Algebra and Trigonometry Study Guide
7 units with lessons, worked examples, graphs, and practice PDFs.
Units
Functions, Transformations, and Inverses
Function notation, domain and range, and the transformations that move any graph. Learned once, this unit applies to every family that follows.
3 lessons · Problems and solutions PDFs →
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 →
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