Moderate -0.8 This is a straightforward differentiation question requiring only the power rule applied to terms with surds. Students must rewrite √x as x^(1/2), differentiate each term using standard rules, then substitute x=2. The surd arithmetic is routine for C1/C2 level, making this easier than average.
3. A curve has equation
$$y = \sqrt { 2 } x ^ { 2 } - 6 \sqrt { x } + 4 \sqrt { 2 } , \quad x > 0$$
Find the gradient of the curve at the point \(P ( 2,2 \sqrt { 2 } )\).
Write your answer in the form \(a \sqrt { 2 }\), where \(a\) is a constant.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
\(L\)
M1: reducing the power of one \(x\) term by one: \(x^2 \to x\) or \(x^{\frac{1}{2}} \to x^{-\frac{1}{2}}\). A1: may be left unsimplified.
Sub \(x = 2\) into their \(\frac{dy}{dx}\)
dM1
Previous M1 must be scored. Withhold if candidate uses \(y\) value incorrectly. Can be awarded for sight of awrt 3.54.
\(\frac{dy}{dx} = \frac{5}{2}\sqrt{2}\)
A1 (4 marks)
Accept \(a\sqrt{2} = 2\sqrt{2} \times 2 - \frac{3}{\sqrt{2}} \Rightarrow a = \ldots\) Give bod to students who write \(5/2\sqrt{2}\). Accept \(a = 2.5\).
## Question 3:
$\frac{dy}{dx} = 2\sqrt{2}x - \frac{3}{\sqrt{x}}$ | M1 A1 | M1: reducing the power of one $x$ term by one: $x^2 \to x$ or $x^{\frac{1}{2}} \to x^{-\frac{1}{2}}$. A1: may be left unsimplified.
Sub $x = 2$ into their $\frac{dy}{dx}$ | dM1 | Previous M1 must be scored. Withhold if candidate uses $y$ value incorrectly. Can be awarded for sight of awrt 3.54.
$\frac{dy}{dx} = \frac{5}{2}\sqrt{2}$ | A1 (4 marks) | Accept $a\sqrt{2} = 2\sqrt{2} \times 2 - \frac{3}{\sqrt{2}} \Rightarrow a = \ldots$ Give bod to students who write $5/2\sqrt{2}$. Accept $a = 2.5$.
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3. A curve has equation
$$y = \sqrt { 2 } x ^ { 2 } - 6 \sqrt { x } + 4 \sqrt { 2 } , \quad x > 0$$
Find the gradient of the curve at the point $P ( 2,2 \sqrt { 2 } )$.\\
Write your answer in the form $a \sqrt { 2 }$, where $a$ is a constant.\\
(Solutions based entirely on graphical or numerical methods are not acceptable.)\\
$L$\\
\hfill \mbox{\textit{Edexcel C12 2019 Q3 [4]}}