Mathematics
Algebra 2
Functions in depth: polynomials, complex numbers, logarithms, conics, trigonometry and modeling.
- 11 chapters
- 53 lessons
- 53 visual guides
- All free
Chapters
1
Algebra 1 Bridge and Function Language
Original Algebra 2 chapter on algebra 1 bridge and function language. Import as draft; review and publish when ready.
4 lessons
- 1.1Expressions, Equations, and Inequalities ReviewExplore equivalent expressions, equation solution checks, inequality and interval review.Visual guide
- 1.2Functions, Domain, and RangeExplore function rule, domain restrictions, range and graph reading.Visual guide
- 1.3Parent Functions and TransformationsExplore parent functions, horizontal and vertical shifts, reflections and stretches.Visual guide
- 1.4Composition and Inverse RelationshipsExplore composition order, inverse relation, one-to-one check.Visual guide
2
Polynomial and Quadratic Functions
Original Algebra 2 chapter on polynomial and quadratic functions. Import as draft; review and publish when ready.
5 lessons
- 2.1Quadratic Forms and FeaturesExplore standard form, factored form, vertex form.Visual guide
- 2.2Transformations and Modeling with QuadraticsExplore quadratic shift, feasible vertex, units in a model.Visual guide
- 2.3Polynomial Functions and End BehaviorExplore degree and leading term, even and odd degree, interpreting graphs.Visual guide
- 2.4Zeros, Multiplicity, and Graph ShapeExplore zeros as factors, even multiplicity, odd multiplicity.Visual guide
- 2.5Building Polynomial ModelsExplore constructing from roots, using a point, checking a model.Visual guide
3
Polynomial Operations and Complex Numbers
Original Algebra 2 chapter on polynomial operations and complex numbers. Import as draft; review and publish when ready.
5 lessons
- 3.1Polynomial ArithmeticExplore like-term addition, distribution and products, special products.Visual guide
- 3.2Polynomial DivisionExplore long division, synthetic division, quotient-remainder identity.Visual guide
- 3.3Factor and Remainder TheoremsExplore remainder theorem, factor theorem, factoring after division.Visual guide
- 3.4Complex NumbersExplore imaginary unit, complex arithmetic, conjugates and powers.Visual guide
- 3.5Solving Polynomial EquationsExplore real roots, nonreal roots, multiplicity and checks.Visual guide
4
Rational Expressions and Functions
Original Algebra 2 chapter on rational expressions and functions. Import as draft; review and publish when ready.
5 lessons
- 4.1Rational Expressions and Excluded ValuesExplore original denominator, factoring and cancellation, equivalent restricted rules.Visual guide
- 4.2Multiplying and Dividing Rational ExpressionsExplore multiplication, division and reciprocals, checking a product.Visual guide
- 4.3Adding and Subtracting Rational ExpressionsExplore least common denominator, equivalent numerators, final simplification.Visual guide
- 4.4Graphing Rational FunctionsExplore vertical asymptotes, horizontal asymptotes, holes and intercepts.Visual guide
- 4.5Rational Equations and VariationExplore solving rational equations, direct variation, inverse variation.Visual guide
5
Radicals and Rational Exponents
Original Algebra 2 chapter on radicals and rational exponents. Import as draft; review and publish when ready.
5 lessons
- 5.1Nth Roots and Rational ExponentsExplore principal even roots, odd roots, rational exponents.Visual guide
- 5.2Simplifying Radical ExpressionsExplore perfect-power factors, product rule conditions, equivalent forms.Visual guide
- 5.3Radical OperationsExplore like radical addition, multiplying radicals, division and restrictions.Visual guide
- 5.4Radical Functions and InversesExplore square-root graph, cube-root graph, inverse pair.Visual guide
- 5.5Radical EquationsExplore isolate before squaring, extraneous solutions, real-domain checks.Visual guide
6
Exponential, Logarithmic, and Inverse Functions
Original Algebra 2 chapter on exponential, logarithmic, and inverse functions. Import as draft; review and publish when ready.
5 lessons
- 6.1Exponential Growth and DecayExplore initial value and base, decay factor, percent change and context.Visual guide
- 6.2Inverse FunctionsExplore one-to-one requirement, swapping inputs and outputs, inverse graphs.Visual guide
- 6.3Logarithms as InversesExplore logarithm definition, equivalent forms, logarithm graph.Visual guide
- 6.4Logarithm Properties and EquationsExplore product rule, quotient and power rules, solving and checking.Visual guide
- 6.5Exponential and Logarithmic ModelsExplore compound growth, half-life, logarithmic time.Visual guide
7
Sequences, Series, and the Binomial Theorem
Original Algebra 2 chapter on sequences, series, and the binomial theorem. Import as draft; review and publish when ready.
5 lessons
- 7.1Arithmetic Sequences and SeriesExplore common difference, recursive rule, finite arithmetic sum.Visual guide
- 7.2Geometric Sequences and SeriesExplore common ratio, finite geometric sum, convergent infinite sum.Visual guide
- 7.3Sigma NotationExplore index and bounds, expanding a sum, properties of sums.Visual guide
- 7.4Pascal's Triangle and Binomial CoefficientsExplore combination count, pascal recurrence, binomial coefficients.Visual guide
- 7.5Binomial Theorem and ApplicationsExplore general term, selected coefficient, applied patterns.Visual guide
8
Systems, Matrices, and Inequalities
Original Algebra 2 chapter on systems, matrices, and inequalities. Import as draft; review and publish when ready.
5 lessons
- 8.1Systems of Equations in Two and Three VariablesExplore common solution, elimination, consistency and meaning.Visual guide
- 8.2Matrices and OperationsExplore matrix dimensions, addition and scalar multiplication, matrix multiplication.Visual guide
- 8.3Solving Systems with MatricesExplore augmented matrix, elementary row operations, back-substitution.Visual guide
- 8.4Systems of InequalitiesExplore boundary lines, feasible region, checking points.Visual guide
- 8.5Linear Optimization in ContextExplore objective function, feasible vertices, model limitations.Visual guide
9
Conic Sections
Original Algebra 2 chapter on conic sections. Import as draft; review and publish when ready.
4 lessons
- 9.1CirclesExplore center-radius form, completing the square, coordinate distance.Visual guide
- 9.2Parabolas as LociExplore focus and directrix, vertical standard form, horizontal standard form.Visual guide
- 9.3EllipsesExplore focal definition, standard axes, focal distance.Visual guide
- 9.4Hyperbolas and Conic ComparisonsExplore hyperbola definition, asymptotes and orientation, conic identification.Visual guide
10
Trigonometric Functions
Original Algebra 2 chapter on trigonometric functions. Import as draft; review and publish when ready.
5 lessons
- 10.1Angles, Radians, and Arc LengthExplore degree-radian conversion, coterminal angles, arc length.Visual guide
- 10.2Unit Circle and Trigonometric RatiosExplore unit circle coordinates, reference angles and signs, right-triangle ratios.Visual guide
- 10.3Graphs of Sine and CosineExplore amplitude and midline, period, phase and vertical shifts.Visual guide
- 10.4Trigonometric Identities and EquationsExplore pythagorean identity, reciprocal and quotient rules, solutions on an interval.Visual guide
- 10.5Periodic ModelingExplore period and units, parameters in context, model limits.Visual guide
11
Probability, Statistics, and Modeling
Original Algebra 2 chapter on probability, statistics, and modeling. Import as draft; review and publish when ready.
5 lessons
- 11.1Counting Principles and CombinationsExplore multiplication principle, permutation count, combination count.Visual guide
- 11.2Conditional Probability and IndependenceExplore sample space, conditional probability, independence.Visual guide
- 11.3Random Variables and Expected ValueExplore discrete distribution, expected value, net gain.Visual guide
- 11.4Data Distributions and RegressionExplore center and spread, regression and residual, outliers and association.Visual guide
- 11.5Course Synthesis ProjectExplore model choice, independent calculation steps, limits and communication.Visual guide