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11.1 Integrating Standard Functions

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Question 33

The curve C has equation $\mathrm{f}(x), x > 0$ . Given that:

the point $P (9, - 2)$ lies on $C$
$f′(x)=3x2+ax+b2x\mathrm{f}'(x) = \dfrac{3x^2 + ax + b}{2\sqrt{x}}$ , where $a$ and $b$ are constants
the gradient of the tangent to $C$ at $P$ is $35$

Show that $9 a + b = - 33$ .

[2]

Given also that $a - b = 13$

Find, in simplest form, $f(x)\mathrm{f}(x)$ .

[6]

Curve $C$ is transformed to the curve with equation $\mathrm{f}(x + 4)$ . Given that point $P$ is transformed to the point $Q$ ,

State the coordinates of $Q$ .

[2]

Markscheme

11.1 Integrating Standard Functions Questions

A Level
Maths
11.1 Integrating Standard Functions

80 exam-style questions on Edexcel A Level Maths 11.1 Integrating Standard Functions. Each one has a worked solution and a mark scheme showing where the marks go.

11.1 Integrating Standard Functions

Question bank

11.1 Integrating Standard Functions

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Question 33

The curve C has equation $\mathrm{f}(x), x > 0$ . Given that:

the point $P (9, - 2)$ lies on $C$
$f′(x)=3x2+ax+b2x\mathrm{f}'(x) = \dfrac{3x^2 + ax + b}{2\sqrt{x}}$ , where $a$ and $b$ are constants
the gradient of the tangent to $C$ at $P$ is $35$

Show that $9 a + b = - 33$ .

[2]

Given also that $a - b = 13$

Find, in simplest form, $f(x)\mathrm{f}(x)$ .

[6]

Curve $C$ is transformed to the curve with equation $\mathrm{f}(x + 4)$ . Given that point $P$ is transformed to the point $Q$ ,

State the coordinates of $Q$ .

[2]

Markscheme

11.1 Integrating Standard Functions Questions

A Level
Maths
11.1 Integrating Standard Functions

80 exam-style questions on Edexcel A Level Maths 11.1 Integrating Standard Functions. Each one has a worked solution and a mark scheme showing where the marks go.