Algebra and Graphs

The language of patterns and relationships.

The Language of Logic

You have built a strong foundation with numbers — types, operations, fractions, percentages, and sets. Now let us use letters to describe patterns that work for ANY number.

Algebra is the 'shorthand' of the universe, describing complex relationships with simple symbols. We move from specific numbers to general rules — manipulating expressions, solving equations, and picturing inequalities on graphs.

Formula

Think of algebra as a language where letters stand in for numbers — one rule then works for every case, not just one example.

It matters because it is the foundational tool for engineering, economics, and every scientific discovery. Ever wondered how your phone calculates the fastest route home? That's algebra in action.

Memory trick

Algebra is just generalized arithmetic; letters are placeholders for secrets yet to be revealed.

What You Will Learn

You will build up from rearranging expressions to solving equations, then see those same relationships drawn as curves, and finally measure how a curve changes.

Steps

1
Manipulation: expanding brackets, factorising, algebraic fractions and indices.
2
Solving: linear equations, simultaneous equations and quadratics.
3
Inequalities, and the regions they shade on a graph.
4
Sequences, proportion, and travel graphs for speed, distance and time.
5
Graph shapes — quadratic, reciprocal, exponential — and solving from a graph.
6
Differentiation and functions: gradients, turning points, inverses and composites.

Formula

The one to know by heart — for $a x^{2} + b x + c = 0$ :

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

It solves every quadratic, including the ones that refuse to factorise.

Practise algebra and graphs now

Interactive visual aids, then real past-paper questions marked on your working like the exam. Free to start.

Practise free on Lemmara

Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education or Pearson Edexcel. The lessons and worked examples are Lemmara’s own.