AS Mathematics

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AS Mathematics

Number: Interactive Lessons
Rationalising Denominators using the Complex Conjugate
Ages 16 +

Rationalising Denominators using Conjugate Pairs

Students learn how to rationalise a denominator using the complex conjugate.
Number: Interactive Lessons
Applying the Rules of Indices
Ages 16 +

Index Laws

Students learn how to simplify expressions with fractional and negative powers.
Number: Free Resources
A horizontal transition presentation slide from Mr Mathematics titled Factorising with Powers with a top-right corner ribbon reading Pure 1 AS Maths. The algebraic problem shows an identity where open parenthesis 1 plus y close parenthesis to the power of a half plus 3 times open parenthesis 1 plus y close parenthesis to the power of 3 over 2 is identical to the square root of 1 plus y times open parenthesis a plus b y close parenthesis. A blue box prompt reads Find a and b.
Ages 16 +

Expanding and Factorising Expressions with Fractional Powers

Students learn how to expand and factorise an algebraic expression with fractional powers.
Number: Interactive Lessons
Working with Surds
Ages 16 +

Working with Surds and Rationalising a Denominator

Students learn how to multiply out a pair of brackets involving surds and rationalise a denominator.
Algebra: Interactive Lessons
A horizontal math presentation slide from Mr Mathematics titled The Discriminant with a blue Exam Technique corner ribbon. The problem shows a quadratic function f of x equals x squared plus open parenthesis w minus 5 close parenthesis x plus 1, next to a graph of a parabola touching the x-axis with a label reading Equal Roots. A blue box prompt asks to Find possible values of w.
Ages 16 +

The Discriminant

How to use the discriminant to identify the roots of a quadratic equation.
Algebra: Interactive Lessons
Solving Quadratics by Completing the Square
Ages 16 +

Solving Quadratics by Completing the Square

How to find the roots and vertex of quadratic equation by completing the square.
Algebra: Interactive Lessons
Sketching Quadratics to Identify Turning Points and Roots
Ages 16 +

Sketching Quadratics

How to sketch a quadratic graph to identify its roots and turning point.
Algebra: Interactive Lessons
Solve Quadratic Equations using the Formula
Ages 16 +

Solve Quadratic Equations using the Formula

How to set up and solve quadratic equations using the quadratic formula.
Algebra: Interactive Lessons
Solving Quadratic Inequalities
Ages 16 +

Solving Quadratic Inequalities

Students learn how to solve a quadratic inequalities using a sketched graph.
Algebra: Interactive Lessons
Quadratic inequalities A‑Level preview: line g(x) = x + 12 crossing parabola f(x) = x² at two points, showing the region where f(x) ≤ g(x) – Mr Mathematics lesson pack.
Ages 16 +

Quadratic and Linear Inequalities

Students learn how to solve a pair of quadratic and linear inequalities using a sketched graph.
Algebra: Interactive Lessons
Linear Simultaneous Equations
Ages 16 +

Simultaneous Equations by Substitution

Students learn how to solve linear simultaneous equations using substitution.
Algebra: Free Resources
Solving Quadratic and Linear Simultaneous Equation by Substitution
Ages 16 +

Solving Quadratic and Linear Simultaneous Equation by Substitution

Students learn how to solve a pair of linear and quadratic equation simultaneous equations.
Algebra: Interactive Lessons
Gradient and Midpoint of Line Segments
Ages 16 +

Gradient and Midpoint of Line Segments

Students learn how to work out the gradient and midpoint of line segments.
Algebra: Interactive Lessons
Equation of a Line Between Two Points
Ages 16 +

Equation of a Line Between Two Points

Students learn how to work out the equation of a straight line graph in the form ax + by + c = 0 from two points.
Algebra: Interactive Lessons
Equation of Parallel and Perpendicular Lines
Ages 16 +

Parallel and Perpendicular Lines

Students learn how to find the equation of parallel and perpendicular lines in the form ax + by + c = 0.
Algebra: Interactive Lessons
Sketching Cubic Graphs
Ages 16 +

Sketching Cubic Graphs

Students learn how to sketch a cubic graph by finding the roots of the function.

Mr Mathematics Blog

Developing Mathematical Thinking Beyond Procedural Fluency

July 10, 2026
A research-backed case exploring why over-reliance on automated math homework platforms and repetitive worksheets lowers student expectations, and how departments can build genuine mathematical thinking.

Converting Between Fractions, Decimals and Percentages

July 4, 2026
How to teach converting between fractions, decimals and percentages.

From Key Skills to Deep Connections: Problem Solving in Secondary Maths

June 28, 2026
Four problem solving lessons to develop student's mathematical reasoning and communication skills.