Worked example · Easy
Read a simple scale
A line on a plan measures 6 cm. The scale is 1 cm to 3 m. Find the real length.
Step 1: Every 1 cm means 3 m.
Step 2: \(6\times3=\boxed{18\text{ m}}\).
Chapter 34 · Revised
Scale Drawings
Work confidently with maps, scale plans and accurately measured three-figure bearings. Learn to convert lengths, construct routes and explain each step clearly.
By the end of this chapter, you should be able to
- read and draw scale diagrams using rulers and consistent units;
- convert between measurements on maps or plans and distances in real life;
- recognise that a map measures straight-line distance, not necessarily road distance;
- draw and interpret directions as three-figure bearings measured clockwise from north;
- find reverse bearings and construct multi-stage journeys with a scale and protractor;
- measure an unknown straight-line distance and direction from an accurate diagram.
1
Subtopic 1
Scale drawings and maps
A scale drawing keeps the same shape and proportions as a real object but shows it at a more convenient size. A map is a scale drawing of an area. You can measure the drawing to estimate real lengths or work backwards to draw accurately.
Know what the scale means
1 cm to 4 m: each 1 cm on the drawing represents 4 m in real life. A 3 cm line represents 12 m; a 20 m wall is 5 cm on the drawing.
2 cm to 5 km: each centimetre represents \(5\div2=2.5\) km.
1 : 500 means 1 unit on the drawing represents 500 of the same unit in real life. It can mean 1 cm to 500 cm = 5 m. Do not treat 1 : 500 as 1 cm to 500 m.
For conversion, first find what 1 cm on the drawing represents. Drawing to real: multiply; real to drawing: divide. For numerical ratios, make units match first.
Worked example · Easy
Work backwards from a real length
An actual fence is 35 m long. The scale is 1 cm to 5 m. How long is the fence on the plan?
Step 1: Each centimetre represents 5 m.
Step 2: \(35\div5=\boxed{7\text{ cm}}\) on the plan.
Worked example · Easy
Read a non-unit scale
A map uses 2 cm to 5 km. Two villages are 8.4 cm apart on the map. Find their straight-line distance.
Step 1: \(1\text{ cm}\) represents \(5\div2=2.5\text{ km}\).
Step 2: \(8.4\times2.5=\boxed{21\text{ km}}\).
You may also see a ratio scale such as 1 : 250. Both sides refer to the same unit. Always convert the final answer into a practical unit if the question asks for metres or kilometres.
Worked example · Medium
Ratio scale and unit conversion
A plan is drawn to a scale of 1 : 250. A window is 18 mm wide on the plan. Find its actual width in metres.
Step 1: Actual width \(=18\times250=4500\text{ mm}\).
Step 2: \(4500\div1000=\boxed{4.5\text{ m}}\).
Worked example · Medium
Construct a plan dimension
A room measures 12 m by 8 m. Draw its rectangular outline at 1 : 200.
Step 1: \(1\text{ cm}\) on the plan represents \(200\text{ cm}=2\text{ m}\).
Step 2: Plan length \(=12\div2=6\text{ cm}\); width \(=8\div2=4\text{ cm}\).
Step 3: Draw and label a rectangle \(\boxed{6\text{ cm by }4\text{ cm}}\).
Worked example · Medium
Use a floor plan
At a scale of 1 cm to 2 m, a rectangular kitchen is 2.8 cm by 1.6 cm on the plan. Find the kitchen dimensions and actual floor area.
Step 1: Actual length \(=2.8\times2=5.6\text{ m}\); width \(=1.6\times2=3.2\text{ m}\).
Step 2: Actual area \(=5.6\times3.2=\boxed{17.92\text{ m}^2}\).
Worked example · Medium
Large distance on a small-scale map
A map scale is 1 : 50 000. Two points are 7.6 cm apart. Find the ground distance in kilometres.
Step 1: \(7.6\times50\,000=380\,000\text{ cm}\).
Step 2: \(380\,000\text{ cm}=3800\text{ m}=\boxed{3.8\text{ km}}\).
Worked example · Medium
Measure straight-line distance
On a scale map, two towns are 5.5 cm apart in a straight line. If 1 cm represents 18 km, what distance separates them?
Step 1: Ground distance \(=5.5\times18\).
Step 2: \(\boxed{99\text{ km}}\). This is straight-line distance, not necessarily the driving distance.
Worked example · Medium
Reverse a non-unit scale
A map scale is 3 cm to 8 km. How long must the line be to represent 60 km?
Step 1: Find the drawing length for 1 km: \(3\div8\) cm.
Step 2: For 60 km, \(60\times3\div8=\boxed{22.5\text{ cm}}\).
Worked example · Exam-style
One map, two conversions
A site plan is at 1 : 1250. A path is shown as 5.6 cm long. Another real path is 40 m long. Find (a) the actual length of the first path, (b) the plan length of the second path.
Step 1: (a) \(5.6\times1250=7000\text{ cm}=\boxed{70\text{ m}}\).
Step 2: (b) \(40\text{ m}=4000\text{ cm}\).
Step 3: Plan length \(=4000\div1250=\boxed{3.2\text{ cm}}\).
Worked example · Exam-style
Two legs of a mapped route
A journey follows two straight sections measuring 4.5 cm and 3.8 cm on a map. The scale is 1 cm to 12 km. Find the total length of the two sections and explain why this is not the straight-line distance between start and finish.
Step 1: Add the two route sections: \(4.5+3.8=8.3\text{ cm}\).
Step 2: \(8.3\times12=\boxed{99.6\text{ km}}\).
Step 3: This total follows both route legs; the direct start-to-finish line may be shorter.
Worked example · Exam-style
Choose a scale that fits the page
A rectangular sports ground measures 96 m by 64 m. A drawing must fit within 16 cm by 12 cm. Will the scale 1 cm to 8 m work? Give the drawn dimensions.
Step 1: Length: \(96\div8=12\text{ cm}\). Width: \(64\div8=8\text{ cm}\).
Step 2: \(12\leq16\) and \(8\leq12\), so the drawing \(\boxed{\text{fits}}\).
Step 3: Draw a rectangle \(\boxed{12\text{ cm by }8\text{ cm}}\).
Four steps for accurate scale drawings
- Read the scale and convert before drawing.
- Make a quick sketch so the complete shape fits the page.
- Measure with a ruler, keep lines neat and label important points.
- When reading the finished diagram, measure carefully and convert back to real units. Small differences are possible because of ruler or printing accuracy.
2
Subtopic 2
Bearings
A bearing tells you a direction from one point to another. It is measured clockwise from north, starting at the point named after the word from. Every bearing has three digits, including any zeros at the beginning.
Three-figure bearing rules
Due north = \(000^\circ\); east = \(090^\circ\); south = \(180^\circ\); west = \(270^\circ\).
Write \(7^\circ\) as 007° and \(65^\circ\) as 065°. A full turn \(360^\circ\) points north again, normally recorded as 000°.
For a reverse bearing, add \(180^\circ\) if the original bearing is less than \(180^\circ\); otherwise subtract \(180^\circ\). The result is always in the range 000°–359°.
Worked example · Easy
Write the direction as a bearing
A ray points 43° clockwise from north. Write the three-figure bearing.
Step 1: Bearings have exactly three figures.
Step 2: \(43^\circ\) is written as \(\boxed{043^\circ}\).
Worked example · Easy
Cardinal directions
Write the bearings for (a) north-east, (b) due south, (c) due west.
Step 1: NE lies 45° clockwise from north: \(\boxed{045^\circ}\).
Step 2: Due south is \(\boxed{180^\circ}\); due west is \(\boxed{270^\circ}\).
Worked example · Easy
Reverse bearing below 180°
The bearing of B from A is 062°. Find the bearing of A from B.
Step 1: Opposite directions differ by 180°.
Step 2: \(062^\circ+180^\circ=\boxed{242^\circ}\).
Worked example · Medium
Reverse bearing above 180°
The bearing of C from D is 230°. Find the bearing of D from C.
Step 1: Since \(230^\circ\) is greater than \(180^\circ\), subtract 180°.
Step 2: \(230^\circ-180^\circ=\boxed{050^\circ}\).
Worked example · Medium
Measure a bearing using a protractor
A point P lies south-east of O, with ray OP making 35° south of east. Find the bearing of P from O.
Step 1: East is \(090^\circ\). Turn a further 35° clockwise towards south.
Step 2: Bearing \(=090^\circ+35^\circ=\boxed{125^\circ}\).
Worked example · Medium
Measure the correct direction
A point Q is on a bearing 298° from P. Find the bearing of P from Q.
Step 1: We need the opposite direction, not the bearing from P again.
Step 2: \(298^\circ-180^\circ=\boxed{118^\circ}\).
Construct a bearing with ruler and protractor
- Mark the starting point and draw a north arrow through it.
- Centre the protractor on the starting point and measure the stated angle clockwise from north.
- Draw a ray along this direction.
- Use the scale to convert the real distance to the correct length on the paper.
- Measure that length along the ray, mark the destination, and label it.
Always draw a fresh north line at each new starting point in a multi-leg journey.
Worked example · Medium
Construct a single bearing
B is 15 km from A on a bearing of 055°. Use a scale of 1 cm to 5 km. State exactly how to plot B.
Step 1: Convert: \(15\div5=3\text{ cm}\).
Step 2: At A, draw north. Measure 55° clockwise from north and draw a ray.
Step 3: Mark B \(\boxed{3\text{ cm}}\) along the ray, and label the bearing \(055^\circ\).
Worked example · Medium
Plot a longer leg
A boat sails 18 km on a bearing of 130°. The plan scale is 1 cm to 3 km. What length and direction should be drawn?
Step 1: Drawing length \(=18\div3=\boxed{6\text{ cm}}\).
Step 2: Measure \(\boxed{130^\circ}\) clockwise from north at the starting point and draw a 6 cm line.
Worked example · Medium
Find a bearing from a sketch
A path runs 20° north of west. Find its three-figure bearing.
Step 1: West is \(270^\circ\). Moving 20° towards north increases the bearing.
Step 2: \(270^\circ+20^\circ=\boxed{290^\circ}\).
Worked example · Exam-style
Two-leg route: distance on a drawing
A goes 8 km due east to B, then 6 km due south to C. Use a scale of 1 cm to 2 km. Find the straight-line distance AC and the bearing of C from A from your drawing.
Step 1: Draw AB = \(8\div2=4\text{ cm}\) east and BC = \(6\div2=3\text{ cm}\) south.
Step 2: Measure AC on the accurate drawing: \(5\text{ cm}\). Convert: \(5\times2=\boxed{10\text{ km}}\).
Step 3: At A, measure clockwise from north to AC: approximately \(\boxed{127^\circ}\). A small variation is acceptable from an accurately drawn diagram.
Worked example · Exam-style
A turn produces a right-angled route
From A to B the bearing is 060° and the distance is 16 km. From B to C the bearing is 150° and the distance is 12 km. Use 1 cm to 4 km. Find AC.
Step 1: Draw AB \(=16\div4=4\text{ cm}\) on bearing 060°.
Step 2: At B draw BC \(=12\div4=3\text{ cm}\) on bearing 150°. The legs meet at 90° because \(150-60=90\).
Step 3: Measure AC \(\approx5\text{ cm}\), so \(AC\approx5\times4=\boxed{20\text{ km}}\).
Worked example · Exam-style
Route home on the reverse bearing
A campsite lies 22 km from a starting point on a bearing of 285°. State the return bearing and the two drawing lengths if the scale is 1 cm to 5.5 km.
Step 1: Reverse bearing \(=285-180=\boxed{105^\circ}\).
Step 2: Each leg is \(22\div5.5=\boxed{4\text{ cm}}\) long on the plan.
Step 3: Draw the return bearing from the campsite, not the starting point.
Worked example · Exam-style
Plan carefully before measuring
A navigation diagram requires points B and C: B is 18 km from A on 085°; C is 12 km from B on 150°. The scale is 1 cm to 3 km. State the two line lengths and the correct north-line positions.
Step 1: \(AB=18\div3=\boxed{6\text{ cm}}\); \(BC=12\div3=\boxed{4\text{ cm}}\).
Step 2: At A draw a north line, then 085° clockwise, and measure 6 cm to B.
Step 3: At B draw a second north line parallel to the first; measure 150° clockwise and mark C 4 cm along that ray.
Step 4: To find AC and the bearing of A from C, measure them on your completed accurate plan.
Common examination mistakes
- Measuring bearings anti-clockwise or beginning from east rather than north.
- Forgetting the first zero: write 009°, not 9°.
- Measuring from the wrong point: “A from B” starts at B.
- Using 1 : 200 as though 1 cm means 200 m—it means 200 cm.
- Forgetting to start a new north line at each point in a compound route.
- Quoting an exact distance when the answer was obtained by ruler measurement; use a sensible level of accuracy.
Chapter 34 practice — easy to exam-style
Try each question on paper before opening its Show Answer toggle. Early questions build confidence; the final questions require multi-step reasoning, construction descriptions and careful units. All questions are original exam-style practice, not copied past-paper questions.
A: Questions 1–22, scale drawings and maps. B: Questions 23–44, bearings and combined plans.
A. Scale drawings and maps
1Simple scaleConfidence-building · [2 marks]
A line is 4 cm on a drawing. Scale: 1 cm to 6 m. Find the real length.
Show Answer
Step 1: \(1\text{ cm}\to6\text{ m}\).
Step 2: \(4\times6=\boxed{24\text{ m}}\)
2From real to planConfidence-building · [2 marks]
A wall is 28 m long. Scale: 1 cm to 7 m. Find the drawn length.
Show Answer
Step 1: Every centimetre represents 7 metres.
Step 2: \(28\div7=\boxed{4\text{ cm}}\)
3Two-centimetre scaleConfidence-building · [2 marks]
A map has scale 2 cm to 12 km. How far is a 5 cm map line?
Show Answer
Step 1: One centimetre represents \(12\div2=6\) km.
Step 2: \(5\times6=\boxed{30\text{ km}}\)
4Centimetres to millimetresConfidence-building · [2 marks]
On a scale diagram, 1 cm represents 4 m. A road measures 45 mm. Find its real length.
Show Answer
Step 1: \(45\text{ mm}=4.5\text{ cm}\).
Step 2: \(4.5\times4=\boxed{18\text{ m}}\)
51 : 100 ratioConfidence-building · [2 marks]
A model is drawn at 1 : 100. A measured length is 9 cm. Find the actual length in metres.
Show Answer
Step 1: Actual length \(=9\times100=900\text{ cm}\).
Step 2: \(900\div100=\boxed{9\text{ m}}\)
6Cardinal length scaleConfidence-building · [1 marks]
A strip is 18 m long. On a plan 1 cm represents 3 m. How long is the strip on the plan?
Show Answer
Step 1: \(18\div3=\boxed{6\text{ cm}}\)
7Map scaleConfidence-building · [2 marks]
Two villages are 3.4 cm apart. The scale is 1 cm to 25 km. Calculate their straight-line separation.
Show Answer
Step 1: \(3.4\times25=\boxed{85\text{ km}}\)
8Simple 1 : 500 scaleConfidence-building · [2 marks]
Scale 1 : 500. A line is 2.6 cm on the plan. Find its actual length in metres.
Show Answer
Step 1: \(2.6\times500=1300\text{ cm}\).
Step 2: \(1300\div100=\boxed{13\text{ m}}\)
9Draw a scaled lineConfidence-building · [2 marks]
Draw a line to represent 30 km using a scale 1 cm to 5 km. How long is your drawn line?
Show Answer
Step 1: \(30\div5=\boxed{6\text{ cm}}\).
Step 2: Use a ruler to draw and label a 6 cm line.
10Read a non-unit scaleDeveloping · [3 marks]
The scale is 3 cm to 24 km. A pair of points is 7.5 cm apart. Find their real separation.
Show Answer
Step 1: \(1\text{ cm}\to24\div3=8\) km.
Step 2: \(7.5\times8=\boxed{60\text{ km}}\)
11Actual to map at non-unit scaleDeveloping · [3 marks]
A real distance is 42 km; the map scale is 2 cm to 7 km. Find the map distance.
Show Answer
Step 1: For 7 km draw 2 cm.
Step 2: \(42\div7\times2=\boxed{12\text{ cm}}\)
12A site rectangleDeveloping · [3 marks]
A court measures 36 m by 24 m. The plan scale is 1 cm to 6 m. Find both planned dimensions.
Show Answer
Step 1: Length \(36\div6=\boxed{6\text{ cm}}\).
Step 2: Width \(24\div6=\boxed{4\text{ cm}}\)
13Plot boundariesDeveloping · [3 marks]
A field 150 m by 90 m is to be drawn to scale 1 : 3000. Find the drawn dimensions.
Show Answer
Step 1: \(150\text{ m}=15\,000\text{ cm}\) and \(90\text{ m}=9000\text{ cm}\).
Step 2: Divide by 3000: \(\boxed{5\text{ cm by }3\text{ cm}}\)
14Find a scale from measurementsDeveloping · [2 marks]
A 40 m building is drawn as an 8 cm line. Express the scale as 1 cm to ? m.
Show Answer
Step 1: \(40\div8=5\).
Step 2: Scale \(\boxed{1\text{ cm to }5\text{ m}}\)
15Ratio scale 1 : 20 000Developing · [3 marks]
A map is at 1 : 20 000. A route is shown as 15 cm. Find the ground length in kilometres.
Show Answer
Step 1: \(15\times20\,000=300\,000\text{ cm}\).
Step 2: \(300\,000\div100\,000=\boxed{3\text{ km}}\)
16Metres to mapped lengthDeveloping · [3 marks]
A map is 1 : 10 000. Two sites are 750 m apart. How many centimetres apart should they appear?
Show Answer
Step 1: \(750\text{ m}=75\,000\text{ cm}\).
Step 2: \(75\,000\div10\,000=\boxed{7.5\text{ cm}}\)
17Compare two mapsDeveloping · [3 marks]
Map A has scale 1 cm to 4 km and map B has scale 1 cm to 10 km. Find the length representing the same 60 km route on each.
Show Answer
Step 1: On A: \(60\div4=\boxed{15\text{ cm}}\).
Step 2: On B: \(60\div10=\boxed{6\text{ cm}}\).
Step 3: Smaller ground distance per cm means a longer drawing for the same route.
18Plan areaDeveloping · [3 marks]
A room measures 5 cm by 3 cm on a plan at 1 cm to 2 m. Find the real floor area.
Show Answer
Step 1: Real dimensions \(10\text{ m}\) by \(6\text{ m}\).
Step 2: Area \(10\times6=\boxed{60\text{ m}^2}\)
19Map route with two legsExam-style · [3 marks]
A walking trail on a map follows sections 2.5 cm and 4.8 cm. Scale: 1 cm to 2 km. Find the total distance travelled.
Show Answer
Step 1: Sum the measured route: \(2.5+4.8=7.3\text{ cm}\).
Step 2: \(7.3\times2=\boxed{14.6\text{ km}}\)
20A plan must fitExam-style · [3 marks]
A park is 210 m long and 120 m wide. An A4 plan has 18 cm of usable width and 14 cm of usable height. Can the scale 1 cm to 15 m fit the park on it?
Show Answer
Step 1: Drawing dimensions \(210\div15=14\text{ cm}\) and \(120\div15=8\text{ cm}\).
Step 2: Both fit within 18 cm by 14 cm, so \(\boxed{\text{yes}}\).
21Three lengths from a site planExam-style · [4 marks]
A scale model shows three consecutive walls of 5.2 cm, 3.4 cm and 1.9 cm. At 1 : 400, find their total real length in metres.
Show Answer
Step 1: Total drawing length \(5.2+3.4+1.9=10.5\text{ cm}\).
Step 2: \(10.5\times400=4200\text{ cm}\).
Step 3: \(4200\div100=\boxed{42\text{ m}}\)
22Find the missing plan lengthExam-style · [4 marks]
On a 1 : 250 map, a rectangular courtyard has actual perimeter 38 m and length 12 m. Find the width to draw, in centimetres.
Show Answer
Step 1: Actual width \(=38\div2-12=7\text{ m}\).
Step 2: \(7\text{ m}=700\text{ cm}\).
Step 3: On plan \(700\div250=\boxed{2.8\text{ cm}}\)
B. Bearings and scale-bearing routes
23Bearing notationConfidence-building · [1 marks]
Write 6° clockwise from north as a three-figure bearing.
Show Answer
Step 1: Add leading zeros to three digits: \(\boxed{006^\circ}\)
24Due eastConfidence-building · [1 marks]
What is the three-figure bearing of due east?
Show Answer
Step 1: Clockwise from north to east is 90°: \(\boxed{090^\circ}\)
25South-west directionConfidence-building · [2 marks]
What bearing represents south-west exactly halfway between south and west?
Show Answer
Step 1: South is 180°, west is 270°.
Step 2: Halfway: \(180+45=\boxed{225^\circ}\)
26Reverse of 065°Confidence-building · [2 marks]
B is on a bearing 065° from A. Find the bearing of A from B.
Show Answer
Step 1: \(065^\circ+180^\circ=\boxed{245^\circ}\)
27Reverse of 240°Confidence-building · [2 marks]
C is on a bearing 240° from D. Find the bearing of D from C.
Show Answer
Step 1: \(240^\circ-180^\circ=\boxed{060^\circ}\)
28South from a pointConfidence-building · [2 marks]
Town R is due south of town S. State the bearing of R from S and S from R.
Show Answer
Step 1: R from S: \(\boxed{180^\circ}\).
Step 2: S from R: \(\boxed{000^\circ}\)
29Bearing to south-eastConfidence-building · [2 marks]
Find the three-figure bearing corresponding to south-east.
Show Answer
Step 1: South-east is halfway between east (90°) and south (180°).
Step 2: \(90+45=\boxed{135^\circ}\)
30A turn from northConfidence-building · [2 marks]
The direction is 25° west of north. Find its clockwise bearing.
Show Answer
Step 1: Turn anticlockwise 25°, equivalent to clockwise \(360-25\).
Step 2: Bearing \(=\boxed{335^\circ}\)
31A compass turnConfidence-building · [2 marks]
A ship sails on a bearing of 318°. How many degrees west of north is this?
Show Answer
Step 1: \(360-318=\boxed{42^\circ}\) west of north
32Reverse near northConfidence-building · [2 marks]
The bearing of K from L is 350°. Find the reverse bearing.
Show Answer
Step 1: \(350-180=\boxed{170^\circ}\)
33Construct a 070° bearingDeveloping · [3 marks]
Plot B 20 km from A on a bearing 070°, scale 1 cm to 5 km. How many centimetres should AB measure?
Show Answer
Step 1: \(20\div5=\boxed{4\text{ cm}}\).
Step 2: Draw north at A; measure clockwise 70°; mark B 4 cm along the ray.
34Construct two directionsDeveloping · [3 marks]
From a point O, plot P at 040° and Q at 210°. Each point is 4 cm from O. Describe the construction.
Show Answer
Step 1: Draw one north arrow at O.
Step 2: Measure 40° clockwise and mark P 4 cm away.
Step 3: Measure 210° clockwise from the same north line and mark Q 4 cm away.
35Destination bearingDeveloping · [2 marks]
A village lies 28° north of east from a farm. Find its bearing from the farm.
Show Answer
Step 1: East = 090°; toward north subtract 28°.
Step 2: \(90-28=\boxed{062^\circ}\)
36Reverse from large bearingDeveloping · [2 marks]
P is on bearing 302° from Q. Find the bearing of Q from P.
Show Answer
Step 1: \(302-180=\boxed{122^\circ}\)
37Plan a sea routeDeveloping · [3 marks]
A boat sails 36 km on bearing 125°. On a scale 1 cm to 6 km, give the length of the line and instructions for drawing it.
Show Answer
Step 1: \(36\div6=\boxed{6\text{ cm}}\).
Step 2: Draw a north line at the port, measure 125° clockwise, and mark the boat 6 cm along that ray.
38Returning directlyDeveloping · [3 marks]
An aircraft flies 45 km on bearing 040°. State its direct return bearing and the return line length at 1 cm to 9 km.
Show Answer
Step 1: Reverse \(=040+180=\boxed{220^\circ}\).
Step 2: Drawing length \(45\div9=\boxed{5\text{ cm}}\)
39Unknown leg from a diagramDeveloping · [2 marks]
On an accurately constructed map at 1 cm to 3 km, the line joining two points measures 7.4 cm. Find the ground distance.
Show Answer
Step 1: \(7.4\times3=\boxed{22.2\text{ km}}\)
40Reverse bearing checkDeveloping · [3 marks]
On a diagram, the bearing of T from S is 178°. Find the bearing of S from T. Explain why 358° is correct.
Show Answer
Step 1: \(178+180=\boxed{358^\circ}\).
Step 2: The reversed ray points just west of north, consistent with a 358° bearing.
41A two-leg routeExam-style · [3 marks]
A walks 10 km due east to B then 24 km due south to C. Give the lengths AB and BC for a plan at 1 cm to 2 km.
Show Answer
Step 1: \(AB=10\div2=\boxed{5\text{ cm}}\).
Step 2: \(BC=24\div2=\boxed{12\text{ cm}}\).
Step 3: Bearings: 090° then 180° measured at their respective starting points.
42Straight route from planExam-style · [4 marks]
Using the journey in Question 41, find the straight-line distance from A to C, and estimate the bearing of C from A.
Show Answer
Step 1: At scale 1 cm to 2 km draw 5 cm east followed by 12 cm south.
Step 2: Direct AC on the drawing is \(13\text{ cm}\); hence \(13\times2=\boxed{26\text{ km}}\).
Step 3: From A, AC is south-east, about \(\boxed{157^\circ}\) clockwise from north (measured).
43Three destinationsExam-style · [4 marks]
A is at O. B lies 12 km on 025° from O, and C lies 12 km on 115° from O. Use 1 cm to 4 km. Find OB and OC on the drawing and explain what angle BOC is.
Show Answer
Step 1: \(OB=OC=12\div4=\boxed{3\text{ cm}}\).
Step 2: At O draw bearings 025° and 115°.
Step 3: Angle \(BOC=115-25=\boxed{90^\circ}\).
44Construct a multi-leg journeyExam-style · [5 marks]
From P travel 16 km on bearing 065° to Q. From Q travel 12 km on bearing 155° to R. For a 1 cm to 4 km scale, write exact construction instructions and find PR.
Show Answer
Step 1: Draw PQ \(=16\div4=4\text{ cm}\) along 065° from north at P.
Step 2: At Q draw a fresh north line and QR \(=12\div4=3\text{ cm}\) along 155°.
Step 3: The legs meet at 90° (155°−65°=90°), so a correct drawing gives PR ≈ 5 cm.
Step 4: \(PR\approx5\times4=\boxed{20\text{ km}}\)
Chapter 34 high-grade checklist
- I can explain what a map scale represents and interpret 1 cm to 5 m, 2 cm to 3 km and 1 : 500.
- I convert mm, cm, m and km correctly before applying scale ratios.
- I can find actual lengths and draw lengths, and can draw a simple plan neatly.
- I distinguish a direct straight-line map distance from the length of several journey legs.
- I start every bearing at north at the stated point, measure clockwise and write three digits.
- I can reverse bearings by 180°, including bearings close to 000° and 360°.
- I can construct a journey using separate north arrows, measured angles and scaled lengths.
- I can measure distances and directions from an accurate drawing and give sensible units and accuracy.