Precalculus Honors Course Outline
Every unit and lesson in Precalculus Honors: functions, analytic trigonometry, polar coordinates, sequences and series, and the foundations of calculus, preparing students for AP® Calculus AB.
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: Functions and Their GraphsProperties of functions, transformations, composition, inverses and modeling.5 lessons + review
- 1.1MCQ Sample
Functions and Their Properties
Analyze domain, range, symmetry, extrema and continuity.
- 1.2FRQ Sample
Parent Functions and Transformations
Transform graphs and describe the changes.
- 1.3Enroll Now
Combining Functions and Composition
Combine and compose functions and decompose them.
- 1.4Enroll Now
Inverse Functions
Find and verify inverses and restrict domains.
- 1.5Enroll Now
Modeling with Functions
Build function models from words and data.
- 1REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 1.
2Unit 2: Polynomial and Rational FunctionsPower and polynomial behavior, division, complex zeros, rational functions and inequalities.6 lessons + review
- 2.1Enroll Now
Quadratic and Power Functions
Analyze quadratics and power functions.
- 2.2Enroll Now
Polynomial Behavior
Use end behavior, multiplicity and rate of change.
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Division and the Remainder Theorem
Use division and the Remainder Theorem.
- 2.4Enroll Now
Real and Complex Zeros
Find all zeros and use the Fundamental Theorem.
- 2.5Enroll Now
Rational Functions and Asymptotes
Analyze asymptotes, holes and end behavior.
- 2.6Enroll Now
Polynomial and Rational Inequalities
Solve inequalities with sign charts.
- 2REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 2.
3Unit 3: Exponential, Logistic and Logarithmic FunctionsExponential, logistic and logarithmic functions, equation solving, models and finance.6 lessons + review
- 3.1Enroll Now
Exponential and Logistic Functions
Analyze exponential growth and logistic limits.
- 3.2Enroll Now
Exponential and Logistic Modeling
Fit and interpret growth models.
- 3.3Enroll Now
Logarithmic Functions
Graph logs and use them as inverses.
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Properties of Logarithms
Use log properties and change of base.
- 3.5Enroll Now
Equation Solving and Modeling
Solve equations and build log and exponential models.
- 3.6Enroll Now
Financial Mathematics
Compute compound and continuous interest and annuities.
- 3REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 3.
4Unit 4: Trigonometric FunctionsRadian measure, the six trig functions, their graphs, inverses and sinusoidal models.7 lessons + review
- 4.1Enroll Now
Angles and Radian Measure
Use radians, arc length and angular speed.
- 4.2Enroll Now
Trigonometric Functions of Acute Angles
Define the six trig functions on right triangles.
- 4.3Enroll Now
Trigonometric Functions of Any Angle
Extend the trig functions with the unit circle.
- 4.4Enroll Now
Graphs of Sine and Cosine
Graph sinusoids with amplitude, period and phase.
- 4.5Enroll Now
Graphs of Tangent, Cotangent, Secant and Cosecant
Graph the other four trig functions.
- 4.6Enroll Now
Inverse Trigonometric Functions
Evaluate and graph inverse trig functions.
- 4.7Enroll Now
Sinusoidal Modeling
Build periodic models from data and context.
- 4REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 4.
5Unit 5: Analytic TrigonometryProving identities, sum, difference and multiple-angle formulas, trig equations and the laws of sines and cosines.7 lessons + review
- 5.1Enroll Now
Fundamental Identities
Use reciprocal, quotient, Pythagorean and cofunction identities.
- 5.2Enroll Now
Proving Trigonometric Identities
Prove identities with algebraic strategies.
- 5.3Enroll Now
Sum and Difference Identities
Apply angle sum and difference identities.
- 5.4Enroll Now
Multiple-Angle Identities
Use double-angle, half-angle and power-reducing identities.
- 5.5Enroll Now
Solving Trigonometric Equations
Find general and interval solutions.
- 5.6Enroll Now
The Law of Sines
Solve oblique triangles, including the ambiguous case.
- 5.7Enroll Now
The Law of Cosines
Solve triangles and find area with Heron's formula.
- 5REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 5.
6Unit 6: Vectors, Parametric and Polar CoordinatesVectors and the dot product, parametric equations, polar graphs and complex numbers in polar form.6 lessons + review
- 6.1Enroll Now
Vectors in the Plane
Use components, magnitude, direction and operations.
- 6.2Enroll Now
The Dot Product
Find angles, projections and work.
- 6.3Enroll Now
Parametric Equations
Model motion with parameters and eliminate t.
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Polar Coordinates
Convert between polar and rectangular forms.
- 6.5Enroll Now
Graphs of Polar Equations
Graph roses, limaçons and other polar curves.
- 6.6Enroll Now
Complex Numbers in Polar Form and De Moivre's Theorem
Use trig form, powers and nth roots of complex numbers.
- 6REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 6.
7Unit 7: Sequences and SeriesSequences, series, mathematical induction and the Binomial Theorem.4 lessons + review
- 7.1Enroll Now
Sequences
Write explicit and recursive rules and test limits.
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Series and Sigma Notation
Find sums of finite and infinite series.
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Mathematical Induction
Prove statements with induction.
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The Binomial Theorem
Expand binomials using combinations and Pascal's triangle.
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Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 7.
8Unit 8: Foundations of CalculusLimits, continuity, rates of change, the derivative and area: a bridge into calculus.7 lessons + review
- 8.1Enroll Now
Limits: Graphical and Numerical
Estimate limits from graphs and tables.
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Limit Laws and One-Sided Limits
Evaluate limits algebraically and one-sided.
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Continuity
Classify discontinuities and test continuity.
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Limits at Infinity
Find horizontal asymptotes as limits.
- 8.5Enroll Now
Average and Instantaneous Rates of Change
Compute rates with difference quotients.
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Introducing the Derivative
Define the derivative as a limit and find tangent lines.
- 8.7Enroll Now
Area Under a Curve
Approximate area with rectangles and preview integrals.
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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.