Mathematics

Precalculus: scope and sequence

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.

There is no fixed calendar for this course. The units are written to be taken in order, and most families spend one to two weeks on each.

The units, in order

#	Unit and what it covers	Lessons
1	Composing & Inverting Functions Functions can be bolted together end to end, and any chain can be run backwards.	5
2	Parent Functions & Transformations A handful of basic shapes, moved and stretched, account for almost every graph you will meet.	5
3	Dividing Polynomials & the Factor Theorem Dividing polynomials is the long division you already know, and a remainder of zero names a factor.	5
4	Polynomial Functions & Their Graphs The degree and the leading coefficient decide the shape before you plot a single point.	5
5	Rational Expressions & Equations Fractions with letters in them obey the fraction rules you already know — plus one forbidden value.	5
6	Radical Functions & Equations Squaring both sides is legal, and it can still hand you an answer that is wrong.	5
7	Complex Numbers One new number, $i$, and every polynomial equation finally has a solution.	5
8	Logarithms A logarithm is the exponent — nothing more, and nothing less.	5
9	Exponential & Logarithmic Models Growth and decay that depend on how much is already there, and the logs that solve them.	5
10	Radians & the Unit Circle Measure angles by the arc they cut, and trigonometry escapes the right triangle.	5
11	Graphs of Sine & Cosine Going round in circles, drawn flat, gives a wave — and four numbers describe any wave.	5
12	Trigonometric Identities & Equations One identity comes straight from Pythagoras, and it unlocks nearly every trig equation.	5
13	Inverse Trigonometric Functions Sine repeats forever, so its inverse has to be told which answer to give back.	5
14	The Law of Sines & Cosines Two rules extend trigonometry to every triangle, not just the right-angled ones.	5
15	Polar Coordinates Distance and direction describe a point just as well as across and up.	5
16	Vectors Some quantities need a direction as well as a size, and they do not add like numbers.	5
17	Matrices & Systems Strip the letters from a system of equations and what is left is a grid of numbers that can be solved mechanically.	5
18	Conic Sections Slice a cone four ways and you get every curve in this unit.	5
19	Parametric Equations Let a third variable drive both coordinates, and curves that were impossible become easy.	5
20	Series & Sigma Notation Adding a long list of terms without adding them one at a time.	5
21	Counting, Permutations & the Binomial Theorem Expanding a bracket and counting arrangements turn out to be the same question.	5
22	The Normal Distribution Some measurements cluster in a bell-shaped pattern that a normal distribution can approximate.	5
23	Limits & Continuity Where a function is heading matters more than whether it ever arrives.	5
24	Rates of Change & the Derivative Average speed over a shorter and shorter trip settles on the speed at one instant.	5
25	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.	5

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