Algebra
The complete algebra curriculum for ages 10 to 16, with every topic taught in its own bite-sized video lesson. Nothing skipped, nothing rushed, with an AI tutor on hand whenever you get stuck.
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Explore every Algebra topic
Solving equations, sequences, quadratics and simultaneous equations. Practise with expert-selected questions and an AI tutor besides you anytime.
Expressions and Simplifying
Distributive Law
The distributive law is why 3(x + 2) becomes 3x + 6.
Deriving and Evaluating Expressions with One Variable
Write algebraic expressions from words and evaluate them: if x = 4, then 3x + 2 = 14.
Simplifying Expressions
Simplifying expressions means collecting like terms: 3a + 2b + a = 4a + 2b.
Simplifying Expressions with Multiple Variables
Simplifying algebraic expressions with several letters: 4xy + 2x − xy = 3xy + 2x.
Expanding Double Brackets
Expanding double brackets: (x + 2)(x + 3) = x² + 5x + 6.
Square of a Binomial
Square a bracket in one step: (x + 3)² = x² + 6x + 9, using (a + b)² = a² + 2ab + b².
Formulas and Functions
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Introduction to Mapping
A mapping diagram shows how each input becomes an output, like x → 2x + 1.
Introduction to Formulas
Substitution into formulae: put numbers in for letters, so A = lw with l = 5, w = 3 gives 15.
Introduction to Functions and Graphs
From function machines to graphs: each input x gives one output, and the points make the curve.
Linear Equations and Graphs
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Solving Equations
Solving equations: do the same to both sides, so 2x + 3 = 11 gives 2x = 8 and x = 4.
Solving Rational Equations
Equations with fractions: multiply every term by the denominator, so x/3 = 4 becomes x = 12.
Gradient and Y-Intercept in Linear Equations
In y = mx + c, m is the gradient and c is the y-intercept: y = 2x + 1 rises 2 for every 1 across.
Finding the Equation of a Straight Line
Find the equation of a straight line from two points: work out the gradient, then find c.
How to Find X-Intercept, Y-Intercept and Intersections
The x-intercept is where y = 0 and the y-intercept where x = 0; two lines meet where both equations hold.
Sequences
Finding the nth Term of a Linear Sequence
How to find the nth term: 5, 8, 11, 14 goes up by 3, so the nth term is 3n + 2.
Quadratic Sequence and Geometric Sequence
Quadratic sequences: constant second difference. Geometric sequence: multiply each time, like 2, 6, 18.
Fibonacci Sequence and Fibonacci-Type Sequences
In the Fibonacci sequence each term is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13.
Quadratic Equations and Graphs
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Simple Quadratic Equations
What is a quadratic equation? One with an x² term, like x² − 9 = 0, so it can have two solutions.
Solving Simple Quadratic Equations
How to solve quadratic equations like x² = 25: square root both sides and keep both answers, 5 and −5.
Vertex Form and Parabola Transformations
Vertex form y = a(x − h)² + k puts the turning point at (h, k): y = (x − 2)² + 3 has vertex (2, 3).
Converting Quadratics: Standard Form and Vertex Form
Completing the square turns x² + 6x + 1 into (x + 3)² − 8, which reveals the turning point.
How to Write Quadratic Equations in Vertex Form and Standard Form
Expand vertex form to get standard form, or complete the square to find the vertex of a parabola.
Solving Quadratic Equations by Factorising
Factorising quadratics: x² + 5x + 6 = (x + 2)(x + 3), so x = −2 or x = −3.
Solving Quadratic Equations: Quadratic Formula
The quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a solves any quadratic, factorisable or not.
Simultaneous Equations
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Solving Equations with 2 Variables
One equation with two unknowns, like x + y = 7, has many solutions; a second equation pins them down.
Solving Simultaneous Equations Graphically
Solving simultaneous equations graphically: plot both lines and read off where they cross.
Simultaneous Equations: Equal Values and Substitution Method
The substitution method: if y = 2x and x + y = 9, replace y to get 3x = 9, so x = 3 and y = 6.
Elimination Method for Solving Simultaneous Equations
How to solve simultaneous equations by elimination: add or subtract them to remove one unknown.
Explore other Maths categories
Maths Angel covers the whole maths curriculum for ages 10 to 16. Algebra is one of six categories, so jump into any of the others.