**Bearings**are a way of describing and using**directions**as**angles**- They are specifically defined for use in navigation because they give a precise
**location**and/or**direction**

- There are
**three rules**which must be followed every time a bearing is defined**They are measured from the North direction**North is usually straight up in terms of a scale drawing or map drawn on a piece of paper and should be shown somewhere on the diagram

**They are measured clockwise (from North)**If you get muddled up look at a clock on the wall**The angle should always be written (said) with 3 figures**So angles under 100° should have zero(es) to fill in the missing figures, eg 059, 008

Notice also that the degree symbols are not usually included when talking about bearings

- Bearings questions will normally involve the use of Pythagoras or trigonometry to find missing distances (lengths) and directions (angles) within navigation questions
- You should always
**draw a diagram**

- You should always
- There may be a scale given or you may need to consider using a scale
- Some questions may involve the use of angle facts to find the missing directions
- To answer a question involving
**drawing bearings**the following steps may help:- STEP 1: Draw a diagram adding in any points and distances you have been given
- STEP 2: Draw a North line (arrow pointing vertically up) at the point you wish to measure the bearing
**from**- If you are given the bearing
**from A to B**draw the North line at**A**

- If you are given the bearing
- STEP 3: Measure the angle of the bearing given
**from the North line**in the**clockwise direction** - STEP 4:

- You will likely then need to use Pythagoras’s theorem or trigonometry to calculate another distance

**Make sure you have all the equipment you need for your maths exams, along with a spare pen and pencil****A rubber and pencil sharpener can be essential on these questions as they are all about accuracy****Make sure you have compasses that aren’t loose and wobbly****Make sure you can see and read the markings on your ruler and protractor**

**Always**draw a big, clear diagram and annotate it, be especially careful to label the angles in the correct places!

A ship sets sail from the point P, as shown on the map below.

It sails on a bearing of 105 until it reaches the point Q, 70 km away. The ship then changes path and sails on a bearing of 065 for a further 35km, where its journey finishes.

Show on the map below the point Q and the final position of the ship.

Draw in a north line at the point P.

Measure an angle of 105° clockwise from the north line.

Make sure you are accurate, carefully make a small but visible mark on the map.

Draw a line from P through the mark you have made. Make this line longer than you expect to need it to be so that you can easily measure along it accurately.

Use the scale given on the map (1 cm = 10 km) to work out the number of cm that would represent 70 km.

70 km = 70 ÷ 10 = 7 cm

Accurately measure 7 cm from the point P along the line and make a clear mark on the line.

This is the point Q.

A bearing of 065 means 65° clockwise from the North.

First, draw a north line at the point Q, then carefully measure an angle of 65° clockwise from this line. Make a mark and then draw a line from Q through this mark.

Using the scale, find the distance in cm along the line you will need to measure.

35 km = 35 ÷ 10 = 3.5 cm

Accurately measure 3.5 cm from the point Q along this new line and make a clear mark on the line.

This is the final position of the ship.

- Mathematical Operations
- Negative Numbers
- Money Calculations
- Number Operations
- Related Calculations
- Counting Principles

- Types of Number
- Prime Factor Decomposition
- HCF & LCM

- Powers, Roots & Indices
- Standard Form

- Basic Fractions
- Operations with Fractions

- Basic Percentages
- Working with Percentages

- Interest & Depreciation
- Exponential Growth & Decay

- Converting between FDP
- Converting between FDP

- Rounding & Estimation
- Bounds

- Simplifying Surds
- Rationalising Denominators

- Using a Calculator

- Algebraic Notation & Vocabulary
- Algebra Basics

- Algebraic Roots & Indices

- Expanding Single Brackets
- Expanding Multiple Brackets

- Factorising
- Factorising Quadratics
- Quadratics Factorising Methods

- Completing the Square

- Rearranging Formulae

- Algebraic Proof

- Solving Linear Equations

- Solving Quadratic Equations
- Quadratic Equation Methods

- Simultaneous Equations

- Iteration

- Forming Equations
- Equations & Problem Solving

- Functions Toolkit
- Composite & Inverse Functions

- Coordinates
- Coordinate Geometry

- Straight Line Graphs (y = mx + c)
- Parallel & Perpendicular Lines

- Types of Graphs
- Graphical Solutions
- Trig Graphs

- Equation of a Circle
- Equation of a Tangents

- Finding Gradients of Tangents
- Finding Areas under Graphs

- Distance-Time & Speed-Time Graphs
- Conversion Graphs
- Rates of Change of Graphs

- Solving Linear Inequalities
- Conversion Graphs
- Solving Quadratic Inequalities

- Graphing Inequalities

- Reflections of Graphs

- Introduction to Sequences
- Types of Sequences
- Linear Sequences
- Quadratic Sequences

- Simple Ratio
- Working with Proportion

- Ratios & FDP
- Multiple Ratios

- Direct & Inverse Proportion

- Time
- Unit Conversions
- Compound Measures

- Symmetry
- 2D & 3D Shapes
- Plans & Elevations

- Basic Angle Properties
- Angles in Polygons
- Angles in Parallel Lines

- Bearings
- Scale & Maps
- Constructing Triangles
- Constructions & Loci

- Angles at Centre & Semicircles
- Chords & Tangents
- Cyclic Quadrilaterals
- Segment Theorems
- Circle Theorem Proofs

- Area & Perimeter
- Problem Solving with Areas

- Area & Circumference of Circles
- Arcs & Sectors

- Volume
- Surface Area

- Congruence
- Similarity
- Geometrical Proof

- Similar Area & Volumes

- Pythagoras Theorem
- Right-Angled Trigonometry
- Exact Trig Values

- Sine & Cosine Rules
- Area of a Triangle
- Applications of Trigonomet

- 3D Pythagoras & Trigonometry

- Introduction to Vectors
- Working with Vectors

- Translations
- Reflections
- Rotations
- Enlargements
- Combination of Transformations

- Basic Probability
- Relative & Expected Frequency

- Two Way Tables
- Frequency Trees
- Set Notation & Venn Diagrams

- Tree Diagrams

- Combined Probability
- Conditional Probability
- Combined Conditional Probabilities

- Mean, Median & Mode
- Averages from Tables
- Range & Quartiles
- Comparing Distributions
- Population & Sampling

- Bar Charts & Pictograms
- Pie Charts
- Time Series Graphs
- Working with Statistical Diagrams

- Histograms

- Cumulative Frequency Diagrams
- Box Plots

- Scatter Graphs

Menu