| Exam Board | AQA |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| 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 an algorithm tracing exercise requiring only careful step-by-step execution of given instructions with simple arithmetic. No problem-solving, conceptual understanding, or mathematical insight is needed—just methodical bookkeeping of variable values through loops, making it significantly easier than average A-level questions. |
| Spec | 7.03c Working with algorithms: trace, interpret, adapt |
| Answer | Marks | Guidance |
|---|---|---|
| SCA trace with columns \((A),(B),(N),T,D,H,E\) values \((1),(5),(2)\); \(T=126\); \(T=180\); \(D\) values \(0,1,3,5\) | M1, A1, m1 | SCA trace as far as a second value for \(T\) with at least 1 value for all other variables; \(T=(180)\) trace as far as a third value for \(T\) and 2 values for \(D\) |
| ("Area \(=\)") \(180\) | A1 | 4 |
| Answer | Marks | Guidance |
|---|---|---|
| SCA as above with \((N)=(4)\); \(T=142\); \(T=196,324\); \(D\) values \(0,1,2,3,4,5\); \(H=0.5,1\) | M1, A1, m1 | SCA as above |
| ("Area \(=\)") \(162\) | A1 | 4 |
## Question 6:
### Part (a)
| SCA trace with columns $(A),(B),(N),T,D,H,E$ values $(1),(5),(2)$; $T=126$; $T=180$; $D$ values $0,1,3,5$ | M1, A1, m1 | SCA trace as far as a second value for $T$ with at least 1 value for all other variables; $T=(180)$ trace as far as a third value for $T$ and 2 values for $D$ |
| ("Area $=$") $180$ | A1 | 4 | All correct values including final value of 180 and no extra values, but including $A$, $B$, $N$ and their values $1, 5, 2$ |
### Part (b)
| SCA as above with $(N)=(4)$; $T=142$; $T=196,324$; $D$ values $0,1,2,3,4,5$; $H=0.5,1$ | M1, A1, m1 | SCA as above |
| ("Area $=$") $162$ | A1 | 4 | All correct values including final value of 162 and no extra values, but including $A$, $B$, $N$ and their values $1, 5, 4$ |
---6 A student is finding a numerical approximation for the area under a curve.\\
The algorithm that the student is using is as follows:\\
Line 10 Input $A , B , N$\\
Line 20 Let $T = 0$\\
Line 30 Let $D = A$\\
Line $40 \quad$ Let $H = ( B - A ) / N$\\
Line $50 \quad$ Let $E = H / 2$\\
Line 60 Let $T = T + A ^ { 3 } + B ^ { 3 }$\\
Line $70 \quad$ Let $D = D + H$\\
Line 80 If $D = B$ then go to line 110\\
Line 90 Let $T = T + 2 D ^ { 3 }$\\
Line 100 Go to line 70\\
Line $110 \quad$ Print 'Area $=$, $T \times E$\\
Line 120 End\\
Trace the algorithm in the case where the input values are:
\begin{enumerate}[label=(\alph*)]
\item $A = 1 , B = 5 , N = 2$;
\item $A = 1 , B = 5 , N = 4$.
\end{enumerate}
\hfill \mbox{\textit{AQA D1 2010 Q6 [8]}}