# Videos

###### Author and programmer: Ron Barrow

Videos for iPods, iPhones and other hand-held devices

**Foreword** The videos marked with 2 asterisks(**) are embedded videos from my youTube channel. (NB They are still my Copyright). The videos in Flash format are marked with an asterisk (*), and require your browser to have the Flash plugin. Those with no asterisk are in Windows .wmv format, which does not display well in some browsers (eg. Firefox) unless you have a WMV plugin.

### Advanced Level (16 to 19 years)

#### Pure (core) mathematics

**Geometric Series - Proof of the Sum Formula for the First n Terms new!

**Arithmetic Series - Proof of the Sum Formula for the First n Terms

**Surds 5 - Rationalising the Denominator 2 - division by more complex surds

*Algebraic Long Division 1 - cubic expression divided by a linear one

*Quadratic sequences - nth term - in the form a`n`² + b`n` + c

*Cubic sequences - nth term - in the form a`n`³ + b`n`² + c`n` + d

#### Decision mathematics

*Planar graphs and Euler's relationship - demonstrated with examples

*Planarity proofs - that K5 and K3,3 are not planar

*The Bubble Sort Algorithm - with a step-by-step example

*The Shuttle Sort Algorithm - with a step-by-step example

*Chinese Postman Algorithm - some worked examples and explanations

### Years 11 to 16

#### Number, Algebra and Graphs

*Percentage Multipliers 1 - percentage changes as a multiplying number

*Direct and inverse proportionality - with some worked examples

*Factors of Numbers - all the factors of a number

*Prime Numbers 1 - The Sieve of Eratosthenes - primes less than 100

*Prime Factors 1 - number as products of prime factors

*Prime Factors 2 - HCF - prime factors for the Highest Common Factor

*Prime Factors 3 - LCM - prime factors for the Lowest Common Multiple

*Reciprocals 1 - finding the reciprocal of a number

Multiplying by Fractions 1 - some simple examples

Dividing Numbers by Fractions - some simple examples

Converting Recurring Decimals to Fractions 1

**Indices 1 - Multiplying

**Indices 2 - Dividing

**Indices 3 - Powers of powers

**Indices 4 - Zero and negative powers

**Upper and Lower Bounds 1 - of numbers to a given degree of accuracy

Squaring Brackets - expressions like (`x` - 3)²

Making Formulae 1

Making Formulae 2

Making Formulae 3

Equations 1

Equations 2

*Simultaneous (systems of) equations 1

*Simultaneous (systems of) equations 1a

*Simultaneous (systems of) equations 2

*nth Term of a Linear Sequence

*Trial and Improvement 1

*Inequalities - Regions of Graphs

*Straight Line Graphs 1 - Gradients

*Straight Line Graphs 2 - Gradients and Equations

*Straight Line Graphs 3 - Intercepts and Equations

#### Higher Number, Algebra and Graphs

**Indices 5 - Fractional powers

**Indices 6 - Solving exponential equations

*Direct and inverse proportionality 2

*Upper and lower bounds 2 - calculations - addition, division, etc.

**Surds 1 - What are surds? - introduction to surd (radical) expressions

**Surds 2 - Some basic rules - adding, multiplying, etc.

**Surds 3 - Simplifying 1 - changing to conventional simplest form

**Surds 4 - Simplifying 2 - Rationalising the Denominator 1 - simple division

*Equations of parallel and perpendicular lines 1 - a worked example

*Equations of parallel and perpendicular lines 2 - a worked example

Completing the Square 1 - an algebraic method

*Simplifying Algebraic Fractions 2 - factorising and cancelling

*Algebraic Fractions 3 - Equations

*Changing the subject when it appears twice

*Simultaneous (systems of) equations with quadratic terms 1

*Simultaneous (systems) equations with quadratic terms 2

#### Shape, Space and Measure

*Areas of Trapeziums - building a formula

*Constructions - Bisecting Angles

*Constructions - Perpendicular Bisectors

*3 More Constructions - drawing 60°, perpendiculars from and to a line

**Reflections 1 - drawing the image, finding the mirror line

**Rotations 1 - drawing the image, finding the centre

**Translations 1 - using vector notation, combining shifts

*Symmetry 1 - combining reflections and rotations

**Circles and Isosceles Triangles - triangles with two radii

**Angles in Cyclic Quadrilaterals - opposite angles

Cyclic Quadrilaterals in Reverse - which shapes are cyclic?

Angles in Cyclic Quadrilaterals - Proof - using algebra

**Angle in a Semicircle - demonstration

*Angle in a Semicircle ... Proof - using algebra

**Angles in the Same Segment - demonstration

**Angle at the Centre - is twice the angle at the circumference

*Angle at the Centre ... Proof - using algebra

**Circles and Tangents - 2 Theorems - demonstration

**Angle in the Alternate Segment ...

*Circles - Sector Areas and Arc Lengths - demonstrations

*Circles - Triangle and Segment Areas - demonstrations

*Loci 1

*Loci 2

*Similar Triangles 1 - ratios of sides

*Similar Shapes - Lengths and Distances - scale factors

*Similar Shapes - Areas - area factors

**Congruent Triangles 1 - Introduction

**Congruent Triangles 2 - SSS - with examples

**Congruent Triangles 3 - SAS - with examples

**Congruent Triangles 4 - AAS - with examples

**Congruent Triangles 5 - RHS - with examples

*Lengths and angles inside cuboids

#### Probability and Data Handling

*Probability - tree diagrams 1 - independent events

*Tree diagrams 2 - dependent events

Estimating the Mean of Grouped Data - a worked example

**Cumulative Frequency Diagrams 1 - Introduction

**Cumulative Frequency Diagrams 2 - Median and Quartiles

**Cumulative Frequency Diagrams 3 - Boxplots

**Frequency Polygons 1 - drawing and interpreting

**Moving Averages 1 - drawing the graphs

**Moving Averages 2 - extrapolation of a trend line

*Histograms 1 - Drawing Histograms - using frequency densities

*Histograms 2 - Interpreting Histograms - getting the data back

*Histograms 3 - A Common Type of Question - exam practice