Mathematics
Pre-Calculus
Functions, trigonometry, vectors and conics, with a first look at limits before calculus.
- 11 chapters
- 42 lessons
- 42 visual guides
- All free
Chapters
- 1.1Functions, Domain, and RangeDevelop function rule, domain restrictions, range and graph reading.Visual guide
- 1.2Parent Functions and TransformationsDevelop parent functions, horizontal and vertical shifts, reflections and stretches.Visual guide
- 1.3Composition and Inverse RelationshipsDevelop composition order, inverse relation, one-to-one check.Visual guide
- 1.4Transformations and Modeling with QuadraticsDevelop quadratic shift, feasible vertex, units in a model.Visual guide
2
Polynomial and Rational Functions
Polynomial and rational functions.
4 lessons
- 2.1Polynomial Functions and End BehaviorDevelop degree and leading term, even and odd degree, interpreting graphs.Visual guide
- 2.2Zeros, Multiplicity, and Graph ShapeDevelop zeros as factors, even multiplicity, odd multiplicity.Visual guide
- 2.3Factor and Remainder TheoremsDevelop remainder theorem, factor theorem, factoring after division.Visual guide
- 2.4Graphing Rational FunctionsDevelop vertical asymptotes, horizontal asymptotes, holes and intercepts.Visual guide
3
Exponential and Logarithmic Functions
Exponential and logarithmic functions.
4 lessons
- 3.1Exponential Growth and DecayDevelop initial value and base, decay factor, percent change and context.Visual guide
- 3.2Logarithms as InversesDevelop logarithm definition, equivalent forms, logarithm graph.Visual guide
- 3.3Logarithm Properties and EquationsDevelop product rule, quotient and power rules, solving and checking.Visual guide
- 3.4Exponential and Logarithmic ModelsDevelop compound growth, half-life, logarithmic time.Visual guide
- 4.1Radians and Circular MeasurementDevelop radian measure, arc length and sector area.Visual guide
- 4.2Unit Circle and Reference AnglesDevelop coterminal and reference angles, coordinates and trigonometric values.Visual guide
- 4.3Right-Triangle TrigonometryDevelop ratios and similarity, reference angles across quadrants.Visual guide
5
Trigonometric Functions and Models
Trigonometric functions and models.
4 lessons
- 5.1Sine and Cosine GraphsDevelop amplitude and range, period and frequency factor.Visual guide
- 5.2Transformations and Periodic ModelsDevelop phase shift in factored form, choosing a midline and model.Visual guide
- 5.3Tangent and Reciprocal GraphsDevelop tangent period and asymptotes, secant and cosecant.Visual guide
- 5.4Inverse Trigonometric FunctionsDevelop principal arcsine and arccosine, arctangent and compositions.Visual guide
6
Trigonometric Identities and Equations
Trigonometric identities and equations.
4 lessons
- 6.1Fundamental Trigonometric IdentitiesDevelop pythagorean relationships, quotients and valid cancellation.Visual guide
- 6.2Angle-Sum and Double-Angle IdentitiesDevelop sum and difference formulas, double-angle forms.Visual guide
- 6.3Solving Trigonometric EquationsDevelop roots on a specified interval, general solution families.Visual guide
- 6.4Factoring and Checking Trigonometric EquationsDevelop zero-product method and lost roots, squared ratios and both signs.Visual guide
7
Triangle Applications and Vectors
Triangle applications and vectors.
4 lessons
- 7.1Law of Sines and the Ambiguous CaseDevelop corresponding side-angle pairs, ssa feasibility and ambiguity.Visual guide
- 7.2Law of Cosines and Triangle AreaDevelop included angles and side lengths, area from two sides and an angle.Visual guide
- 7.3Vectors and ComponentsDevelop vector addition and scalar multiplication, magnitude and unit vectors.Visual guide
- 7.4Dot Products and ProjectionsDevelop dot product and orthogonality, vector projection.Visual guide
8
Polar Parametric and Complex Representations
Polar parametric and complex representations.
3 lessons
- 8.1Polar Coordinates and GraphsDevelop radius and angle representations, converting and reading polar curves.Visual guide
- 8.2Parametric Equations and MotionDevelop eliminating a parameter, direction and rate along a curve.Visual guide
- 8.3Complex Numbers in Polar FormDevelop modulus and argument, de moivre and complex roots.Visual guide
9
Systems Matrices and Conic Sections
Systems matrices and conic sections.
6 lessons
- 9.1Systems of Equations in Two and Three VariablesDevelop common solution, elimination, consistency and meaning.Visual guide
- 9.2Solving Systems with MatricesDevelop augmented matrix, elementary row operations, back-substitution.Visual guide
- 9.3CirclesDevelop center-radius form, completing the square, coordinate distance.Visual guide
- 9.4Parabolas as LociDevelop focus and directrix, vertical standard form, horizontal standard form.Visual guide
- 9.5EllipsesDevelop focal definition, standard axes, focal distance.Visual guide
- 9.6Hyperbolas and Conic ComparisonsDevelop hyperbola definition, asymptotes and orientation, conic identification.Visual guide
10
Sequences Series and the Binomial Theorem
Sequences series and the binomial theorem.
3 lessons
- 10.1Arithmetic Sequences and SeriesDevelop common difference, recursive rule, finite arithmetic sum.Visual guide
- 10.2Geometric Sequences and SeriesDevelop common ratio, finite geometric sum, convergent infinite sum.Visual guide
- 10.3Binomial Theorem and ApplicationsDevelop general term, selected coefficient, applied patterns.Visual guide
- 11.1Limits from Graphs and AlgebraDevelop approaching a value, removable discontinuities.Visual guide
- 11.2Continuity and End BehaviorDevelop continuity at a point, rational limits at infinity.Visual guide
- 11.3Rates of Change and the Calculus BridgeDevelop average rate and secant lines, difference quotients and tangent rates.Visual guide