BetterGrades Precalculus · Course map
Precalculus: Functions, Models, and Change
A continuous Precalculus course built around functions, multiple representations, exact reasoning, modeling, and change.
Continuous course
Functions, models, and change
Open a unit to follow its lesson and assessment sequence.
Open the 64-item final assessment
Unit 1Algebra and Function ReadinessA readiness diagnostic separates prerequisite strands so that a learner receives targeted repair rather than one vague total score.8 lessons
Algebra and Function Readiness
A readiness diagnostic separates prerequisite strands so that a learner receives targeted repair rather than one vague total score.
Open the unit mapUnit 2Functions and Multiple RepresentationsAn input is supplied to a relationship, an output is determined by it, and parameters remain fixed for one selected model.10 lessons
Functions and Multiple Representations
An input is supplied to a relationship, an output is determined by it, and parameters remain fixed for one selected model.
Open the unit mapUnit 3Transformations and Function OperationsA parent function is a convenient reference member identified by domain, range, symmetry, endpoints, asymptotes, and rate patterns.10 lessons
Transformations and Function Operations
A parent function is a convenient reference member identified by domain, range, symmetry, endpoints, asymptotes, and rate patterns.
Open the unit mapUnit 4Composition, Inverses, and ModelingComposition represents an ordered chain in which the inner function acts first.9 lessons
Composition, Inverses, and Modeling
Composition represents an ordered chain in which the inner function acts first.
Open the unit mapUnit 5Polynomial FunctionsPower functions f(x)=ax^p connect positive, negative, and fractional exponent behavior.13 lessons
Polynomial Functions
Power functions f(x)=ax^p connect positive, negative, and fractional exponent behavior.
Open the unit mapUnit 6Rational FunctionsA rational function P/Q excludes every real input where the original denominator Q is zero.11 lessons
Rational Functions
A rational function P/Q excludes every real input where the original denominator Q is zero.
Open the unit mapUnit 7Exponential and Logarithmic FunctionsConstant first differences indicate additive linear change; constant ratios indicate multiplicative exponential change.13 lessons
Exponential and Logarithmic Functions
Constant first differences indicate additive linear change; constant ratios indicate multiplicative exponential change.
Open the unit mapUnit 8Systems, Matrices, and Multivariable ModelsA system solution satisfies every equation simultaneously and appears graphically as a common intersection.10 lessons
Systems, Matrices, and Multivariable Models
A system solution satisfies every equation simultaneously and appears graphically as a common intersection.
Open the unit mapUnit 9Angles, Radians, and the Unit CircleA radar arm begins on the positive x-axis, rotates 765 degrees counterclockwise, then 180 degrees clockwise. Where is its terminal side, and what is the smallest positive coterminal angle?10 lessons
Angles, Radians, and the Unit Circle
A radar arm begins on the positive x-axis, rotates 765 degrees counterclockwise, then 180 degrees clockwise. Where is its terminal side, and what is the smallest positive coterminal angle?
Open the unit mapUnit 10Trigonometric Functions and Periodic ModelsA point starts at (1,0) and rotates counterclockwise one revolution in 8 seconds. Sketch its vertical coordinate against time and label zeros, extrema, and period.12 lessons
Trigonometric Functions and Periodic Models
A point starts at (1,0) and rotates counterclockwise one revolution in 8 seconds. Sketch its vertical coordinate against time and label zeros, extrema, and period.
Open the unit mapUnit 11Trigonometric Identities and EquationsIs (1-cos^2 x)/sin x=sin x an identity? State the exact common domain on which the equality is valid.12 lessons
Trigonometric Identities and Equations
Is (1-cos^2 x)/sin x=sin x an identity? State the exact common domain on which the equality is valid.
Open the unit mapUnit 12Triangle Trigonometry and VectorsA ramp rises 0.84 meter over a horizontal run of 7.2 meters. Find its angle of inclination and length.10 lessons
Triangle Trigonometry and Vectors
A ramp rises 0.84 meter over a horizontal run of 7.2 meters. Find its angle of inclination and length.
Open the unit mapUnit 13Conic Sections and Implicit RelationsFind the locus of points exactly 5 units from (-2,3) and determine its x- and y-intercepts.10 lessons
Conic Sections and Implicit Relations
Find the locus of points exactly 5 units from (-2,3) and determine its x- and y-intercepts.
Open the unit mapUnit 14Parametric, Polar, and Complex RepresentationsFor x=2t-1 and y=t^2, -2≤t≤3, find endpoints, direction, and the Cartesian curve.12 lessons
Parametric, Polar, and Complex Representations
For x=2t-1 and y=t^2, -2≤t≤3, find endpoints, direction, and the Cartesian curve.
Open the unit mapUnit 15Sequences, Series, and Discrete ModelsThe first five terms are 4,7,12,19,28. Plot them as a discrete function and propose a formula.12 lessons
Sequences, Series, and Discrete Models
The first five terms are 4,7,12,19,28. Plot them as a discrete function and propose a formula.
Open the unit mapUnit 16Calculus Readiness and Function SynthesisA graph is positive, decreasing, concave upward, has domain all reals, and approaches y=2 as x grows. Name plausible families and identify one additional feature needed.12 lessons
Calculus Readiness and Function Synthesis
A graph is positive, decreasing, concave upward, has domain all reals, and approaches y=2 as x grows. Name plausible families and identify one additional feature needed.
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