Algebra: an interactive algebra course

Algebra is an interactive algebra course that starts with what a variable is and builds up to the quadratic formula and simultaneous equations. Its 34 short sections cover substitution, collecting like terms, expanding brackets, solving equations and inequalities, factoring, exponent rules and rearranging formulas, with a hands-on demo or a practice question in most of them.

It suits anyone meeting algebra for the first time, students revising for an exam, and adults coming back to maths who want the rules explained properly rather than memorised.

What the algebra course covers

The language of algebra

The first sections make the vocabulary precise. A variable stands for a value you do not know yet, a constant is fixed, an expression has no equals sign, an equation says two expressions are equal, and an identity is true for every value. Substitution, putting a number in place of a letter, turns an expression into a number you can check.

Manipulating and solving

The middle of the course is the core toolkit: collecting like terms, expanding brackets, and solving equations by doing the same thing to both sides, pictured as a balance scale. Inequalities follow the same rules, with one exception the course stresses: multiplying or dividing by a negative number flips the sign.

Quadratics and beyond

The last third covers factoring, the quadratic formula, the discriminant (which tells you how many real solutions there are), solving two equations at once, the rules of exponents, and rearranging formulas. These are the skills physics, chemistry and every later maths course lean on.

Try a question from the course

Like terms have the same letter raised to the same power, so you can add their numbers together. In 4x + 3y − x + 5y − 2, the x terms give 4x − x = 3x and the y terms give 3y + 5y = 8y. The number −2 has no like term, so it stays. The answer is 3x + 8y − 2.

Now try one with new terms. Simplify it, then press Mark to check your answer in the course.

Who this course is for

• Students starting algebra, in middle school, early secondary school or an Algebra 1 class, who want each rule explained before they practise it.
• Students revising for exams such as GCSE Maths or the SAT, who want to jump to factoring, the quadratic formula or simultaneous equations.
• Adults returning to maths for a course, a test or a job that needs it.

What you need to know first

Arithmetic with negative numbers, fractions and the order of operations. No algebra is assumed: the course starts from what a letter in maths means. If negative numbers or fractions are shaky, sort those first, because nearly every step of algebra uses them.

How long it takes

There are 34 sections, and most take a few minutes: a short explanation, then a demo or a practice question. Practice questions use fresh numbers each time, so you can repeat them until a method sticks. Learners without a plan can open two sections of a course a day, in order, which takes 17 days. A plan removes the daily limit and lets you go straight to any topic.

Read next

Maths · AlgebraQuadratic simultaneous equations: method and examplesHow to solve simultaneous equations where one is quadratic: substitute, solve the quadratic, find both pairs. Circles, parabolas, tangents and practice.