Precalculus
The Grade 12 course: every function type revisited, then inverse and oblique trigonometry, polar form, vectors, matrices, conics and parametric curves — finishing with limits, derivatives and the area under a curve.
Precalculus covers 25 units across 6 strands, with 400 practice questions, worked examples, and a printable page for every unit. Each unit has a lesson, practice with worked steps, challenge problems, and a chapter review; the course has chapter quizzes, a midterm and a final.
Every unit below is a page of its own: read the explanation, work the examples, then practise. Answers and worked steps are shown after each attempt, so a parent does not have to mark the routine questions.
Units in Precalculus
- Composing & Inverting Functions — Functions can be bolted together end to end, and any chain can be run backwards.
- Parent Functions & Transformations — A handful of basic shapes, moved and stretched, account for almost every graph you will meet.
- Dividing Polynomials & the Factor Theorem — Dividing polynomials is the long division you already know, and a remainder of zero names a factor.
- Polynomial Functions & Their Graphs — The degree and the leading coefficient decide the shape before you plot a single point.
- Rational Expressions & Equations — Fractions with letters in them obey the fraction rules you already know — plus one forbidden value.
- Radical Functions & Equations — Squaring both sides is legal, and it can still hand you an answer that is wrong.
- Complex Numbers — One new number, i, and every polynomial equation finally has a solution.
- Logarithms — A logarithm is the exponent — nothing more, and nothing less.
- Exponential & Logarithmic Models — Growth and decay that depend on how much is already there, and the logs that solve them.
- Radians & the Unit Circle — Measure angles by the arc they cut, and trigonometry escapes the right triangle.
- Graphs of Sine & Cosine — Going round in circles, drawn flat, gives a wave — and four numbers describe any wave.
- Trigonometric Identities & Equations — One identity comes straight from Pythagoras, and it unlocks nearly every trig equation.
- Inverse Trigonometric Functions — Sine repeats forever, so its inverse has to be told which answer to give back.
- The Law of Sines & Cosines — Two rules extend trigonometry to every triangle, not just the right-angled ones.
- Polar Coordinates — Distance and direction describe a point just as well as across and up.
- Vectors — Some quantities need a direction as well as a size, and they do not add like numbers.
- Matrices & Systems — Strip the letters from a system of equations and what is left is a grid of numbers that can be solved mechanically.
- Conic Sections — Slice a cone four ways and you get every curve in this unit.
- Parametric Equations — Let a third variable drive both coordinates, and curves that were impossible become easy.
- Series & Sigma Notation — Adding a long list of terms without adding them one at a time.
- Counting, Permutations & the Binomial Theorem — Expanding a bracket and counting arrangements turn out to be the same question.
- The Normal Distribution — Some measurements cluster in a bell-shaped pattern that a normal distribution can approximate.
- Limits & Continuity — Where a function is heading matters more than whether it ever arrives.
- Rates of Change & the Derivative — Average speed over a shorter and shorter trip settles on the speed at one instant.
- Accumulation & Area Under a Curve — Add up enough thin strips and the total is exactly the area — and usually a distance, a cost or a volume.