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1.10 Numerical Methods (A-level only)

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Question 54

The curve $C\,$ has the equation

$x)\ln x$ , $x > 0$

a.

Find $dydx\displaystyle \frac{dy}{dx}$ .

$C\,$ has a stationary point at $P$ .

[2]

b.

Show that the $x$ -coordinate of $P\,$ lies between 4.5 and 5.

[2]

c.

Show that the $x$ -coordinate of $P\,$ is a solution of $\dfrac{12}{1 + \ln x}$ .

[2]

d.

Use the iteration formula

$xn+1=121+ln⁡xn\displaystyle x_{n+1} = \frac{12}{1 + \ln x_n}$

with $x_0 = 4.75$ to find, to three decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[2]

Markscheme

1.10 Numerical Methods (A-level only) Questions

A Level
Maths
1.10 Numerical Methods (A-level only)

133 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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