Precalculus Study Guide
9 units with lessons, worked examples, graphs, and practice PDFs.
Units
Quadratic and Polynomial Functions
Zeros, multiplicity, and end behavior. Together these three facts determine the shape of any polynomial graph before a single point is plotted.
3 lessons · Problems and solutions PDFs →
Radical and Rational Functions
Two families defined by what they exclude. Radicals restrict the domain; rationals introduce asymptotes and holes, and both create extraneous solutions.
3 lessons · Problems and solutions PDFs →
Exponential and Logarithmic Functions
Growth by constant ratio, and the inverse that recovers the exponent. Most of the unit follows from those two sentences.
3 lessons · Problems and solutions PDFs →
Unit Circle and Trigonometric Functions
Extending trigonometry beyond right triangles. Structure and symmetry replace memorisation, which is what makes unfamiliar angles tractable.
3 lessons · Problems and solutions PDFs →
Trigonometric Graphs and Models
Four parameters that describe any sinusoid, and using them to model anything that repeats.
3 lessons · Problems and solutions PDFs →
Identities and Trigonometric Equations
Rewriting trigonometric expressions into a form that can be evaluated or solved, and reporting every solution the interval demands.
3 lessons · Problems and solutions PDFs →
Analytic and Applied Trigonometry
Triangles that are not right-angled, and the inverse functions that recover an angle. Choosing the correct law from the given parts is most of the work.
3 lessons · Problems and solutions PDFs →
Polar Coordinates
A second way to locate a point, and the curves that are far easier to describe in it than in rectangular form.
3 lessons · Problems and solutions PDFs →
Sequences, Series, and Integrated Modeling
Sequences and series alongside the model-selection judgement that closes the course.
3 lessons · Problems and solutions PDFs →
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