1.2 Algebraic Fractions

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The curve $C$ has equation $2x^3 + \frac{18}{x} + 5, \quad x > 0$

Find $dydx\frac{\mathrm{d}y}{\mathrm{d}x}$ , giving your answer in simplest form.

[2]

Given that

the point $P$ lies on $C$
the line with equation $y = k - 24 x$ , where $k$ is a constant, is the tangent to $C$ at $P$

Show that the $x$ -coordinate of $P$ satisfies the equation $x^4 + 4x^2 - 3 = 0$

[3]

Hence find the exact value of $k$ .

[4]

1.2 Algebraic Fractions Questions

Practise Edexcel A Level Maths 1.2 Algebraic Fractions with exam-style questions for A Level Maths. 16 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.