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1.12 I: Numerical methods (A-level only)

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Question 32

The curve C has the equation y=(12−x)ln⁡xy = (12 - x) \ln xy=(12−x)lnx, x>0x > 0x>0

a.

Find dydx\displaystyle \frac{dy}{dx}dxdy​

[3]
b.

C has a stationary point at P. Show that the x x\,x coordinate of P lies between 4.5 and 5

[3]
c.

Show that the x x\,x coordinate of P is a solution of x=121+ln⁡x\displaystyle x = \frac{12}{1 + \ln x}x=1+lnx12​

[3]
d.

Use the iteration formula xn+1=121+ln⁡xn\displaystyle x_{n+1} = \frac{12}{1 + \ln x_n}xn+1​=1+lnxn​12​ with x0=4.75x_0 = 4.75x0​=4.75 to find, to 3 decimal places, the values of x1x_1x1​, x2 x_2\,x2​ and x3x_3x3​.

[3]

1.12 I: Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.12 I: Numerical methods (A-level only)

Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only), matched to the AQA A Level Maths (7357) 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.

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