Edexcel FP1 Specimen — Question 1 6 marks

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
SessionSpecimen
Marks6
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TopicNewton-Raphson method
TypeNewton-Raphson with derivative given or simple
DifficultyModerate -0.8 This is a straightforward application of the Newton-Raphson formula with explicit guidance: the derivative is asked for in part (a), the starting value is given, and only one iteration is required. It's purely procedural with no problem-solving or insight needed, making it easier than average but not trivial since it involves careful calculation.
Spec1.07i Differentiate x^n: for rational n and sums1.09d Newton-Raphson method

1. $$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 5 x - 4$$
  1. Use differentiation to find \(\mathrm { f } ^ { \prime } ( x )\). The equation \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) in the interval \(1.4 < x < 1.5\)
  2. Taking 1.4 as a first approximation to \(\alpha\), use the Newton-Raphson procedure once to obtain a second approximation to \(\alpha\). Give your answer to 3 decimal places.

1.

$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 5 x - 4$$
\begin{enumerate}[label=(\alph*)]
\item Use differentiation to find $\mathrm { f } ^ { \prime } ( x )$.

The equation $\mathrm { f } ( x ) = 0$ has a root $\alpha$ in the interval $1.4 < x < 1.5$
\item Taking 1.4 as a first approximation to $\alpha$, use the Newton-Raphson procedure once to obtain a second approximation to $\alpha$. Give your answer to 3 decimal places.
\end{enumerate}

\hfill \mbox{\textit{Edexcel FP1  Q1 [6]}}