Skip to content

Course home

1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106
Question 77

The equation x3−3x2+5=0x^3 - 3x^2 + 5 = 0x3−3x2+5=0 has exactly one real root.

a.

Show that, for this equation, the Newton-Raphson formula can be written

xn+1=2xn3−3xn2−53xn2−6xn\displaystyle x_{n+1} = \frac{2x_n^3 - 3x_n^2 - 5}{3x_n^2 - 6x_n}xn+1​=3xn2​−6xn​2xn3​−3xn2​−5​

[3]
b.

Using the formula in part (a) with x1=−1x_1 = -1x1​=−1, find the values of x2 x_2\,x2​ and x3x_3x3​. Give your answers to four decimal places.

[2]
c.

Explain why, for this equation, the Newton-Raphson method cannot be used with x1=0x_1 = 0x1​=0.

[1]
Markscheme

1.9 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.9 Numerical Methods (A-level only)

125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank