Scale Drawings Maps and Bearings

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Scale Drawings Maps and Bearings — Free MYP3 Mathematics Practice Questions

1QuestionCreating and Interpreting Scale DiagramsConcept Practice

2 marks~3 minCriterion A

A scale diagram of a park uses a scale where

1 \text{ cm}

represents

5 \text{ m}

.

On the diagram, the distance between the fountain and the bench measures

3 \text{ cm}

.

(a) Calculate the actual distance, in metres, between the fountain and the bench. [2]

Solutions

2QuestionCreating and Interpreting Scale DiagramsAssessment Practice

4 marks~6 minCriterion D

A hiker plans a route using a map with a scale of

1:50\,000

. The straight-line trail measures

24\ \text{cm}

on the map. A fold in the map causes a measurement error of

3\ \text{mm}

Calculate the actual distance, in kilometres, represented by the

3\ \text{mm}

error. [2]

Explain how this measurement error and the fact that a map is a flat representation of curved terrain affect the reliability of using the map to plan the hiking route. [2]

Solutions

3QuestionMeasuring Bearings with a ProtractorAssessment Practice

5 marks~8 minCriterion C

A surveyor stands at point

A

and measures the bearing of point

B

056°

. The interior angle

\angle BAC

of the triangular field is

47°

, with

C

lying clockwise from

B

as seen from

A

State what a three-figure bearing measures. [1]

Calculate the bearing of

C

from

A

. [2]

Justify whether a bearing of

009°

for

C

from

A

would be consistent with the given information. [2]

Solutions

4QuestionMeasuring Bearings with a ProtractorAssessment Practice

8 marks~12 minCriterion B

A ship sails in a straight line past a lighthouse

L

. The table shows the bearing of

L

measured from the ship at four equally spaced positions.

Position	$P_1$	$P_2$	$P_3$	$P_4$
Bearing of $L$	$340°$	$350°$	$010°$	$020°$

Describe the pattern in the bearings as the ship moves from

P_1

P_4

. [2]

Apply the pattern to predict the bearing of

L

from position

P_5

, the next equally spaced position along the same line. Explain your reasoning. [3]

Using the scale

1 \text{ cm} = 10 \text{ m}

, the spacing between consecutive positions is

2 \text{ cm}

. A scaled diagram is provided showing

P_1

P_5

and the lighthouse

L

. Measure the bearing of

L

from

P_5

using a protractor, and analyse whether your measurement supports your prediction from part (b). [3]

Solutions

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