# Question 4:

## Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Starting by choosing row $C$ in column $A$ | M1 | For starting by choosing row $C$ in column $A$ |
| Choosing more than one entry from column $C$ | M1 | For choosing more than one entry from column $C$ |
| Correct order $(A)$, $C$, $B$, $D$, $E$, $G$, $F$, $H$ | A1 | For a correct order |
| Correct entries chosen or a correct tree drawn | B1 | For correct entries chosen or a correct tree drawn |
| Quickest time is at least 25 hours | B1 | For 25; accept 'more than 25' |

## Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct graph drawn | M1 | For a correct graph drawn |
| Correct weights shown | A1 | For correct weights shown |

## Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| If $AC$ is used then either $B$ or $D$ is excluded. Or must pass through $C$ in getting between $B$ and $D$, so $AC$ is impossible | B1 | For explaining what happens if $AC$ is used or why $AC$ cannot be included. Follow through graph if possible, provided same conclusion is valid |

## Part (iv)
| Answer | Mark | Guidance |
|--------|------|----------|
| If $EF$ is not used then passing through either $E$ or $F$ will take the team to $H$; the team will not be able to visit both $E$ and $F$ | B1 | For stating the effect of not using arc $EF$ or for considering all possible routes into $H$. Follow through graph if possible, provided same conclusion is valid |

## Part (v)
| Answer | Mark | Guidance |
|--------|------|----------|
| $ABEFCDGH$ | M1 | For this route |
| $ADGCBEFH$ | M1 | For this route |
| The second route is quicker (32 hours compared with 36 hours) | A1 | For identifying $ADGCBEFH$ as the quicker or for calculating 32. Follow through graph if possible |

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