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Algebra

Letters stand in for numbers, turning one problem into a general rule. Equations, graphs and patterns are all algebra's language.

23 topics

  1. 01Variables & the Function MachineLetters that stand in for numbers, and a machine that processes them — the gate to algebra.Lesson 1 of 23
  2. 02Equation of a Straight LineEvery line carries an ID card — m says how it climbs, b says where it starts.Lesson 2 of 23
  3. 03SubstitutionHand the letter a concrete number and follow the rules step by step — a formula turns into an answer.Lesson 3 of 23
  4. 04Solving Linear EquationsAn equation is a balance scale — do the same thing to both sides and x gets cornered step by step.Lesson 4 of 23
  5. 05ExponentsMultiplying a number by itself, written with one small superscript — exponents are multiplication's shortcut.Lesson 5 of 23
  6. 06Cartesian CoordinatesTwo number lines cross, and every point on the plane gets an address of its own.Lesson 6 of 23
  7. 07InequalitiesReal life rarely says "exactly equal" — the territory of "at least" and "no more than" belongs to inequalities.Lesson 7 of 23
  8. 08Quadratic EquationsThe moment x² appears, the graph bends into a parabola — every thrown ball is drawing one.Lesson 8 of 23
  9. 09FactorisingExpanding unpacks the brackets, factorising packs the result back in — algebra's reverse gear.Lesson 9 of 23
  10. 10Simultaneous EquationsTwo unknowns, two equations — hunt them down by substitution or elimination.Lesson 10 of 23
  11. 11Functions & Their GraphsPut a number in, the rule spits a number out — graph the machine and its temperament becomes a curve.Lesson 11 of 23
  12. 12Expanding BracketsOpen the brackets and multiply into every term — the distributive law is the only engine, the minus sign is the only trap.Lesson 12 of 23
  13. 13Midpoint & DistanceAverage the coordinates to find the middle, use Pythagoras to measure the slanted road — two pocket tools for the coordinate plane.Lesson 13 of 23
  14. 14Direct & Inverse ProportionDoubling together is direct proportion, a constant product is inverse — the two tidiest patterns of change.Lesson 14 of 23
  15. 15Simplifying ExpressionsOnly like terms may merge — tidy the clutter in an expression, and substitution later costs half the effort.Lesson 15 of 23
  16. 16Formulas & RearrangingFormulas are recipes in symbols — substitute to cook them forward, rearrange to ask them backwards, and the balance keeps every step fair.Lesson 16 of 23
  17. 17Special Binomial ProductsThe perfect-square and difference-of-squares identities — plus the classic lesson that (a+b)² never equals a²+b².Lesson 17 of 23
  18. 18Graphing QuadraticsOpening direction, axis of symmetry and vertex — the three things to read on a parabola, plus counting x-intercepts with the discriminant.Lesson 18 of 23
  19. 19Rational ExpressionsFractions with algebra inside — cancel by factorising, and keep one red line, a denominator that must never be zero.Lesson 19 of 23
  20. 20LogarithmsAsk 2 to what power gives 8 and you have a logarithm — the inverse of exponents, speaking behind earthquake magnitudes and pH.Lesson 20 of 23
  21. 21Sequences and SeriesArithmetic walks at a constant pace, geometric doubles as it runs, and Gauss summed 1 to 100 with one pairing trick — numbers in a queue follow rules too.Lesson 21 of 23
  22. 22VectorsDisplacement, velocity and force refuse to fit in a single number — they need size and direction, and components turn their algebra back into primary-school arithmetic.Lesson 22 of 23
  23. 23Introduction to MatricesNumbers arranged in a grid, added cell by cell, multiplied row times column — and at the end one matrix rotates an entire figure by 90 degrees.Lesson 23 of 23

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