Algebra & Trigonometry Course Outline
Every unit and lesson in Algebra & Trigonometry: the main function families, then the unit circle, trig graphs, identities and equations, as a bridge into Precalculus.
Try the student practice samples in the first expanded unit below. The detailed notes will be discussed during the course, with worked examples, guided practice, and time for questions. Enroll to work through the remaining lessons with your tutor.
Explore the study guide1Unit 1: Linear and Piecewise FunctionsFunction notation, linear models, piecewise and absolute value functions.4 lessons + review
- 1.1MCQ Sample
Functions and Function Notation
Evaluate functions and use domain and range.
- 1.2FRQ Sample
Linear Functions and Models
Write, graph and interpret linear models.
- 1.3Enroll Now
Piecewise Functions
Graph and write piecewise-defined functions.
- 1.4Enroll Now
Absolute Value Functions
Graph absolute value functions and their transformations.
- 1REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 1.
2Unit 2: Transformations of FunctionsParent functions, translations, reflections, stretches, composition and inverses.5 lessons + review
- 2.1Enroll Now
Parent Functions
Recognize the graphs of the core function families.
- 2.2Enroll Now
Translations
Shift graphs horizontally and vertically.
- 2.3Enroll Now
Reflections, Stretches and Compressions
Reflect and scale graphs.
- 2.4Enroll Now
Combining Transformations
Apply several transformations in the right order.
- 2.5Enroll Now
Composition and Inverse Functions
Compose functions and find inverses.
- 2REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 2.
3Unit 3: Polynomial FunctionsQuadratics, polynomial graphs, division and real and complex zeros.5 lessons + review
- 3.1Enroll Now
Quadratic Functions
Analyze vertex, zeros and forms of quadratics.
- 3.2Enroll Now
Polynomial Graphs and End Behavior
Use degree, end behavior and multiplicity to sketch.
- 3.3Enroll Now
Dividing Polynomials
Divide by long and synthetic division.
- 3.4Enroll Now
Zeros and Factors
Use the Factor Theorem and the Rational Root Theorem.
- 3.5Enroll Now
Complex Zeros
Find complex zeros and write full factorizations.
- 3REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 3.
4Unit 4: Rational FunctionsAsymptotes, graphing rational functions, rational expressions and equations.4 lessons + review
- 4.1Enroll Now
Rational Functions and Asymptotes
Find vertical, horizontal and slant asymptotes.
- 4.2Enroll Now
Graphing Rational Functions
Sketch rational functions with holes and intercepts.
- 4.3Enroll Now
Operations with Rational Expressions
Simplify and combine rational expressions.
- 4.4Enroll Now
Solving Rational Equations
Solve rational equations and check solutions.
- 4REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 4.
5Unit 5: Exponential and Logarithmic FunctionsExponential functions, logarithms and their properties, equations and models.5 lessons + review
- 5.1Enroll Now
Exponential Functions
Graph and model exponential growth and decay.
- 5.2Enroll Now
Logarithms
Convert between exponential and log forms.
- 5.3Enroll Now
Properties of Logarithms
Expand and condense logarithms.
- 5.4Enroll Now
Solving Exponential and Logarithmic Equations
Solve equations with logs and exponents.
- 5.5Enroll Now
Exponential and Logarithmic Models
Apply models to growth, decay and compound interest.
- 5REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 5.
6Unit 6: Angles and the Unit CircleRadians, right-triangle trig, the unit circle and trig functions of any angle.4 lessons + review
- 6.1Enroll Now
Angles and Radian Measure
Convert between degrees and radians; find arc length.
- 6.2Enroll Now
Right-Triangle Trigonometry
Solve right triangles with the six ratios.
- 6.3Enroll Now
The Unit Circle
Use exact unit-circle values for special angles.
- 6.4Enroll Now
Trigonometric Functions of Any Angle
Use reference angles and signs by quadrant.
- 6REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 6.
7Unit 7: Graphs of Trigonometric FunctionsSine, cosine and tangent graphs, transformations and inverse trig functions.4 lessons + review
- 7.1Enroll Now
Graphs of Sine and Cosine
Graph sine and cosine and key features.
- 7.2Enroll Now
Amplitude, Period and Phase Shift
Transform sinusoids and write their equations.
- 7.3Enroll Now
Tangent and Reciprocal Functions
Graph tangent, secant, cosecant and cotangent.
- 7.4Enroll Now
Inverse Trigonometric Functions
Evaluate inverse trig with restricted ranges.
- 7REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 7.
8Unit 8: Trigonometric Identities and EquationsFundamental identities, proofs, sum, difference and double-angle formulas, and trig equations.5 lessons + review
- 8.1Enroll Now
Fundamental Identities
Use reciprocal, quotient and Pythagorean identities.
- 8.2Enroll Now
Verifying Identities
Prove identities by transforming one side.
- 8.3Enroll Now
Sum and Difference Formulas
Expand sin(A ± B), cos(A ± B) and tan(A ± B).
- 8.4Enroll Now
Double-Angle Formulas
Apply double-angle identities.
- 8.5Enroll Now
Solving Trigonometric Equations
Find all solutions on an interval and in general.
- 8REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 8.
Independently developed by Code Scholars Tutoring. Lesson order and pacing can be adapted to the student’s school syllabus.