Mathematics 4024 · O Level · Scale drawings

Scale drawings — practice question

The diagram plots boats $A$ and $B$ on a scale of $1:m$. In reality, the separation between the two boats is $4\text{ km}$.
(a)[2]

Find $m$, and give your answer correct to $1$ significant figure.

(b)[1]

Measure the bearing from $B$ to $A$.

(c)[2]

A third boat lies at $C$. $C$ is on a bearing of $120^\circ$ from $A$ and on a bearing of $195^\circ$ from $B$. Find and label $C$ on the diagram.

(d)[2]

Find, by measuring, the actual distance from $A$ to $C$ in kilometres.

(e(i))[3]

The diagram shows boats $A$ and $B$ together with a harbour $H$. $AB = 4\text{ km}$, $AH = 6\text{ km}$ and $\angle ABH = 70^\circ$. Calculate $\angle AHB$.

(e(ii))[3]

The boat at $A$ travels straight to the harbour at $H$. Its average speed is $p\text{ km/h}$. The journey from $A$ to $H$ takes $12$ minutes $20$ seconds. Calculate $p$.

Worked solution & mark scheme

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