OCR C1 2010 June — Question 6 5 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2010
SessionJune
Marks5
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Mark schemeDownload PDF ↗
TopicTangents, normals and gradients
TypeFind derivative after algebraic simplification (fractional/mixed powers)
DifficultyEasy -1.2 This is a straightforward differentiation question requiring rewriting the term as a power (x^{-1/2}), applying the power rule, and substituting x=4. It's simpler than average A-level questions as it involves only basic differentiation with no problem-solving or multi-step reasoning required.
Spec1.07i Differentiate x^n: for rational n and sums1.07l Derivative of ln(x): and related functions
6 Find the gradient of the curve \(y = 2 x + \frac { 6 } { \sqrt { x } }\) at the point where \(x = 4\).
Question 6:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(y = 2x + 6x^{-\frac{1}{2}}\)M1 Attempt to differentiate
\(\frac{dy}{dx} = 2 - 3x^{-\frac{3}{2}}\)A1 \(kx^{-\frac{3}{2}}\)
A1Completely correct expression (no \(+c\))
When \(x=4\), gradient \(= 2 - \frac{3}{\sqrt{4^3}}\)M1 Correct evaluation of either \(4^{-\frac{3}{2}}\) or \(4^{-\frac{1}{2}}\)
\(= \frac{13}{8}\)A1 5 
# Question 6:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $y = 2x + 6x^{-\frac{1}{2}}$ | M1 | Attempt to differentiate |
| $\frac{dy}{dx} = 2 - 3x^{-\frac{3}{2}}$ | A1 | $kx^{-\frac{3}{2}}$ |
| | A1 | Completely correct expression (no $+c$) |
| When $x=4$, gradient $= 2 - \frac{3}{\sqrt{4^3}}$ | M1 | Correct evaluation of either $4^{-\frac{3}{2}}$ or $4^{-\frac{1}{2}}$ |
| $= \frac{13}{8}$ | A1 | **5** |

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6 Find the gradient of the curve $y = 2 x + \frac { 6 } { \sqrt { x } }$ at the point where $x = 4$.

\hfill \mbox{\textit{OCR C1 2010 Q6 [5]}}
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