| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2004 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sorting Algorithms |
| Type | Algorithm Tracing |
| Difficulty | Easy -1.2 This is a straightforward algorithm trace question requiring systematic execution of given steps with no problem-solving or insight needed. Part (a) is mechanical computation (prime factorization of 90), part (b) asks for simple observation that the output is prime factors, and part (c) requires noticing c counts the factors. Below average difficulty as it's purely procedural with no conceptual challenge beyond following instructions. |
| Spec | 7.03c Working with algorithms: trace, interpret, adapt |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | 2 | 2.5 |
| 5 | 3 | 1 2 |
| 3 | No | |
| 5 | 5 | 1 |
| Answer | Marks |
|---|---|
| (c) | See overlay |
| Answer | Marks |
|---|---|
| Identifies (8,4) profit 32. | B5, 4, 3, 2, |
| Answer | Marks |
|---|---|
| (e) | x = 0, y = 7, z = 9 |
| Answer | Marks |
|---|---|
| 22 hours | B1, B1, B1, |
Question 5:
5 | 2 | 2.5 | No
5 | 3 | 1 2
3 | No
5 | 5 | 1 | Yes | 5 | Yes
7. (a)
(b)
(c) | See overlay
Either point testing or profit line
5 1 1 1 1 1
A (3 ,3 ) → 25 , B (8 ,3 ) →34 ,
6 2 6 2 2 2
Accept C (4,8) → 48 and D (3,6) →36
2
Profit line gradient
5
5 1 1
Identifies A (3 ,3 ) cost 25
6 2 6
Either point testing or profit line
5 1
A (3 , 3 )→not integer so try (4,4) → 20 Profit line
6 2
1 1
B (8 , 3 )→not integer so try (8,4) → 32
2 2
→ try (7,5) → 31 gradient -
3
2
Accept C (4,8) → 28 and D (3,6) → 21
Identifies (8,4) profit 32. | B5, 4, 3, 2,
1, 0 (5)
M1
A1
A1, A1
(4)
M1
A1
A1 A1
(4)
(13)
8. (a)
(b)
(c) (i)
(ii)
(d)
(e) | x = 0, y = 7, z = 9
Length = 22, critical activities B D E L
Float on N = 22 – 14 – 3 = 5
Float on H = 16 – 5 – 3 = 8
See overlay
Attempt at 1. e.t. and e.e.t.
22 hours | B1, B1, B1,
(3)
B1, B1, (2)
B1
M1 A1 (3)
B4, 3,2,1,0
(4)
M1
A1 (2)
(14)\includegraphics{figure_3}
Figure 3 describes an algorithm in the form of a flow chart, where $a$ is a positive integer.
List $P$, which is referred to in the flow chart, comprises the prime numbers 2, 3, 5, 7, 11, 13, 17, ...
\begin{enumerate}[label=(\alph*)]
\item Starting with $a = 90$, implement this algorithm. Show your working in the table in the answer book. [7]
\item Explain the significance of the output list. [2]
\item Write down the final value of $c$ for any initial value of $a$. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2004 Q5 [10]}}