AS AQA Pure Maths Videos

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General

Formulae Booklet

Algebra and Functions

Indices

Practice question

Multiplication Indices

Rule 1 tutorial

Rule 1 practice questions

Rule 2 tutorial

Rule 2 practice questions

Division Indices

Practice questions

Negative Indices

Practice questions

Fractions with Negative Indices

Practice questions

Rational Indices

Practice questions

More Indices

Simplifying negative powers

Expressions terms in the form axⁿ

Surds

Addition and subtraction

Factorising

Quadratic Expressions

Difference of two square types

Trinomials by grouping

Trinomials by inspection 1

Trinomials by inspection 2

Trinomials by inspection 3

Trinomials by inspection 4

Trinomials by inspection 5

Trinomials by inspection 6

Trinomials by inspection 7

Completing the Square

Completing the square for x² terms

Completing the square for 2x², 3x², ... terms

Completing the square for negative terms

Sketching positive graphs

Sketching negative graphs

Quadratic Equations

Solve by factorising

Solve by completing the square

Solve by the quadratic formula

Solving in some function of x

Roots and discriminant

Common types of discriminant questions

Simultaneous Equations

Elimination method 1

Elimination method 2

Elimination method 3

Elimination method 4

Elimination method 5

Elimination method 6

Substitution method

Substitution method example

Inequalities

Rules for reversing the inequality sign

Solving linear inequalities

Solving double inequalities

Linear inequalities in two variables

Solving quadratic inequalities

Polynomials

Algebraic Long Division

Handling missing terms

Factor Theorem

The factor theorem

Showing that x-1 is a factor of a cubic polynomial

Factorising a cubic polynomial (Method 1)

Factorising a cubic polynomial (Method 2)

Solving a cubic equation

Finding constants in a polynomial given the factors

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Coordinate Geometry

Gradient of Straight Lines

Perpendicular lines

Straight Lines

Equation of a line in the form y = mx + c

Equation of a line in the form y - y₁ = m(x - x₁)

Distance between two points

Mid-point of a line segment

Equation of a parallel line

Equation of a perpendicular bisector

Intersection of Graphs

Two straight lines

Parabola and a straight line

Nature of intersection

Tangent to a curve

Hyperbola and straight line

Circles

Equation of a circle

Finding the centre and radius

Equation of a tangent

Equation of a circle through 3 points

Circle properties

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Algebra and Functions 2

Sketching Curves

Sketching quadratic curves

Sketching cubic curves

Sketching y = k/x curves

Graph Transformations

Basic graphs used in transformations

Translations

y = f(x + a) and y = f(x) + a

y = f(x + a): how it works

y = f(x) + a: how it works

Reflections

y= -f(x) and y=f(-x)

Stretches

y = af(x) and y = f(ax)

How y = af(x) stretches y = f(x) by scale factor a parallel to the y-axis

How y = f(ax) stretches y = f(x) by scale factor 1/a parallel to the x-axis

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Sequences and Series

Binomial Expansion

Binomial Expansion using the nCr method

Finding a certain term or coefficient in a Binomial expansion

Binomial expansion using Pascal's triangle method

Binomial expansion formula as an alternative to the nCr method

Rational powers

Partial fractions

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Trigonometry

Trigonometric Ratios

Simple way to learn the trig. ratios for 30, 45 and 60 degrees

Simple way to work out the trig. ratios for multiples of 30, 45 and 60 degrees

Graphs and Transformations

Trigonometric graphs

Translations parallel to the y-axis

Translations parallel to the x-axis

Reflection in the x-axis

Reflection in the y-axis

Stretch parallel to the y-axis: y = kf(x)

Stretch parallel to the x-axis: y = f(kx)

Combining transformations

Applications

Finding the area of a triangle with two sides and an included angle

Sine Rule

Finding the length of a side of a non-right triangle

Finding an angle of a non-right triangle

The Ambiguous Case

Cosine Rule

Finding the length of a side of a non-right triangle

Finding an angle of a non-right triangle

Trig. Equations and the Quadrant Rule

What is the Quadrant Rule/CAST diagram?

Using the Quadrant Rule to solve trig. equations

Solving trig. equations in various ranges

Solving trig. equations with multiple angles

Solving trig. equations that can be factorised 1

Solving trig. equations that can be factorised 2

Solving trig. equations that can be factorised 3

A common mistake

Identities

tanθ = sinθ/cosθ and sin²θ+cos²θ = 1

Proving trig. identities 1

Proving trig. identities 2

Proving trig. identities 3

cos(θ) = cos(-θ) and sin(θ) = -sin(-θ)

Solving trig. equations using identities 1

Solving trig. equations using identities 2

Solving trig. equations using identities 3

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Logarithmic and Exponential Functions

Logarithmic and Exponential Functions

What is an exponential function?

Logarithm Rules

Proofs of these rules

Equations

Logarithms - change of base

Logarithms - change of base (examples)

Simplifying and expanding equations

Solving equations where x is in the power

Solving equations that contain log terms

Solving equations that contain logs with different bases

Solving equations that contain exponential functions

Simultaneous equations 1

Simultaneous equations 2

Simultaneous equations 3

Solving inequalities

The Exponential Function e^x and Natural Log Functions

Exponential Functions

Transformations of exponential graphs

The natural log function: ln(x)

Modelling Curves of the form y=kxⁿ and y=ka^x

Modelling curves - converting to linear form

Modelling curves - converting to linear form - example 1

Modelling curves - converting to linear form - example 2

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Differentiation

Introduction

The gradient function dy/dx

Differentiation from 1st principles

Terms of the form axⁿ

Extending to root types

Extending to fractional types

The second derivative

Stationary Points

What are stationary points?

An example of finding a stationary point

Nature of a stationary point using 1st differential

Nature of a stationary point using 2nd differential

An example of finding stationary points and their nature

Applications of stationary points

Increasing and decreasing functions

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Integration

Introduction

Terms of the form axⁿ

Fractional and root type terms

Equation of Curves

Finding the equation of a curve given dy/dx

Using f'(x) notation

Definite Integration

What is a definite integral?

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Vectors

Vectors

What is a vector and a scalar quantity?

2D vector notation

Vector notation

2D position vectors

Position vectors

Equal and negative vectors

2D multiplying a vector by a scalar

Multiplying a vector by a scalar

2D addition and subtraction

2D addition and subtraction of vectors

Addition and subtraction of vectors

Magnitude of a 2 dimensional vector

Distance between 2 points (2D)

Magnitude of a 3 dimensional vector

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Proof

Proof identities

Proof by exhaustion and deduction

Proof by exhaustion and deduction - example

Proof using a counter example

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