Last updated on Oct 23, 2026

Solving Equations (Edexcel A-Level Mathematics): Flashcards

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Newton-Raphson

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What is the Newton-Raphson method used for?

Finding approximate solutions to equations $f(x) = 0$ .

What is the iterative formula in Newton-Raphson method?

$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$

What do $f(x)$ and $f'(x)$ represent in the formula?

$f(x)$ is the function; $f'(x)$ is its derivative.

What is required to begin the Newton-Raphson method?

An initial guess $x_0$ for the root.

How do we check convergence in this method?

Ensure $|x_{n+1} - x_n| < \varepsilon$ for desired tolerance.

What is the first step in an iterative method?

Choose an initial approximation for the solution.

What issue can arise if $f'(x)$ is close to zero?

The method may fail or converge slowly.

What happens if the initial guess is poorly chosen?

It may converge to the wrong root or fail to converge.

What is a potential problem with functions having multiple roots?

The method may converge to different roots based on $x_0$ .

What should be done before applying the Newton-Raphson method?

Graphically or analytically assess the function.

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