Home

Maths

Angles and geometry

Maps and scale drawings

Maps and scale drawings

Videos

Summary

Exercises

Select Lesson

Exam Board

Select an option

Statistics


Sets and Venn diagrams

Sampling and bias

Collecting data: types and classes of data

Mean, median, mode and range

Simple charts and graphs

Pie charts

Scatter graphs

Frequency tables: finding averages

Grouped frequency tables

Box plots - Higher

Cumulative frequency - Higher

Histograms and frequency density - Higher

Interpreting data

Comparing data sets

Probability


Basics of probability

Calculating theoretical probabilities

Probability: Expected and relative frequency

The AND / OR rules

Probability tree diagrams

Conditional probability - Higher

Experimental probability: frequency trees

Trigonometry


Pythagoras' theorem

Sin, cos, tan

Trigonometry: Finding angles and sides

Exact trigonometric values

Sine and cosine rules - Higher

3D Pythagoras - Higher

3D Trigonometry - Higher

Vectors

Vectors - Higher

Angles and geometry


Angles: types, notation and measuring

Basic angle rules

Angles in parallel lines

Circle theorems - Higher

Constructing triangles: SSS, SAS, ASA

Construction: angle and perpendicular bisectors

Construction: Loci

Bearings

Maps and scale drawings

Shapes and area


Properties of 2D shapes

Congruence: conditions for congruent triangles

Similar shapes: Scaling

The four transformations

Area and perimeter: Formulae

Area and circumference of circles: Formulae

3D shapes: faces, edges, vertices

Surface area of 3D shapes: Nets, formulae

Volume of 3D shapes: Formulae

Volume of 3D shapes: Comparing, rates of flow

Area and volume scale factors

Projections and elevations of 3D shapes

Ratio proportion and rates of change


Ratio

Direct and inverse proportion

Finding percentages and percentage change

Compound growth and decay

Converting units: metric and imperial

Converting units: area and volume

Time intervals: converting units of time

Speed, density and pressure: Formulae and units

Graphs


Coordinates and midpoints

Straight line graphs

Drawing straight line graphs

Finding the gradient of a straight line

Equation of a straight line: y = mx + c

Coordinates and ratio

Parallel and perpendicular lines

Quadratic graphs

Reciprocal and cubic graphs

Exponential graphs and circles - Higher

Trigonometric graphs - Higher

Solving equations using graphs

Graph transformations - Higher

Real-life graphs

Distance-time graphs

Velocity-time graphs - Higher

Gradients of real-life graphs - Higher

Algebra


Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Double brackets: Expanding and factorising

Double and triple brackets - Higher

Solving equations

Expressions, equations, formulae, functions and identities

Writing formulae and equations from word problems

Writing formulae and equations from diagrams

Rearranging formulae

Factorising quadratics

The quadratic formula - Higher

Complete the square - Higher

Algebraic fractions - Higher

Sequences

Finding the nth term

Solving inequalities

Inequalities on graphs - Higher

Iteration - Higher

Simultaneous equations: elimination and substitution

Non-linear simultaneous equations - Higher

Algebraic proof - Higher

Composite and inverse functions - Higher

Number


Types of numbers

Order of operations: BODMAS

Multiplying and dividing by powers of 10

Multiplying and dividing whole numbers

Multiplying and dividing decimals

Negative numbers: add, subtract, multiply, divide

Prime numbers and prime factorisation

Multiples, factors and prime factors

LCM and HCF

Fractions

Fractions, decimals and percentages

Writing recurring decimals as fractions

Rounding: Integers, decimal places, significant figures

Estimation

Error intervals

Upper and lower bounds - Higher

Powers and roots: Square and cube numbers

Laws of indices: multiply, divide, brackets

Index laws: negative and fractional indices - Higher

Surds: Simplify, add and subtract - Higher

Rationalising surds - Higher

Standard form calculations

Explainer Video

Tutor: Dylan

Summary

Maps and scale drawings

​​In a nutshell

Many maps and drawings come equipped with a scale, so that you can measure the drawing and use the scale to compute the true distances on the map or dimensions of the drawing. This lesson covers how to read and use scales on maps, or drawings in general.



Reading maps

Most maps are drawn so that north is up. Whenever this is not the case, you should expect the map to feature a compass point indicating the direction of north.


A map must have a scale. You can measure the distance between two points on the map with a ruler, then use the scale to work out what the distance between the corresponding two points in the real world is, via the following procedure:


PROCEDURE

1.
Measure the length of the given scale with a ruler.
2.
Measure the distance between the two points on the map you wish to compute the real distance between with a ruler.
3.
DIvide the distance you measured in step 222. by the length of the scale.​
4.
Multiply the number computed in step 333. by the length written on the scale.​


Example 1

On the following map, what is the real distance between the points AAA​ and BBB?

Maths; Angles and geometry; KS4 Year 10; Maps and scale drawings


Use your ruler to measure the length of one of the boxes. The scale given in the bottom right is one box length long.


Measure the distance between AAA​ and BBB on your screen with a ruler, and divide it by the length of one of the boxes on your screen (which you just measured), to get that the distance corresponds to 555 box lengths​.

(Alternatively, you could notice that the point BBB is 333 box lengths to the right, and 444 box lengths up, from AAA.  Using Pythagoras' theorem, the distance between AAA and BBB on the map is 32+42=5\sqrt{3^2 + 4^2} = 532+42​=5 box lengths.)


Using the scale, compute that the real distance between the points AAA and BBB must be:


5×10m=50m5 \times 10m = 50m5×10m=50m​​


Therefore, the real distance between the points AAA and BBB is 50m‾\underline{50m}50m​.


​

Scales as a ratio

Scales can be given as a ratio. Suppose in example 111, you measured one box length to be 1cm1cm1cm. There are 10×100=100010 \times 100 = 100010×100=1000​ centimetres in 10m10m10m. So, any distance you measured on the map with your ruler would need to be multiplied by 100010001000 to give you the corresponding distance in the real world. This is a scale of 1:10001:10001:1000​.


In general, the most simplified form of the ratio:


Measured length of scale on map ::: Length written on scale


If the scale given as a ratio. The scale factor is:


(((​Length written on scale))) ÷\div÷ (((Measured length of scale on map)))​


This is what you multiply the distances you measure on the map by to find the corresponding real world distance.



Scale drawings

Drawings can come equipped with a scale too, and all of the above holds true for drawings the same way it does for maps, including the procedure described for computing real distances between points - just replace the word "map" with drawing.


You might be asked to compute the scale factor of a drawing, to compute the true size of an object from a drawing with a given scale, or you could be asked to produce scale drawings given a scale factor and measurements.


Example 2

The following sketch of a house comes equipped with a scale. How tall is the house in metres? Suppose you measure the length of the scale to be 2cm2cm2cm. What is the scale factor of the drawing?

Maths; Angles and geometry; KS4 Year 10; Maps and scale drawings


The house is five blocks tall, and each block length corresponds to a real distance of 130cm130cm130cm, so the real height of the house is:


130cm×5=650cm=6.5m\begin{aligned}130cm \times 5 &= 650cm \\&= 6.5m\end{aligned}130cm×5​=650cm=6.5m​​​

​

If you measure the length of the scale to be 2cm2cm2cm, then the scale factor is given by (((length written on scale)))​ ÷\div÷​ (((​measured length of scale)))​, which is:


​130cm2cm=65\dfrac{130cm}{2cm} = 652cm130cm​=65​​

And as a ratio, the scale is 1:651:651:65.


Therefore, the house is 6.5m‾\underline{6.5m}6.5m​ tall, and the scale factor of the drawing is 65‾\underline{65}65​.



Read more

Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Scale factor problems

Scale factor problems

Maps and scale drawings

Maps and scale drawings

Jump Ahead

Score 80% to jump directly to the final unit.

This is the current lesson and goal (target) of the path

Maps and scale drawings

Maps and scale drawings

Final Test

Test reviewing all units to claim a reward planet.

Create an account to complete the exercises

FAQs - Frequently Asked Questions

Do maps come with a scale?

A map must have a scale.

Why is map scale important?

You can measure the distance between two points on the map with a ruler, then use the scale to work out what the distance between the corresponding two points in the real world is.

What are the scales of a map?

You can use the scale to compute the true dimensions of the map.

Beta

© 2020 - 2025 evulpo AG