AS Pure Maths

Proof 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.

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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

A binomial expansion followed by finding missing coefficients when multiplied by a linear factor.


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.


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 question that requires equating coefficients.

An integral with limits that involves an unknown constant.


Finding the vector between two points and its magnitude.

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.–8Qy_Xayf0

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.