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3.6.1 Integration (A-level only)

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Question 48

The curve $C\,$ has equation

\frac{18}{4(2x - k)}, \quad x \not= \frac{k}{2}

where $k\,$ is a positive constant and $\neq 2$ .

Find $dydx\displaystyle \frac{dy}{dx}$ giving your answer in simplest form in terms of $k$ .

[2]

The point $P\,$ with $x\,$ coordinate 1 lies on $C$ . Given that the gradient of the curve at $P\,$ is -9, find the two possible values of $k$ .

[3]

Given also that $k < 2$ , find the equation of the normal to $C\,$ at $P$ , writing your answer in the form $a x + b y + c = 0$ , where $b\,$ and $c\,$ are integers to be found.

[3]

Show, using algebraic integration, that

\int_{1}^{3} \frac{18}{4(2x - k)} \, dx = \lambda \ln(5)

where $\lambda\,$ is a constant to be found.

[3]

Markscheme

3.6.1 Integration (A-level only) Questions

A Level
Maths
3.6.1 Integration (A-level only)

59 exam-style questions on CCEA A Level Maths 3.6.1 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

3.6.1 Integration (A-level only)

Question bank

3.6.1 Integration (A-level only)

Easy Medium

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

Question 48

The curve $C\,$ has equation

\frac{18}{4(2x - k)}, \quad x \not= \frac{k}{2}

where $k\,$ is a positive constant and $\neq 2$ .

Find $dydx\displaystyle \frac{dy}{dx}$ giving your answer in simplest form in terms of $k$ .

[2]

The point $P\,$ with $x\,$ coordinate 1 lies on $C$ . Given that the gradient of the curve at $P\,$ is -9, find the two possible values of $k$ .

[3]

Given also that $k < 2$ , find the equation of the normal to $C\,$ at $P$ , writing your answer in the form $a x + b y + c = 0$ , where $b\,$ and $c\,$ are integers to be found.

[3]

Show, using algebraic integration, that

\int_{1}^{3} \frac{18}{4(2x - k)} \, dx = \lambda \ln(5)

where $\lambda\,$ is a constant to be found.

[3]

Markscheme

3.6.1 Integration (A-level only) Questions

A Level
Maths
3.6.1 Integration (A-level only)

59 exam-style questions on CCEA A Level Maths 3.6.1 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.