# AS Maths Videos

# AS Pure Maths

## Proof

How to show that a specific expression is always even, regardless of the choice of integer.

Proof by Exhaustion that all square numbers are either a multiple of 4 or one more than a multiple of 4

Correcting student work and using a counterexample to disprove an algebraic statement.

## Algebra & Functions

Factorising and sketching a simple cubic with a little coordinate geometry thrown in.

Sketching a cubic then performing a transformation from an unknown constant.

Sketching and finding the discriminant of a quadratic in a completing the square style question.

Sketching a quadratic against a cubic and using algebra to find their intersection points.

Solving a linear equation by simplifying a surd and rationalising a denominator first.

## Coordinate Geometry

Testing for perpendicularity of straight lines.

Equation of a circle by finding centre and radius and equation of a tangent.

## Sequences & Series

## Trigonometry

Using a trigonometric identity to determine a cos value which is used in an application of the cosine rule.

Using trigonometric identities to transform one identity into a quadratic in cos then using this to solve a trigonometric equation.

Solution of a relatively simple trigonometric equation without using CAST or transforming a trigonometric graph.

Identifying possible values of an unknown constant by considering transformations to a sine curve.

## Exponentials & Logs

Correcting mistakes made in a typical student solution to a logs question.

A simple example of evaluating and differentiating a basic exponential function.

## Differentiation

The differentiation of a polynomial that requires reformatting before differentiating.

Using derivatives to show that a function is always decreasing.

Using differentiation to locate and classify the minimum of the cost of a journey.

Finding the derivative of a polynomial function and using it to find the equation of a normal at a given point on the function’s curve.

A simple example of evaluating and differentiating a basic exponential function.

## Integration

Integration question that requires equating coefficients.

An integral with limits that involves an unknown constant.

## Vectors

Finding the vector between two points and its magnitude.

Navigating along various known vectors to obtain unknown vectors and showing that three points are colinear.

# AS Mechanics

## SUVAT Equations

How to select which SUVAT equation to use to calculate time for a ball to be thrown upwards before reaching the ground.

Using SUVAT Equations and a velocity-time graph question.

## Newton's Laws of Motion

A very basic introduction to balanced and unbalanced forces and Newton’s First Law of Motion.

Using Newtons 2nd Law to find the mass of a particle accelerating under gravity in two opposing directions.

Using Newton’s Laws to find the thrust between two connected particles acted on by an external force as well as gravity

## Motion in a Straight Line

How to find velocity from variable acceleration using integration and finding the constant of integration.

# AS Statistics

## Discrete Probability Distributions

Simultaneous Equations where not all the unknowns are found in a Discrete Probability Distributions exam question.

A brief explanation of the uniform distribution and using the Binomial Cumulative Distribution Function on a scientific calculator to find some cumulative binomial probabilities.

## Hypothesis Testing

Calculating binomial probabilities and performing a basic hypothesis test at the 5% significance level using the binomial probability of the outcome of an experiment.