OCR C1 2009 June — Question 1 5 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2009
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicChain Rule
TypeSecond derivative and nature determination
DifficultyEasy -1.2 This is a straightforward differentiation exercise requiring only basic power rule application (rewriting 1/x² as x^(-2)) and computing the second derivative. No chain rule is actually needed despite the topic label, and it's purely mechanical recall with no problem-solving element—easier than average for A-level.
Spec1.07d Second derivatives: d^2y/dx^2 notation1.07i Differentiate x^n: for rational n and sums

1 Given that \(y = x ^ { 5 } + \frac { 1 } { x ^ { 2 } }\), find
  1. \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
  2. \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).

1 Given that $y = x ^ { 5 } + \frac { 1 } { x ^ { 2 } }$, find\\
(i) $\frac { \mathrm { d } y } { \mathrm {~d} x }$,\\
(ii) $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$.

\hfill \mbox{\textit{OCR C1 2009 Q1 [5]}}