

7 The gradient of a curve \(y = \mathrm { f } ( x )\) is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { 2 } - 10 x + 6\). The curve passes through the point \(( 2,3 )\) Find the equation of the curve.

AnswerMarks Guidance
Integrating each term \(x^3 - 5x^2 + 6x + c\)M1, A1, A1 1 for integration, 1 for \(c\)
Substituting \((2, 3)\)M1
\(c = 3\)A1
\(y = x^3 - 5x^2 + 6x + 3\) Total: 5 marks
Integrating each term $x^3 - 5x^2 + 6x + c$ | M1, A1, A1 | 1 for integration, 1 for $c$
Substituting $(2, 3)$ | M1 |
$c = 3$ | A1 |
$y = x^3 - 5x^2 + 6x + 3$ | | **Total: 5 marks**
7 The gradient of a curve $y = \mathrm { f } ( x )$ is given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { 2 } - 10 x + 6$. The curve passes through the point $( 2,3 )$ Find the equation of the curve.

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