Skip to content

Course home

1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only)

EasyMediumHard
1234567891011
Question 9

The function f f\,f is defined by

f(x)=exx−1f(x) = e^x\sqrt{x} - 1f(x)=exx​−1, x≥0x \geq 0x≥0

a.

The equation f(x)=0f(x) = 0f(x)=0 has a single solution at x=αx = \alphax=α. By considering a suitable change of sign, show that α \alpha\,α lies between 0 and 1.

[2]
b.

Show that f′(x)=ex(2x+1)2xf'(x) = \dfrac{e^x(2x + 1)}{2\sqrt{x}}f′(x)=2x​ex(2x+1)​.

[3]
c.

Use the Newton-Raphson method with x1=1x_1 = 1x1​=1 to find x3x_3x3​, an approximation for α\alphaα. Give your answer to five decimal places.

[2]
d.

Explain why the Newton-Raphson method cannot be used to find α \alpha\,α 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