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Bearings and Scale Drawings — Free MYP4 Mathematics (Standard) Practice Questions
1QuestionMeasuring and Drawing BearingsConcept Practice
2 marks~3 minCriterion A
A coast guard vessel departs from port A. A north line is shown at A. Point B marks a lighthouse.
a
Determine the three-figure bearing of B from A. [1]
b
The coast guard must travel on a bearing of to reach a rescue zone C from A. Justify whether the lighthouse at B or the rescue zone at C is further clockwise from north when viewed from A. [1]
Solutions
2QuestionCreating and Interpreting Scale DiagramsAssessment Practice
6 marks~9 minCriterion D
A nautical chart has a scale of 1:50 000. A narrow channel measures 2 cm wide on the chart, representing an actual width of 1 000 m. The chart has been exposed to moisture and has uniformly shrunk by 2%.
a
Calculate the new width of the channel on the shrunken chart. [2]
b
Deduce the new scale of the shrunken chart, expressing your answer in the form , and calculate the percentage error in the scale compared to the original. [2]
c
The ship is 900 m wide. Advise the captain whether the shrunken chart can be used safely to navigate the channel, justifying your advice with calculations of the actual clearance on each side of the ship. [2]
Solutions
3QuestionWord Problems Involving Bearings and MapsAssessment Practice
6 marks~9 minCriterion D
A pilot must fly from Airport A to Airport B, located 350 km away on a bearing of . A wind blows from at 50 km/h. The pilot maintains an airspeed of 280 km/h.
a
Construct a labelled vector diagram and calculate the required heading and ground speed so that the plane tracks directly to Airport B. [3]
b
Deduce the estimated flight time, in minutes, using your results from part (a). [1]
c
Advise the pilot on whether the single calculated heading of approximately and flight time of approximately 85 minutes can be relied upon for the flight plan, referring to at least two real-world factors and their effect on arrival time and position. [2]
Solutions
4QuestionCreating and Interpreting Scale DiagramsAssessment Practice
6 marks~9 minCriterion B
A cartographer is creating maps of the same region at different scales. The table below shows the relationship between scale factor and the measured map distance between two landmarks.
The actual distance between the two landmarks remains constant throughout.
| Scale factor denominator | 5 000 | 10 000 | 20 000 | 40 000 |
|---|---|---|---|---|
| Map distance (cm) | 20 | 10 | 5 | 2.5 |
The actual distance between the two landmarks remains constant throughout.
a
Analyse the relationship between the scale factor denominator and the map distance, identifying any pattern. [2]
b
Deduce the map distance between the landmarks on a map with scale factor 1:80 000, showing your reasoning clearly. [2]
c
A cartographer claims that a map distance of 8 cm is suitable for a printed map where the minimum legible distance between two labelled landmarks is 6 cm. Identify the scale factor that produces this 8 cm map distance and justify whether the cartographer's claim is valid. [2]
Solutions
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