YEARS 10–12 · FREE COURSE
Algebra Masterclass
Ten lessons covering the full algebra syllabus, taught from first principles. Watch straight through, or jump to the topic you’re stuck on.
Intro to Algebra
Algebra is bookkeeping for unknowns. We start with the flow-chart method, build the machine that turns x into your answer, then run it backwards. Once you can reverse a chain of operations reliably, solving linear equations stops being guesswork.
Index Laws
Every index law is one idea repeated: powers count how many copies you’re multiplying. Divide and you cancel copies; that’s why a⁰ = 1 and why negative powers flip the fraction. Memorise the reasoning, not the table.
Expanding Brackets
Distribution is just the area of a rectangle written in symbols. Draw the grid once and double brackets, trinomials and the dreaded sign errors all take care of themselves.
Quadratics
Three forms, one parabola. General form gives you the y-intercept, factored form gives you the roots, and completed square gives you the turning point, the exam question tells you which one it wants before you touch the algebra.
Factorising
A four-step checklist that never fails: common factor, difference of two squares, trinomial pairs, then grouping. Run it in that order and you’ll never stare at a blank page again.
Binomials
Perfect squares and the difference of two squares are the two patterns worth knowing cold, they turn multi-line expansions into one line of work, and they’re the backbone of completing the square later.
Algebraic Division
Long division with letters instead of digits. The layout is the lesson: keep like terms in columns, subtract carefully, and the remainder theorem falls out of the process for free.
Advanced Division
Cubics, missing terms and awkward remainders. We use the factor theorem to find one root by inspection, then divide down to a quadratic you already know how to finish.
Algebra Tricks
The shortcuts markers see in every band-6 paper: substituting to test an answer, factoring out before expanding, and spotting symmetry so you can skip half the work.
Simultaneous Equations
Substitution, elimination, and knowing which one the question is begging for. We finish with non-linear pairs, where a line meets a parabola and geometry tells you how many solutions to expect.