| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Fixed Point Iteration |
| Type | Apply iteration to find root (pure fixed point) |
| Difficulty | Easy -1.8 This is a straightforward trace-through of a flowchart algorithm with simple arithmetic operations (subtraction, multiplication by 0.2). It requires only basic computational skills and following instructions step-by-step, with no problem-solving, algebraic manipulation, or mathematical insight needed. Significantly easier than typical A-level questions. |
| Spec | 7.03a Algorithm definition: input, output, deterministic, finite7.03b Algorithm awareness: uses and practical limitations7.03c Working with algorithms: trace, interpret, adapt |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(S=25000\), \(T=0\), \(R=17000\); \(R>0\)? → y (Lines 1 & 2) | M1A1 | |
| \(T=3400\); \(R=7000\); \(R>0\)? → y; \(T=4450\); \(R=-5000\); \(R>0\)? → n; Output 4450 (Lines 3–7) | M1A1 | |
| Output correct: 4450 | A1 | (5 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Tax on £25,000 is £4450 | B1ft | (1 mark) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Tax free sum \(= £8000\) | B1 | (1 mark) [7 total] |
# Question 5(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $S=25000$, $T=0$, $R=17000$; $R>0$? → y (Lines 1 & 2) | M1A1 | |
| $T=3400$; $R=7000$; $R>0$? → y; $T=4450$; $R=-5000$; $R>0$? → n; Output 4450 (Lines 3–7) | M1A1 | |
| Output correct: 4450 | A1 | **(5 marks)** |
# Question 5(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| Tax on £25,000 is £4450 | B1ft | **(1 mark)** |
# Question 5(c):
| Answer | Mark | Guidance |
|--------|------|----------|
| Tax free sum $= £8000$ | B1 | **(1 mark) [7 total]** |
---5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{17bc9fb2-13bf-4ffa-93ac-bef170467570-6_2228_613_269_861}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}
An algorithm is described by the flowchart shown in Figure 4.
\begin{enumerate}[label=(\alph*)]
\item Given that $\mathrm { S } = 25000$, complete the table in the answer book to show the results obtained at each step when the algorithm is applied.
This algorithm is designed to model a possible system of income tax, T, on an annual salary, £S.
\item Write down the amount of income tax paid by a person with an annual salary of $\pounds 25000$.
\item Find the maximum annual salary of a person who pays no tax.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2010 Q5 [7]}}