Stage 1 Mathematics

Functions and Graphs

• Direct proportion
• Inverse proportion
• Rational Functions
• Testing if a relationship is a function
• Checking if an equation represents a function
• Function notation
• Composite functions
• Range and domain
• Sign diagrams

Polynomials

Quadratics​

• Factorising by sum and product {part 1}
• Factorising by sum and product {part 2}
• Factorising by cross method {part 1}
• Factorising by cross method {part 2}
• Solving quadratics: by factorisation
• Solving quadratics: by completing the square
• Solving quadratics: the quadratic formula
• The discriminant
• Sketching quadratics from factorised form
• Sketching quadratics from vertex form {part 1}
• Sketching quadratics from vertex form {part 2}
• Sketching quadratics by completing the square
• Sketching quadratics from general form
• Finding the quadratic function from its graph {part 1}
• Finding the quadratic function from its graph {part 2}
• Finding the quadratic function from its graph {part 3}
• Finding where functions meet

Student Questions

• Sketching quadratics by completing the square
• Where functions meet

Cubics and Quartics

• Polynomial equality (equating coefficients)
• Factorising cubic polynomials
• Solving cubic polynomials
• Sketching cubic functions
• Finding cubic functions from its graph
• Sketching quartic functions
• ​Finding quartic functions from its graph

Trigonometry

• Finding the area of non right-angled triangles using A = 1/2 abSinC
• The Cosine rule
• The Sine rule: finding sides
• The Sine rule: finding angles
• Properties of the Sine function
• Properties of the Cosine function
• The Tangent as y = sinx/cosx

Growth and Decay

Index Law Review

• ​Multiplying indices
• Dividing indices
• Power of a power
• The zero power
• Expanding quotients
• What are negative indices
• Simplifying with negative indices
• Rational indices

Surds Review

• Simplifying surds
• Operating with surds
• Division by surds

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Expansion & Factorisation With Indices

• Expansion with rational indices
• Factorisation with rational indices (1/2)
• Factorisation with rational indices (2/2)
• Exponential equations (equating indices)
• Solving exponential equations (factorising example)​

Exponential Growth

• Introduction to exponential growth
• Writing numerical exponential growth expressions
• Interpreting values of exponential expressions
• Writing algebraic exponential growth expressions
• Exponential growth worded problem with TI-84 Plus CE

​Exponential Decay

• Introduction to exponential decay
• ​Exponential decay worded problem

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Logarithms

• Introduction to logarithms
• Evaluating logarithms
• Introducing the logarithm product and quotient laws
• Introducing the logarithm power law
• Simplifying using the product and quotient laws
• Simplifying using the power law​

The Natural Exponential & Logarithm

• What is e?
• The natural logarithm

Solving Exponential Equations

• Solving exponential equations using logarithms
• Solving exponential growth problem using logarithms

Introduction to Calculus

PLEASE NOTE: While there are some videos below available now, others are still being made. Please be patient and check back later. Thanks.
Introduction to Differential Calculus

• ​Introducing the concept of instantaneous rate of change
• Estimating the instantaneous rate of change
• Limits
• Gradient of a tangent at a particular point
• What is a derivative function?
• Finding the derivative function from first principles

Properties and Application of Derivatives

• Simple rules of differentiation
• Finding equations of linear lines (gradient-point form)
• Finding the equation of a tangent
• Finding the equation of a tangent (from an external point)
• Finding the equation of a normal
• Increasing and decreasing functions
• Stationary points

Kinematics

• Displacement, velocity and acceleration

Optimisation

• Optimisation with differential calculus

Counting and Binomial Expansion

• Videos coming soon