Skip to content

Course home

Sign up

1.12 I: Numerical methods (A-level only)

EasyMediumHard
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879
Question 3

The curve C C\,C has the equation y=(15−x)ln⁡xy = (15 - x) \ln xy=(15−x)lnx, x>0x > 0x>0.

a.

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

[3]
b.

C C\,C has a stationary point at PPP. Show that the xxx-coordinate of P P\,P lies between 5 and 6.

[3]
c.

Show that the xxx-coordinate of P P\,P is a solution of x=151+ln⁡x\displaystyle x = \frac{15}{1 + \ln x}x=1+lnx15​.

[3]
d.

Use the iteration formula xn+1=151+ln⁡xn\displaystyle x_{n+1} = \frac{15}{1 + \ln x_n}xn+1​=1+lnxn​15​ with x0=5.5x_0 = 5.5x0​=5.5 to find, to 3 decimal places, the values of x1x_1x1​, x2 x_2\,x2​ and x3x_3x3​.

[3]
Markscheme

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

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

125 exam-style questions on AQA A Level Maths 1.12 I: Numerical methods (A-level only), 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). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank