Teaching Precalculus at home

Prepare before the lesson

1. Read the unit's main idea and work through an example. Identify the earlier skill the method relies on.
2. Choose a short practice set that includes both a familiar example and a changed case. Have paper, a diagram or a number line ready when useful.
3. Locate the worked steps and common mistakes. Decide which step the learner should attempt before you offer a hint.

Teach, discuss and check

1. Ask for a prediction or estimate and a representation before starting an algorithm.
2. Explain one worked step and why it is valid. Let the learner complete the next step with less support.
3. Use an incorrect solution to discuss the reasoning, then give a changed problem without the model in view.
4. Check the result by substitution, units, another representation or an estimate. Ask when the method applies.

Judge the reasoning

Use these discussion criteria with the unit’s own marking guidance. They are a feedback framework, not a universal numerical grade.

• Chooses a suitable representation or relationship.
• Uses valid steps and carries the necessary units or conditions.
• Explains why the method answers the question.
• Checks the result and can adapt to a changed case.

Keep one worked example, one corrected error and one independent changed-case solution. Solving a practice question after retries is progress, but does not by itself establish independent mastery.

When the learner needs support

• When a procedure is memorized without meaning, return to a diagram or a small numerical example.
• When a prerequisite is missing, revisit the matching earlier unit rather than repeating a harder set unchanged.
• Separate an arithmetic slip from a misunderstanding of the relationship, and choose feedback accordingly.

Plan this course

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.

This math course has no authored weekly timetable in the Parent Center. Schedule its units or your own activities at a pace you choose.

No authored weekly timetable is available here. Schedule individual units and outside activities at your chosen pace.

Materials and records

Use paper, a suitable diagram or manipulatives, and the worked examples in the existing course.

Use the course assessments

Keep one worked example, one corrected error and one independent changed-case solution. Solving a practice question after retries is progress, but does not by itself establish independent mastery.

Read the full course guide

Units and teaching goals

• Unit 1 · Composing & Inverting Functions

  Functions can be bolted together end to end, and any chain can be run backwards.

• Unit 2 · Parent Functions & Transformations

  A handful of basic shapes, moved and stretched, account for almost every graph you will meet.

• Unit 3 · Dividing Polynomials & the Factor Theorem

  Dividing polynomials is the long division you already know, and a remainder of zero names a factor.

• Unit 4 · Polynomial Functions & Their Graphs

  The degree and the leading coefficient decide the shape before you plot a single point.

• Unit 5 · Rational Expressions & Equations

  Fractions with letters in them obey the fraction rules you already know — plus one forbidden value.

• Unit 6 · Radical Functions & Equations

  Squaring both sides is legal, and it can still hand you an answer that is wrong.

• Unit 7 · Complex Numbers

  One new number, i, and every polynomial equation finally has a solution.

• Unit 8 · Logarithms

  A logarithm is the exponent — nothing more, and nothing less.

• Unit 9 · Exponential & Logarithmic Models

  Growth and decay that depend on how much is already there, and the logs that solve them.

• Unit 10 · Radians & the Unit Circle

  Measure angles by the arc they cut, and trigonometry escapes the right triangle.

• Unit 11 · Graphs of Sine & Cosine

  Going round in circles, drawn flat, gives a wave — and four numbers describe any wave.

• Unit 12 · Trigonometric Identities & Equations

  One identity comes straight from Pythagoras, and it unlocks nearly every trig equation.

• Unit 13 · Inverse Trigonometric Functions

  Sine repeats forever, so its inverse has to be told which answer to give back.

• Unit 14 · The Law of Sines & Cosines

  Two rules extend trigonometry to every triangle, not just the right-angled ones.

• Unit 15 · Polar Coordinates

  Distance and direction describe a point just as well as across and up.

• Unit 16 · Vectors

  Some quantities need a direction as well as a size, and they do not add like numbers.

• Unit 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.

• Unit 18 · Conic Sections

  Slice a cone four ways and you get every curve in this unit.

• Unit 19 · Parametric Equations

  Let a third variable drive both coordinates, and curves that were impossible become easy.

• Unit 20 · Series & Sigma Notation

  Adding a long list of terms without adding them one at a time.

• Unit 21 · Counting, Permutations & the Binomial Theorem

  Expanding a bracket and counting arrangements turn out to be the same question.

• Unit 22 · The Normal Distribution

  Some measurements cluster in a bell-shaped pattern that a normal distribution can approximate.

• Unit 23 · Limits & Continuity

  Where a function is heading matters more than whether it ever arrives.

• Unit 24 · Rates of Change & the Derivative

  Average speed over a shorter and shorter trip settles on the speed at one instant.

• Unit 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.