Built in the order it actually makes sense to learn it — starting from basic operations, then division and factorising, and building up to identities, patterns and functions. Each section has a short video, the notes that matter, a worked example, then five questions that build in difficulty.
Everything in algebra starts here. A polynomial is just a string of terms with whole-number powers, like 5x3 − 3x2 + 4x − 6. Before you can factorise or solve anything, you need to add, subtract and expand these fluently — and know the two special products that appear on every paper.
Division is expansion run backwards. Sometimes you can just cancel; when you can't, you use long division. Either way, a remainder of zero tells you that what you divided by is a factor — which is the doorway into factorising.
Factorising is expanding in reverse, and it's the single most-used skill on Paper 1. Work the checklist in order every time: take out the HCF first, then count the terms.
Algebraic fractions follow exactly the same rules as ordinary fractions — the only difference is that you usually have to factorise first before anything cancels. That's why this comes after factorising.
Now that you can factorise, you can solve. Solving means finding the values of x that make the equation true — and the method depends entirely on the type. With surds, you must always check your answers.
"Make x the subject" means rearrange until x sits alone on one side. It's the same skill as solving, just with letters instead of numbers — and you'll use it constantly in calculus, trigonometry and every time you open the Formulae & Tables booklet.
Two unknowns need two equations; three unknowns need three. You're finding the values that satisfy all of them at once — graphically, where the lines cross.
Back to expanding — but faster. Expanding (a + b)2 by hand is fine. (a + b)5 is not, so we use Pascal's triangle or the nCr formula to get the coefficients without multiplying it all out.
An equation is true for particular values of x. An identity (written ≡) is true for every value of x — and that's exactly what lets you compare coefficients.
Write a polynomial as a function — f(x) — and everything you've learned pays off. Evaluating is just substitution; finding roots is just solving f(x) = 0, which is just factorising.
Given a list of numbers, you're expected to spot the type of pattern and write a formula for the nth term. The differences tell you everything — and this is the doorway into Sequences & Series later in the course.
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