OCR C2 2010 January — Question 2 7 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2010
SessionJanuary
Marks7
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 linear function and use a point to find the constant, followed by solving a simple quadratic equation. Both parts are routine C2 techniques with no conceptual challenges beyond basic integration and substitution.
Spec1.07a Derivative as gradient: of tangent to curve1.08a Fundamental theorem of calculus: integration as reverse of differentiation

2 The gradient of a curve is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x - 4\). The curve passes through the distinct points ( 2,5 ) and ( \(p , 5\) ).
  1. Find the equation of the curve.
  2. Find the value of \(p\).

2 The gradient of a curve is given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x - 4$. The curve passes through the distinct points ( 2,5 ) and ( $p , 5$ ).\\
(i) Find the equation of the curve.\\
(ii) Find the value of $p$.

\hfill \mbox{\textit{OCR C2 2010 Q2 [7]}}