Skip to content

Course home

1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109
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]
Markscheme

1.10 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.10 Numerical Methods (A-level only)

137 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.

Question bank