On-demand lessons are offered by topic. The price starts at $55 and depends on the number of students per session and the number and type of topics, as some topics could require more than an hour or multiple sessions. Please contact the teacher to get a quote for your needs and the time for the service.
Fundamental Skills Topics
Exponent Rules; Polynomial Operations; Factoring Polynomials; Rational Expressions (Simplifying and Operations); Radicals (Simplifying and Operations); Complex Numbers (Simplifying and Operations); Solving Linear Equations; Solving Absolute Value Equations; Solving Quadratic Equations (solve by factoring, square roots, completing the square, quadratic formula); Solving Radical Equations; Solving Rational Equations; Writing Inequalities in Interval Notation; Solving Linear Inequalities; Solving Absolute Value Inequalities
Functions and Their Graphs Topics
Relations and Functions; Implicit vs. Explicit Equations; Function Notation; Evaluating Functions; x- and y-intercepts, zeros; Critical Points (Extrema, Point of Inflection); Increasing and Decreasing Intervals; Continuity, Types of Discontinuity; End Behavior; Tests of Symmetry; Even and Odd Functions; Average Rate of Change; Parent Functions (Linear, Absolute Value, Quadratic, Cubic, Square Root, Cube Root, Reciprocal, Exponential, Logarithmic, Greatest Integer, Sine, Cosine); Transformations (Vertical and Horizontal Translations, x- and y-axis Reflections, Vertical and Horizontal Dilations); Graphing Functions (absolute value, quadratic, cubic, square root, cube root, reciprocal, and greatest integer functions only); Piecewise Functions; Operations with Functions; Compositions of Functions; Inverse Relations and Functions; Verifying Inverses Graphically and Algebraically
Polynomial and Rational Functions Topics
Graphing Power Functions; Graphing Power Functions with Negative Exponents; Graphing Power Functions with Rational Exponents; Graphing Polynomial Functions; End Behavior and Turning Points of Polynomial Functions; Zeros, Linear Factors, and Multiplicity; Effects of Multiplicity on the Graph of a Polynomial Function; Dividing Polynomials using Long Division; Dividing Polynomials using Synthetic Division; Factoring Polynomials using Division; Remainder Theorem; Factor Theorem; Rational Zero Theorem; Irrational Zeros; Descartes' Rule of Signs; Complex Zeros; Fundamental Theorem of Algebra; Using Zeros to Write Polynomial Functions; Graphing Rational Functions; Vertical, Horizontal, and Slant (Oblique) Asymptotes; Solving Nonlinear Inequalities (Polynomial and Rational)
Exponential and Logarithmic Functions Topics
Graphing Exponential Functions; Graphing Natural Base (base e) Functions; Exponential Growth and Decay Applications; Applications of the Logistic Growth Function; Compound Interest; Continuous Compound Interest; Logarithms; Converting between Exponential and Logarithmic Form; Evaluating Logarithms and the Change of Base Formula; Natural Logarithms; Properties of Logarithms (Product Property, Quotient Property, Power Property); Expanding and Condensing Logarithms; Solving Exponential Equations using a Common Base; Solving Logarithmic Equations; Solving Exponential Equations using Logarithms; Applications with Solving Equations; Nonlinear Regression: Exponential, Power, Logistic, Logarithmic
Trigonometric Functions Topics
Angles in Standard Position; Degrees and Radians; Coterminal Angles; Degree-Minute-Second (DMS) Form; Arc Lengths; Area of Sectors; Circular Motion: Linear Speed and Angular Speed; Six Trigonometric Functions (Sine, Cosine, Tangent, Cosecant, Secant, Cotangent); Trigonometric Functions Values in Special Right Triangles; Finding Sides and Angles in Right Triangles; Solving Right Triangles; Right Triangle Applications (Angle of Elevation and Angle of Depression); Trigonometric Functions of Angle Angle; Reference Angles; The Unit Circle; Law of Sines; Law of Cosines; Applications of Law of Sines and Law of Cosines; Area of Triangles and Heron's Formula; Graphing Sine, Cosine, and Tangent Functions; Translating Trigonometric Functions (Vertical and Horizontal Phase Shifts); Graphing Reciprocal Functions (with and without translations); Evaluating Inverse Trigonometric Functions; Graphing Inverse Trigonometric Functions; Compositions of Trigonometric Functions
Trigonometric Identities and Equations Topics
Basic Trigonometric Identities (Quotient, Reciprocal, Pythagorean, Cofunction, Even-Odd); Simplifying Trigonometric Expressions; Proving Trigonometric Identities (with Basic Identities); Sum and Difference of Angles Identities; Double Angle Identities; Half-Angle Identities; Product-Sum Identities (Sum-to-Product and Product-to-Sum); Power-Reducing Identities; Proving Trigonometric Identities (with Sum, Difference, Double-Angle, Half-Angle, and Power-Reducing Identities); Solving Trigonometric Equations using Basic Algebraic Methods and Factoring; Solving Trigonometric Equations using Identities (Basic, Sum of Angles, Difference of Angles, Double-Angle, Half-Angle, and Product-Sum Identities)
Polar and Parametric Equations Topics
The Polar Coordinate System; Graphing Polar Coordinates; The Polar Distance Formula; Basic Polar Equations (Lines and Circles); Types and Tests for Symmetry; Maximum r-Values and Zeros of Polar Equations; Classifying Classic Polar Curves (Circles, Limaçons, Lemniscates, Roses, Spirals); Converting Polar and Rectangular Coordinates; Converting Polar and Rectangular Equations; Writing Complex Numbers in Polar Form; Multiplying and Dividing Complex Numbers; Powers of Complex Numbers; Roots of Complex Numbers; Graphing Parametric Equations; Writing Parametric Equations in Rectangular Form; Projectile Motion
Vectors Topics
Naming Vectors; Types of Vectors (Equivalent, Parallel, Opposite); Proving Vectors are Equivalent; Component Form of a Vector; Finding Magnitude and Direction; Operations with Vectors; Unit Vectors; Standard Unit Vectors; Writing Vectors as a Linear Combination; Writing a Vector in Trigonometric Form; Applications: Resultant Force and Velocity Vectors; Horizontal and Vertical Components of a Vector; Dot Products; Orthogonal Vectors; Finding the Angle Between Vectors; Vector Projections; Vector Projections Applications: Force and Work; Three-Dimensional Coordinate System; Vectors in 3D Space: Component Form, Linear Combinations, Magnitude, Operations, Dot Products, and Angle between Vectors
Conic Sections Topics
Circles (graphing and writing equations); Ellipses (graphing, writing equations, eccentricity); Hyperbolas (graphing, writing equations, eccentricity); Parabolas (graphing and writing equations); Applications of Conic Sections; Identifying Conics in General Conic Form (using the discriminant); Converting General Conic Form to Standard Form; Polar Forms of Conic Equations; Graphing Conics in Polar Form; Converting Polar Form to Rectangular Form
Systems of Equations and Matrices Topics
Two-Variable Systems of Linear Equations Review (Graphing, Substitution, and Elimination Methods); Two-Variable Systems of Linear Equations Applications; Nonlinear Systems of Equations (Solve Graphically and Algebraically); Three-Variable Systems of Equations; Three-Variable System of Equations Applications; Matrix Addition, Subtraction, and Scalar Multiplication; Multiplying Matrices; Determinants; Inverse Matrices; Matrices on the Graphing Calculator; Solving Systems of Equations with Cramer's Rule; Solving Systems of Equations with Inverse Matrices; Solving Systems of Equations with Gaussian Elimination and Augmented Matrices; Solving Systems of Equations with Gauss-Jordan Elimination; Recognizing Special Solutions (No Solution and Infinitely Many Solutions); Partial Fractions (Proper and Improper Expressions); Partial Fractions with Special Case Factors: Repeated Linear and Prime Quadratic
Sequences, Series, and Induction Topics
Explicit vs. Recursive Sequences; Writing the Explicit and Recursive Equation of a Sequence; Arithmetic Sequences (writing formulas, finding terms, and finding arithmetic means); Geometric Sequences (writing formulas, finding terms, and finding arithmetic means); Series and Summations; Arithmetic Series; Geometric Series; Infinite Geometric Series (convergent vs. divergent); Applications; Mathematical Induction; Expanding Binomials using Pascal's Triangle; Expanding Binomials using the Binomial Term; Finding a Specific Term a Binomial Expansion
Introduction to Calculus Topics
Limit Notation; Writing End Behavior in Limit Notation; Limits at a Certain Value; Finding Limits Graphically; Limits that Fail to Exist; One-Sided Limits; Finding Limits Algebraically (Properties of Limits and Direct Substitution); More Techniques: Factoring and Rationalizing to Evaluate a Limit; Limits at Infinity of Power, Polynomial, Reciprocal, and Rational Functions; Limits of Sequences; Tangent Lines; Derivative of a Function (Using a limit or derivative rules); Average vs. Instantaneous Rate of Change; Average vs. Instantaneous Velocity
