4.2.4

Shortest Distance from a Point to a Line

Test yourself on Shortest Distance from a Point to a Line

Test your knowledge with free interactive questions on Seneca — used by over 10 million students.

Shortest Distance from a Point to a Line

The shortest distance from a point to a straight line is always the perpendicular distance. Here's how to identify it:

Perpendicular Distance

Perpendicular Distance

The shortest distance from a point to a line is always the perpendicular line.
This means the line connecting the point to the original line must form exactly a $90^\circ$ angle.

Example 1

Example 1

Which path from point P to the line is the shortest?
- Identify the perpendicular path (the one forming a 90° angle).
- Compare the measurements. The perpendicular path is 4 cm, while the slanted path is 5 cm.
- The perpendicular path is always the shortest distance.

1

Number

1.1

Place Value & Ordering

1.1.1Ordering Integers & Decimals 1.1.2Equal Symbols 1.1.3Place Value

1.2

Numerical Operations

1.2.1Adding Integers 1.2.2Subtracting Integers 1.2.3Multiplying Integers 1.2.4Dividing Integers 1.2.5Adding & Subtracting Decimals 1.2.6Multiplying Decimals 1.2.7Dividing Decimals 1.2.8Adding & Subtracting Negative Numbers 1.2.9Multiplying & Dividing Negative Numbers 1.2.10Multiplying by Powers of Ten 1.2.11Dividing by Powers of Ten

1.3

Fractions

1.3.1Writing Fractions 1.3.2Constructing Fractions 1.3.3Simplifying Fractions 1.3.4Ordering Fractions 1.3.5Fractions & Recurring Decimals 1.3.6Mixed Numbers & Improper Fractions

1.4

Numerical Operations on Fractions

1.4.1Adding & Subtracting Fractions 1.4.2Adding & Subtracting Mixed Numbers 1.4.3Multiplying Fractions 1.4.4Multiplying Mixed Numbers 1.4.5Reciprocals 1.4.6Dividing Fractions 1.4.7Dividing Mixed Numbers (sample)1.4.8Dividing Mixed Numbers

1.5

Roots & Powers

1.5.1Integer Powers 1.5.2Roots 1.5.3Estimating Powers & Roots 1.5.4Fractional Indices (1/n)1.5.5Fractional Indices (m/n)1.5.6Laws of Indices (Multiplication)1.5.7Laws of Indices (Division)

1.6

Structure of Calculations

1.6.1Order of Operations (BIDMAS)

1.7

Numerical Skills

1.7.1Using a Calculator - Powers, Roots & Fractions 1.7.2Using a Calculator - Trigonometric Functions

1.8

Factors & Multiples

1.8.1Finding Factors 1.8.2Finding Multiples

1.9

Systematic Listing

1.9.1Systematic Listing

1.10

Surds

1.10.1Multiplying & Dividing Surds 1.10.2Simplifying Surds 1.10.3Expanding Expressions With Surds 1.10.4Rationalising the Denominator

1.11

Standard Form

1.11.1Converting to Standard Form (Positive Powers)1.11.2Converting to Standard Form (Negative Powers)1.11.3Converting From Standard Form (Positive Powers)1.11.4Converting From Standard Form (Negative Powers)1.11.5Adding & Subtracting Standard Form 1.11.6Multiplying & Dividing Standard Form 1.11.7Standard Form on a Calculator

1.12

Fractions, Decimals & Percentages

1.12.1Converting Fractions, Decimals & Percentages 1.12.2Converting Recurring Decimals 1.12.3Numbers as Percentages 1.12.4Fractions of Amounts

1.13

Percentage Change

1.13.1Percentages of Amounts (Calculator)1.13.2Percentages of Amounts (No Calculator)1.13.3Percentage Change 1.13.4Original Values After Percentage Change 1.13.5Growth & Decay Using Multipliers

1.14

Rounding & Estimation

1.14.1Rounding Integers 1.14.2Estimating Calculations 1.14.3Rounding Decimals 1.14.4Rounding With Significant Figures

1.15

Bounds & Accuracy

1.15.1Finding Error Intervals 1.15.2Upper & Lower Bounds 1.15.3Truncating Decimals 1.15.4Error Intervals From Truncation

1.16

Using Numbers

1.16.1Highest Common Factor 1.16.2Lowest Common Multiple 1.16.3Prime Numbers

2

Algebra

2.1

Algebraic Notation

2.1.1Using Algebraic Notation

2.2

Substitution & Simplification

2.2.1Substituting into Expressions 2.2.2Substituting into Real-Life Formulae 2.2.3Simplifying Expressions by Collecting Like Terms

2.3

Brackets

2.3.1Expanding Single Brackets 2.3.2Expanding & Simplifying with Single Brackets 2.3.3Expanding Double Brackets 2.3.4Expanding Multiple Brackets 2.3.5Factorising into One Bracket 2.3.6Factorising Quadratics of the Form x^2 + bx + c 2.3.7Factorising Quadratics - AC Method 2.3.8Factorising Quadratics - Middle Term Method 2.3.9Factorising the Difference of Two Squares 2.3.10Completing the Square

2.4

Algebraic Fractions

2.4.1Simplifying Algebraic Fractions by Cancelling 2.4.2Simplifying Algebraic Fractions by Factorising 2.4.3Operations with Algebraic Fractions

2.5

Rearranging

2.5.1Changing the Subject 2.5.2Changing the Subject (Repeated Subject)

2.6

Functions

2.6.1Finding the Input of a Function 2.6.2Finding Composite Functions 2.6.3Inverse Functions

2.7

Solving Linear Equations

2.7.1Solving Linear Equations (One Step)2.7.2Solving Linear Equations (Multi-Step)2.7.3Linear Equations (Unknown Both Sides)2.7.4Solving Equations: (Unknown Denominator)2.7.5Forming & Solving Linear Equations

2.8

Inequalities

2.8.1Representing Inequalities on a Number Line 2.8.2Solving Linear Inequalities 2.8.3Linear Inequalities with Unknowns on Both Sides 2.8.4Graphs of Linear Inequalities 2.8.5Solving Quadratic Inequalities

2.9

Solving Quadratic Equations

2.9.1Solving Quadratics by Factorising 2.9.2Solving Quadratics Using the Formula

2.10

Simultaneous Equations

2.10.1Solving Simultaneous Equations (Elimination)2.10.2Solving Simultaneous Linear & Quadratic Equations 2.10.3Solving Simultaneous Equations Graphically

2.11

Iteration

2.11.1Iterative Formulae 2.11.2Solutions Using Iteration

2.12

Sequences

2.12.1Term-to-Term Rules 2.12.2Position-to-Term Rules 2.12.3Finding the Nth Term (Linear Sequences)2.12.4Finding the Nth Term (Quadratic Sequences)2.12.5Quadratic Sequence Formulae 2.12.6Simple Geometric Progressions

2.13

Coordinates

2.13.1Coordinate Reading & Plotting 2.13.2Midpoints of Line Segments

2.14

Linear Graphs

2.14.1Plotting Straight Line Graphs 2.14.2Equations of Straight Lines 2.14.3Finding Line Equation from Point & Gradient 2.14.4Finding Line Equation from Two Points 2.14.5Parallel Line Equations 2.14.6Perpendicular Line Equations

2.15

Quadratic Graphs

2.15.1Plotting Quadratics 2.15.2Interpreting & Sketching Quadratics 2.15.3Finding Turning Points by Completing the Square

2.16

More Non-Linear Graphs

2.16.1Cubic Graphs 2.16.2Trigonometric & Exponential Functions 2.16.3Equations of Circles 2.16.4Equations of Tangents

2.17

Graph Transformations

2.17.1Translating Graphs 2.17.2Reflecting Graphs 2.17.3Transforming Graphs

2.18

Real-Life Graphs

2.18.1Distance-Time Graphs 2.18.2Acceleration from Velocity-Time Graphs 2.18.3Distance from Velocity-Time Graphs

3

Ratio

3.1

Unit Conversions

3.1.1Converting Units of Time 3.1.2Metric Conversions 3.1.3Converting Units of Area & Volume

3.2

Compound Units

3.2.1Calculating Speed 3.2.2Best Buy & Unit Pricing 3.2.3Density, Mass & Volume 3.2.4Pressure, Force & Area

3.3

Ratio Fundamentals

3.3.1Ratio Notation & Simplification 3.3.2Ratios as Fractions & Linear Equations 3.3.3Sharing in a Ratio 3.3.4Proportion Problems

3.4

Advanced Ratio & Scale

3.4.1Map Scales & Real Distances

3.5

Proportion

3.5.1Currency Conversions 3.5.2Direct & Inverse Proportion 3.5.3Graphs of Direct & Inverse Proportion

3.6

Algebraic Proportion

3.6.1Direct Proportion Equations 3.6.2Inverse Proportion Equations 3.6.3Direct Proportion with Powers & Roots 3.6.4Inverse Proportion with Powers & Roots

3.7

Percentages & Growth

3.7.1Compound Interest & Depreciation

3.8

Manipulating Ratios

3.8.1Differences in Ratios 3.8.2Fractions in Ratios

3.9

Percentage & Interest

3.9.1Simple Interest

4

Geometry

4.1

Area & Perimeter

4.1.1Perimeter of Simple Shapes 4.1.2Perimeter of Compound Shapes 4.1.3Area of Triangles 4.1.4Area of Rectangles & Parallelograms 4.1.5Area of Trapezia 4.1.6Area of Compound Shapes 4.1.7Area of Shapes Involving Triangles

4.2

Properties of Shapes

4.2.1Properties of Lines 4.2.2Symmetry 4.2.3Rotational Symmetry 4.2.4Shortest Distance from a Point to a Line 4.2.5Properties of 3D Shapes 4.2.6Cross Section

4.3

Angles

4.3.1Classification of Angles 4.3.2Angles on a Line & Around a Point 4.3.3Combining Angle Facts in Triangles 4.3.4Angles on Parallel Lines 4.3.5Interior & Exterior Angles in Polygons

4.4

Trigonometry

4.4.1Sides in Right-Angled Triangles 4.4.2Angles in Right-Angled Triangles 4.4.3Trigonometric Graphs 4.4.4Exact Values of Trigonometric Ratios 4.4.5Trigonometry in 3D Shapes 4.4.6Using the Sine Rule 4.4.7Using the Cosine Rule 4.4.8Area of a Triangle Using Sine

4.5

Similarity & Congruence

4.5.1Congruent Shapes 4.5.2Length Scale Factors in Similar Shapes 4.5.3Area & Volume Scale Factors

4.6

Circle Geometry

4.6.1Identifying Parts of a Circle 4.6.2Calculating Circumference 4.6.3Calculating Area of a Circle 4.6.4Calculating Arc Lengths 4.6.5Calculating Area of Sectors

4.7

Circle Theorems

4.7.1Standard Circle Theorems 4.7.2Cyclic Quadrilaterals & Segment Theorems 4.7.3Chord & Tangent Properties

4.8

Pythagoras

4.8.1Pythagoras' Theorem in 2D 4.8.2Pythagoras’ Theorem in 3D

4.9

3D Representations

4.9.1Nets of 3D Shapes

4.10

Surface Area

4.10.1Surface Area of Cubes & Cuboids 4.10.2Surface Area of Prisms 4.10.3Surface Area of Cylinders 4.10.4Surface Area of Spheres & Cones 4.10.5Surface Area of Composite Solids

4.11

Volume

4.11.1Volume of Prisms 4.11.2Volume of Cylinders 4.11.3Volume of Frustums & Composite Solids

4.12

Vectors

4.12.1Vectors & Column Notation 4.12.2Operations with Column Vectors

4.13

Transformations

4.13.1Translation Using Vectors 4.13.2Rotations 4.13.3Reflections 4.13.4Enlargements & Positive Scale Factors 4.13.5Enlargements & Negative Scale Factors 4.13.6Combining Transformations

4.14

Scale Drawings

4.14.1Scale Diagrams

4.15

Bearings

4.16

Geometry Proof

4.16.1Geometric Proofs Using Vectors

4.17

Introduction to Geometry

4.17.1Geometry Basics 4.17.2Geometry Basics 2 4.17.3Bisectors & Perpendiculars 4.17.4Locus

4.18

Triangles & Quadrilaterals

4.18.1Quadrilaterals

4.19

Transformations

4.19.1Invariant Points

4.20

Measurements & Units

4.21

3D Shapes

4.21.1Types of 3D Shape 4.21.2Plans & Elevations 4.21.3Volume of a Cuboid 4.21.4Volume of a Sphere 4.21.5Volume of a Hemisphere 4.21.6Volume of a Cone 4.21.7Volume of a Pyramid

5

Probability

5.1

Single Events

5.1.1Writing Probabilities as Fractions 5.1.2Mutually Exclusive Events 5.1.3Expected Results

5.2

Combined Events

5.2.1Venn Diagrams 5.2.2Using Set Notation 5.2.3Using Set Notation 2 5.2.4Independent & Mutually Exclusive Events 5.2.5Frequency Trees 5.2.6Tree Diagrams (Independent)5.2.7Tree Diagrams (Dependent)

5.3

Experimental Probability

5.3.1Fairness and Bias 5.3.2Relative Frequency & Convergence

5.4

Counting Outcomes

5.4.1Product Rule for Counting

5.5

Conditional Probability

5.5.1Conditional Probability: Venn Diagrams 5.5.2Conditional Probability: Tree Diagrams 5.5.3Conditional Probability from Tables

5.6

Representing Probabilities

5.6.1Probability Scale 5.6.2Sample Space Diagrams

5.7

Probability Calculations

5.7.1Complex Tree Diagrams

6

Statistics

6.1

Averages & Range

6.1.1Range 6.1.2Median 6.1.3Mode 6.1.4Mean 6.1.5Averages from Frequency Tables 6.1.6Interpreting Two-Way Tables & Frequency Tables

6.2

Bar Charts

6.2.1Bar Charts

6.3

Scatter Graphs

6.3.1Scatter Graphs 6.3.2Lines of Best Fit

6.4

Histograms

6.4.1Interpreting Histograms 6.4.2Drawing Histograms

6.5

Frequency Polygons

6.5.1Frequency Polygons

6.6

Cumulative Frequency

6.6.1Drawing Cumulative Frequency 6.6.2Interpreting Cumulative Frequency

6.7

Box Plots

6.7.1Interpreting Box Plots & Comparing Distributions

6.8

Collecting & Presenting Data

6.8.1Types of Data 6.8.2Designing Questionnaires 6.8.3Capture-Recapture

6.9

Charts & Diagrams

6.9.1Pie Charts 6.9.2Stem & Leaf Diagrams 6.9.3Back to Back Stem & Leaf Diagrams 6.9.4Pictograms 6.9.5Time Series Graphs 6.9.6Correlation & Causation

Jump to other topics

1

Number

1.1

Place Value & Ordering

1.1.1Ordering Integers & Decimals 1.1.2Equal Symbols 1.1.3Place Value

1.2

Numerical Operations

1.2.1Adding Integers 1.2.2Subtracting Integers 1.2.3Multiplying Integers 1.2.4Dividing Integers 1.2.5Adding & Subtracting Decimals 1.2.6Multiplying Decimals 1.2.7Dividing Decimals 1.2.8Adding & Subtracting Negative Numbers 1.2.9Multiplying & Dividing Negative Numbers 1.2.10Multiplying by Powers of Ten 1.2.11Dividing by Powers of Ten

1.3

Fractions

1.3.1Writing Fractions 1.3.2Constructing Fractions 1.3.3Simplifying Fractions 1.3.4Ordering Fractions 1.3.5Fractions & Recurring Decimals 1.3.6Mixed Numbers & Improper Fractions

1.4

Numerical Operations on Fractions

1.4.1Adding & Subtracting Fractions 1.4.2Adding & Subtracting Mixed Numbers 1.4.3Multiplying Fractions 1.4.4Multiplying Mixed Numbers 1.4.5Reciprocals 1.4.6Dividing Fractions 1.4.7Dividing Mixed Numbers (sample)1.4.8Dividing Mixed Numbers

1.5

Roots & Powers

1.5.1Integer Powers 1.5.2Roots 1.5.3Estimating Powers & Roots 1.5.4Fractional Indices (1/n)1.5.5Fractional Indices (m/n)1.5.6Laws of Indices (Multiplication)1.5.7Laws of Indices (Division)

1.6

Structure of Calculations

1.6.1Order of Operations (BIDMAS)

1.7

Numerical Skills

1.7.1Using a Calculator - Powers, Roots & Fractions 1.7.2Using a Calculator - Trigonometric Functions

1.8

Factors & Multiples

1.8.1Finding Factors 1.8.2Finding Multiples

1.9

Systematic Listing

1.9.1Systematic Listing

1.10

Surds

1.10.1Multiplying & Dividing Surds 1.10.2Simplifying Surds 1.10.3Expanding Expressions With Surds 1.10.4Rationalising the Denominator

1.11

Standard Form

1.11.1Converting to Standard Form (Positive Powers)1.11.2Converting to Standard Form (Negative Powers)1.11.3Converting From Standard Form (Positive Powers)1.11.4Converting From Standard Form (Negative Powers)1.11.5Adding & Subtracting Standard Form 1.11.6Multiplying & Dividing Standard Form 1.11.7Standard Form on a Calculator

1.12

Fractions, Decimals & Percentages

1.12.1Converting Fractions, Decimals & Percentages 1.12.2Converting Recurring Decimals 1.12.3Numbers as Percentages 1.12.4Fractions of Amounts

1.13

Percentage Change

1.13.1Percentages of Amounts (Calculator)1.13.2Percentages of Amounts (No Calculator)1.13.3Percentage Change 1.13.4Original Values After Percentage Change 1.13.5Growth & Decay Using Multipliers

1.14

Rounding & Estimation

1.14.1Rounding Integers 1.14.2Estimating Calculations 1.14.3Rounding Decimals 1.14.4Rounding With Significant Figures

1.15

Bounds & Accuracy

1.15.1Finding Error Intervals 1.15.2Upper & Lower Bounds 1.15.3Truncating Decimals 1.15.4Error Intervals From Truncation

1.16

Using Numbers

1.16.1Highest Common Factor 1.16.2Lowest Common Multiple 1.16.3Prime Numbers

2

Algebra

2.1

Algebraic Notation

2.1.1Using Algebraic Notation

2.2

Substitution & Simplification

2.2.1Substituting into Expressions 2.2.2Substituting into Real-Life Formulae 2.2.3Simplifying Expressions by Collecting Like Terms

2.3

Brackets

2.3.1Expanding Single Brackets 2.3.2Expanding & Simplifying with Single Brackets 2.3.3Expanding Double Brackets 2.3.4Expanding Multiple Brackets 2.3.5Factorising into One Bracket 2.3.6Factorising Quadratics of the Form x^2 + bx + c 2.3.7Factorising Quadratics - AC Method 2.3.8Factorising Quadratics - Middle Term Method 2.3.9Factorising the Difference of Two Squares 2.3.10Completing the Square

2.4

Algebraic Fractions

2.4.1Simplifying Algebraic Fractions by Cancelling 2.4.2Simplifying Algebraic Fractions by Factorising 2.4.3Operations with Algebraic Fractions

2.5

Rearranging

2.5.1Changing the Subject 2.5.2Changing the Subject (Repeated Subject)

2.6

Functions

2.6.1Finding the Input of a Function 2.6.2Finding Composite Functions 2.6.3Inverse Functions

2.7

Solving Linear Equations

2.7.1Solving Linear Equations (One Step)2.7.2Solving Linear Equations (Multi-Step)2.7.3Linear Equations (Unknown Both Sides)2.7.4Solving Equations: (Unknown Denominator)2.7.5Forming & Solving Linear Equations

2.8

Inequalities

2.8.1Representing Inequalities on a Number Line 2.8.2Solving Linear Inequalities 2.8.3Linear Inequalities with Unknowns on Both Sides 2.8.4Graphs of Linear Inequalities 2.8.5Solving Quadratic Inequalities

2.9

Solving Quadratic Equations

2.9.1Solving Quadratics by Factorising 2.9.2Solving Quadratics Using the Formula

2.10

Simultaneous Equations

2.10.1Solving Simultaneous Equations (Elimination)2.10.2Solving Simultaneous Linear & Quadratic Equations 2.10.3Solving Simultaneous Equations Graphically

2.11

Iteration

2.11.1Iterative Formulae 2.11.2Solutions Using Iteration

2.12

Sequences

2.12.1Term-to-Term Rules 2.12.2Position-to-Term Rules 2.12.3Finding the Nth Term (Linear Sequences)2.12.4Finding the Nth Term (Quadratic Sequences)2.12.5Quadratic Sequence Formulae 2.12.6Simple Geometric Progressions

2.13

Coordinates

2.13.1Coordinate Reading & Plotting 2.13.2Midpoints of Line Segments

2.14

Linear Graphs

2.14.1Plotting Straight Line Graphs 2.14.2Equations of Straight Lines 2.14.3Finding Line Equation from Point & Gradient 2.14.4Finding Line Equation from Two Points 2.14.5Parallel Line Equations 2.14.6Perpendicular Line Equations

2.15

Quadratic Graphs

2.15.1Plotting Quadratics 2.15.2Interpreting & Sketching Quadratics 2.15.3Finding Turning Points by Completing the Square

2.16

More Non-Linear Graphs

2.16.1Cubic Graphs 2.16.2Trigonometric & Exponential Functions 2.16.3Equations of Circles 2.16.4Equations of Tangents

2.17

Graph Transformations

2.17.1Translating Graphs 2.17.2Reflecting Graphs 2.17.3Transforming Graphs

2.18

Real-Life Graphs

2.18.1Distance-Time Graphs 2.18.2Acceleration from Velocity-Time Graphs 2.18.3Distance from Velocity-Time Graphs

3

Ratio

3.1

Unit Conversions

3.1.1Converting Units of Time 3.1.2Metric Conversions 3.1.3Converting Units of Area & Volume

3.2

Compound Units

3.2.1Calculating Speed 3.2.2Best Buy & Unit Pricing 3.2.3Density, Mass & Volume 3.2.4Pressure, Force & Area

3.3

Ratio Fundamentals

3.3.1Ratio Notation & Simplification 3.3.2Ratios as Fractions & Linear Equations 3.3.3Sharing in a Ratio 3.3.4Proportion Problems

3.4

Advanced Ratio & Scale

3.4.1Map Scales & Real Distances

3.5

Proportion

3.5.1Currency Conversions 3.5.2Direct & Inverse Proportion 3.5.3Graphs of Direct & Inverse Proportion

3.6

Algebraic Proportion

3.6.1Direct Proportion Equations 3.6.2Inverse Proportion Equations 3.6.3Direct Proportion with Powers & Roots 3.6.4Inverse Proportion with Powers & Roots

3.7

Percentages & Growth

3.7.1Compound Interest & Depreciation

3.8

Manipulating Ratios

3.8.1Differences in Ratios 3.8.2Fractions in Ratios

3.9

Percentage & Interest

3.9.1Simple Interest

4

Geometry

4.1

Area & Perimeter

4.1.1Perimeter of Simple Shapes 4.1.2Perimeter of Compound Shapes 4.1.3Area of Triangles 4.1.4Area of Rectangles & Parallelograms 4.1.5Area of Trapezia 4.1.6Area of Compound Shapes 4.1.7Area of Shapes Involving Triangles

4.2

Properties of Shapes

4.2.1Properties of Lines 4.2.2Symmetry 4.2.3Rotational Symmetry 4.2.4Shortest Distance from a Point to a Line 4.2.5Properties of 3D Shapes 4.2.6Cross Section

4.3

Angles

4.3.1Classification of Angles 4.3.2Angles on a Line & Around a Point 4.3.3Combining Angle Facts in Triangles 4.3.4Angles on Parallel Lines 4.3.5Interior & Exterior Angles in Polygons

4.4

Trigonometry

4.4.1Sides in Right-Angled Triangles 4.4.2Angles in Right-Angled Triangles 4.4.3Trigonometric Graphs 4.4.4Exact Values of Trigonometric Ratios 4.4.5Trigonometry in 3D Shapes 4.4.6Using the Sine Rule 4.4.7Using the Cosine Rule 4.4.8Area of a Triangle Using Sine

4.5

Similarity & Congruence

4.5.1Congruent Shapes 4.5.2Length Scale Factors in Similar Shapes 4.5.3Area & Volume Scale Factors

4.6

Circle Geometry

4.6.1Identifying Parts of a Circle 4.6.2Calculating Circumference 4.6.3Calculating Area of a Circle 4.6.4Calculating Arc Lengths 4.6.5Calculating Area of Sectors

4.7

Circle Theorems

4.7.1Standard Circle Theorems 4.7.2Cyclic Quadrilaterals & Segment Theorems 4.7.3Chord & Tangent Properties

4.8

Pythagoras

4.8.1Pythagoras' Theorem in 2D 4.8.2Pythagoras’ Theorem in 3D

4.9

3D Representations

4.9.1Nets of 3D Shapes

4.10

Surface Area

4.10.1Surface Area of Cubes & Cuboids 4.10.2Surface Area of Prisms 4.10.3Surface Area of Cylinders 4.10.4Surface Area of Spheres & Cones 4.10.5Surface Area of Composite Solids

4.11

Volume

4.11.1Volume of Prisms 4.11.2Volume of Cylinders 4.11.3Volume of Frustums & Composite Solids

4.12

Vectors

4.12.1Vectors & Column Notation 4.12.2Operations with Column Vectors

4.13

Transformations

4.13.1Translation Using Vectors 4.13.2Rotations 4.13.3Reflections 4.13.4Enlargements & Positive Scale Factors 4.13.5Enlargements & Negative Scale Factors 4.13.6Combining Transformations

4.14

Scale Drawings

4.14.1Scale Diagrams

4.15

Bearings

4.16

Geometry Proof

4.16.1Geometric Proofs Using Vectors

4.17

Introduction to Geometry

4.17.1Geometry Basics 4.17.2Geometry Basics 2 4.17.3Bisectors & Perpendiculars 4.17.4Locus

4.18

Triangles & Quadrilaterals

4.18.1Quadrilaterals

4.19

Transformations

4.19.1Invariant Points

4.20

Measurements & Units

4.21

3D Shapes

4.21.1Types of 3D Shape 4.21.2Plans & Elevations 4.21.3Volume of a Cuboid 4.21.4Volume of a Sphere 4.21.5Volume of a Hemisphere 4.21.6Volume of a Cone 4.21.7Volume of a Pyramid

5

Probability

5.1

Single Events

5.1.1Writing Probabilities as Fractions 5.1.2Mutually Exclusive Events 5.1.3Expected Results

5.2

Combined Events

5.2.1Venn Diagrams 5.2.2Using Set Notation 5.2.3Using Set Notation 2 5.2.4Independent & Mutually Exclusive Events 5.2.5Frequency Trees 5.2.6Tree Diagrams (Independent)5.2.7Tree Diagrams (Dependent)

5.3

Experimental Probability

5.3.1Fairness and Bias 5.3.2Relative Frequency & Convergence

5.4

Counting Outcomes

5.4.1Product Rule for Counting

5.5

Conditional Probability

5.5.1Conditional Probability: Venn Diagrams 5.5.2Conditional Probability: Tree Diagrams 5.5.3Conditional Probability from Tables

5.6

Representing Probabilities

5.6.1Probability Scale 5.6.2Sample Space Diagrams

5.7

Probability Calculations

5.7.1Complex Tree Diagrams

6

Statistics

6.1

Averages & Range

6.1.1Range 6.1.2Median 6.1.3Mode 6.1.4Mean 6.1.5Averages from Frequency Tables 6.1.6Interpreting Two-Way Tables & Frequency Tables

6.2

Bar Charts

6.2.1Bar Charts

6.3

Scatter Graphs

6.3.1Scatter Graphs 6.3.2Lines of Best Fit

6.4

Histograms

6.4.1Interpreting Histograms 6.4.2Drawing Histograms

6.5

Frequency Polygons

6.5.1Frequency Polygons

6.6

Cumulative Frequency

6.6.1Drawing Cumulative Frequency 6.6.2Interpreting Cumulative Frequency

6.7

Box Plots

6.7.1Interpreting Box Plots & Comparing Distributions

6.8

Collecting & Presenting Data

6.8.1Types of Data 6.8.2Designing Questionnaires 6.8.3Capture-Recapture

6.9

Charts & Diagrams

6.9.1Pie Charts 6.9.2Stem & Leaf Diagrams 6.9.3Back to Back Stem & Leaf Diagrams 6.9.4Pictograms 6.9.5Time Series Graphs 6.9.6Correlation & Causation

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Rotational Symmetry

Properties of 3D Shapes