Question 3 - A-Level Maths

Edexcel C1 — Question 3 5 marks

Exam Board	Edexcel
Module	C1 (Core Mathematics 1)
Marks	5
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Chain Rule
Type	Basic power rule differentiation
Difficulty	Moderate -0.3 This is a straightforward C1 differentiation question requiring rewriting the expression as a sum of powers of x, then applying basic power rule. While it involves 5 marks and requires algebraic manipulation (splitting the fraction and simplifying indices), it's a standard textbook exercise with no conceptual difficulty beyond routine application of index laws and differentiation rules—slightly easier than average for A-level.
Spec	1.02k Simplify rational expressions: factorising, cancelling, algebraic division 1.07i Differentiate x^n: for rational n and sums

Differentiate with respect to $x$ $$\frac{6x^2 - 1}{2\sqrt{x}}.$$ [5]

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Answer	Marks	Guidance
$\frac{6x^2-1}{2\sqrt{x}} = 3x^{\frac{3}{2}} - \frac{1}{2}x^{-\frac{1}{2}}$	M1 A1
$\frac{d}{dx}\left(3x^{\frac{3}{2}} - \frac{1}{2}x^{-\frac{1}{2}}\right) = \frac{9}{2}x^{\frac{1}{2}} + \frac{1}{4}x^{-\frac{3}{2}}$	M1 A2	(5 marks)

$\frac{6x^2-1}{2\sqrt{x}} = 3x^{\frac{3}{2}} - \frac{1}{2}x^{-\frac{1}{2}}$ | M1 A1 |
$\frac{d}{dx}\left(3x^{\frac{3}{2}} - \frac{1}{2}x^{-\frac{1}{2}}\right) = \frac{9}{2}x^{\frac{1}{2}} + \frac{1}{4}x^{-\frac{3}{2}}$ | M1 A2 | (5 marks)

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Differentiate with respect to $x$
$$\frac{6x^2 - 1}{2\sqrt{x}}.$$ [5]

\hfill \mbox{\textit{Edexcel C1  Q3 [5]}}

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Q1 4 Q2 4 Q3 5 Q4 6 Q5 7 Q6 8 Q7 9 Q8 10 Q9 11 Q10 11

Answer	Marks	Guidance
\(\frac{6x^2-1}{2\sqrt{x}} = 3x^{\frac{3}{2}} - \frac{1}{2}x^{-\frac{1}{2}}\)	M1 A1
\(\frac{d}{dx}\left(3x^{\frac{3}{2}} - \frac{1}{2}x^{-\frac{1}{2}}\right) = \frac{9}{2}x^{\frac{1}{2}} + \frac{1}{4}x^{-\frac{3}{2}}\)	M1 A2	(5 marks)