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PreCalculus

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Overview

This course on PreCalculus aims to help learners understand and apply various mathematical concepts and problem-solving techniques. By the end of the course, students will be able to solve polynomial inequalities, find the inverse of functions, graph logarithmic and polynomial functions, evaluate trigonometric equations, and apply laws of sines and cosines. The course covers topics such as algebraic tests for symmetry, writing trig functions as algebraic expressions, and graphing rational functions. The teaching method includes step-by-step examples, multiple problem-solving exercises, and explanations of mathematical strategies. This course is intended for individuals looking to enhance their math skills, particularly those preparing for advanced math courses or exams.

Syllabus

Tangent Sum and Difference Formulas How to Use.
Solving Polynomial Inequalities Algebraically Using Number Line.
Given One Imaginary Zero Find All the Zeros of the Function.
Find Remaining Factors When Given 1 Factor (Synthetic Division).
What Ticket Price Maximizes Revenue? (Quadratic Word Problem Precalculus).
Find the Inverse of a Function with Domain Restrictions.
Find the Inverse of a Function Algebraically.
Algebraic Tests to Check Symmetry With Respect to X-Axis, Y-Axis, and Origin.
Writing a Sinusoidal Equation Given Max and Min (Example 1).
How to Find Slant Asymptote of a Rational Function.
Law of Sines (SSA) Ambiguous Case 2 Triangles Possible.
Determine Which Quadrant(s) Where Point (x,y) is Located Given Restrictions.
Find Reference Angle in Radians and Degrees (Formulas).
Law of Sines AAS, ASA, SSA Ambiguous Case.
Is a Function Even, Odd, or Neither?.
Graphing Logarithmic Functions with Transformations.
Graphing Polynomial Functions Using End Behavior, Zeros, and Multiplicities.
Testing for Symmetry Versus Even or Odd (PreCalculus).
Writing Trig Functions as Algebraic Expressions.
Find the Domain of a Function (Precalculus) Given Equation (4 Examples).
Find the Average Rate of Change of the Function from x1 to x2 (Precalculus).
Write a Quadratic Equation in Standard Form by Completing the Square (3 Examples).
Find the Equation of a Circle Given Endpoints of Diameter.
Writing a Sinusoidal Equation Given Max and Min (Example 2).
Parabola Equation Using Distance Formula.
Cramer's Rule Solving a System of Linear Equations 2x2.
Draw an Angle in Radians (Standard Position).
Linear Programming (Optimization) 2 Examples Minimize & Maximize.
Solving Exponential Equations.
Write Recursive Formulas for Sequences (2 Methods).
Completing the Square to Solve a Quadratic Equation (3 Examples).
Graphing Rational Functions Step-by-Step (Complete Guide 3 Examples).
Solve an Exponential Equation by Getting Bases to be Equal.
Find Horizontal Asymptote of a Rational Function.
Difference Quotient - How to Simplify (3 Types).
Sequences and Series Introduction.
Solving Trigonometric Equations - How to Write General Solution.
Law of Sines and Law of Cosines (4 Examples).
Evaluating Inverse Trigonometric Functions (arcsin, arccos, arctan) Using Unit Circle.
Verifying Trigonometric Identities Easily - Strategy Explained (14 Examples).
Graphing Piecewise Functions - 2 Methods.
Graphing Sine and Cosine Functions with Transformations (Multiple Examples).
Solving Exponential and Logarithmic Equations (Multiple Examples).
Partial Fraction Decomposition All Types (Quick Review).
Radians Intro (What are they? Converting Units, Draw Standard Position).
Evaluating Limits Given a Graph.
Graphing Sine, Cosine, Cosecant, Secant, Tangent & Cotangent (Complete Guide).
Factoring Polynomials Completely - All Types (100 Problems & Free Worksheet).
Sketching Rational Functions Step by Step (6 Examples!).
Equation of Parabola Given 3 Points (System of Equations).
Approximating Limits Using a Table with Ti84 Calculator.
Solving a System 3 Equations (General Solution).
Elimination 3 Variables (Multiple Examples).
Elimination 3 Variables 3 Equations.
Solving Trigonometric Equations Multiple Angles.
Sequences and Series (Arithmetic & Geometric) Quick Review.
Composition of Functions (Examples).
Plotting Points in 3 Dimensions.
PreCalculus Final Exam Review 2nd Quarter.
PreCalculus Final Exam Review First Quarter.
Transformations of Parent Graphs (Advanced).
Verifying Functions are Inverses.
Probability Defective Units Example.
Vertex Form for Quadratic Functions (by Completing the Square).
Double Intercept Equation of a Line.
Absolute Value Function (How to Graph).
Is y a Function of x?.
Equation of Sphere in Standard Form.
Parametric Equations Sketching a Curve (3 Examples).
Descartes Rule of Signs to Determine Number of Positive & Negative Zeros.
Distance and Midpoint Formula in 3 Dimensions.
Distinguishable Permutations of Letters in a Word.
Arithmetic Sequence (Explicit Formula).
Geometric Sequence (Explicit Formula).
Fundamental Counting Principle.
Permutations Combinations Factorials & Probability.
Factorial Expressions (Simplifying).
Binomial Expansion Find a Specific Term.
Binomial Expansion Finding Coefficient.
Graphing Sine and Cosine Functions (More Challenging Examples).
Greatest Integer Function How to Graph.
End Behavior of Polynomial Functions Using Leading Coefficient Test.
Converting Polar Equations to Rectangular Equations.
Converting Rectangular Equations to Polar Equations.
Parent Function Graphs Transformations (Shift, Stretch, Reflect).
How to Graph Tan (Tangent) - More Challenging.
Condensing Logarithms into a Single Log (More Challenging Examples).
Expanding Logarithmic Expressions (More Challenging Examples).
Sine or Cosine Writing Equations Given Graph.
Convert from Rectangular to Polar Coordinates.
Convert from Polar to Rectangular Coordinates.
Polar Coordinates How to Graph Points.
Write Equation of a Parabola Given Vertex and Directrix.
Equation of Parabola Given Focus and Directrix.
Equation of Ellipse Given Vertices and Foci.
Ellipse Equation Given Eccentricity and Foci.
Ellipse Equation Given Vertices and Eccentricity.
Hyperbola Equation Given Asymptotes and Vertices.
Determine if an Equation is a Hyperbola, Ellipse, Parabola or Circle.
Piecewise Functions - How to Evaluate.
Row Reduced Echelon Form.
Partial Fraction Decomposition All Types.
Gaussian Elimination with Back Substitution.
Finding Relative Maximums and Minimums Using Difference Quotient.
Recursive Formulas How to Write.
Logs Everything You Need to Know.
What is a derivative?.
Writing Logarithms in Exponential Form.
Arithmetic Sequence Formula Given 2 Terms Easy Method.
Bearing Math Problems.
Time to Triple Compounding Continuously.
Time to Double Compounding Continuously.
Find Inverse and State Domain Restriction.
How to Graph Arctan (tangent inverse).
How to Graph Arccos (cosine inverse).
How to Graph Arcsin (sine inverse).
Understanding Even Odd Identities.
Cofunction Identities (Trigonometry) - Understanding Them.
Graphing Exponential Functions with Base e.
Converting from Minutes and Seconds to Degrees.
Solving Radical Equations (More Challenging).
Solving Radical Equations.
Convert from Degrees to Degrees, Minutes, Seconds.
Deriving the Quadratic Formula by Completing the Square.
Exponential Growth Model Example.
Writing a Polynomial Given Zeros.
Determining if a Function is a Polynomial.
One-to-One Property to Solve Logarithmic Equations.
Rewriting Logs in Exponential Form.
One to One Property for Exponential Equations.
Completing the Square to Solve Quadratic Equations.
Finding Zeros of Rational Functions.
Half Life Formula & Example.
Domain of Logarithmic Functions.
Find Two Positive Real Numbers Whose Product is a Maximum (PreCalculus).
Describing End Behavior Using Limit Notation.
Finding Horizontal and Vertical Asymptotes Graphing Rational Functions.
Holes, Removable Discontinuities, Graphing Rational Functions.
Completing the Square Leading Coefficient (More Challenging Examples).
Sum of 2 Squares Factoring.
Find the Equation of a Quadratic (Parabola) Given 3 Points.
Inverse Variation or Direct Variation? (Given a Table).
Powers of i (Simplifying).
Solving Quadratic Inequalities Using Sign Analysis.
Volume of Open Box Made From Rectangle with Squares Cut Out.
Decomposing Functions Using Composition of Functions.
Interval notation for where functions Increase, Decrease, Constant.
Shifting, Stretching and Reflecting Parent Function Graphs.
Graphing Step Functions.
Piecewise Functions Graphing.
Interval Notation (What is It?).
Absolute Value Inequality Special Cases.
Finding a Sinusoidal Equation Given a Maximum and Minimum.
Half Angle Formula Positive or Negative?.
Verifying Trigonometric Identities (Examples).
What are Imaginary Numbers?.
How to Graph Tangent (Simplified).
Ellipses Vs. Hyperbolas Similarities and Differences.
Matrices Quick Tip for Rotating and Reflecting.
Which Way Does the Hyperbola Open?.
Finding Equation of Parabola Given Vertex and Directrix.
Finding Equation of Parabola Given Focus and Vertex.
Finding Tangent Line to a Parabola Using Distance Formula.
Finding Distance from Point to Line (Formula).
Finding Angle Between 2 Lines (Formula).
Finding Angle of Inclination of a Line.
Heron's Area Formula for Triangles.
Master the Unit Circle!.
Equation of Hyperbola Given Asymptotes and Foci.
TI84 TI83 Pascal's Triangle Binomial Expansion.
Area under a Curve - PreCalculus.
Parametric Equations - How to Eliminate the Parameter.
Bouncing Ball Distance Traveled Example.
Writing Summations in Sigma Notation.
More Difference Quotient Examples.
Derivative at a Point Using Difference Quotient.
Area of a Region using Limits.
Limits at Infinity.
Tangent Line Using Difference Quotient.
Finding Limits Precalculus Methods.
Expanding and Condensing Logs (Challenging).
Solving (Challenging) Log Equations Different Bases.
TI84 TI83 Calculating Standard Deviation.
Using Matrices to Solve Systems of Equations on Ti84 Calculator.
Cramer's Rule Matrices.
Inverse Matrices Solving Systems of Equations.
Inverse of a 2x2 Matrix.
Area of a Triangle Using Determinant.
Determinant of a Matrix - How to Find (2x2 & 3x3).
How to do Matrix Multiplication.
Matrices - Dimensions, Add, Subtract Scalar Multiplication.
Mathematical Induction Examples.
Probability Examples with Cards.
Writing Conic Sections in Standard Form.
Binomial Probability.
How to Use Permutations and Combinations.
Hyperbolas - How to Graph.
How to Graph Ellipses and Write the Equation.
How to Graph Parabolas and Write the Equation.
Binomial Expansion Theorem.
Sum of Infinite Geometric Series.
Sum of a Geometric Series.
Geometric Sequence Formula.
Sum of an Arithmetic Series Formula.
Arithmetic Sequence - Write Equation (Formula).
Partial Fractions Repeated Quadratic Factors.
Partial Fractions Quadratic Factors.
Partial Fractions Repeated Linear Factors.
Partial Fractions with Improper Fractions.
TI-84 TI-83 Finding Log Values.
Finding Relative Maximum and Relative Minimum Ti84 Ti83.
Zeros How to Find Ti84 Ti83.
Solving Systems of 3 Equations Elimination.
Solving Systems of Equations Elimination Method.
Substitution Method for Solving Systems of Equations.
Solve Systems of Linear Equations by Graphing.
Factoring by Grouping (4 terms).
Factoring Quadratic Form Trinomials.
How to factor the Sum of 2 Cubes.
Finding nth Roots of a Complex Number.
Complex Number to a Power Using DeMoiver's Theorem.
Multiply and Divide Complex Numbers in Trigonometric Form (Formulas).
Trigonometric Form of a Complex Number.
Compounding Continuously Pert Formula.
Compound Interest Formula.
Absolute Value of a Complex Number.
Angle Between 2 Vectors (Formula).
Dot Product to Multiply Vectors.
Inverse Trigonometric Functions Using Unit Circle to Find Angles Between 0 and 2 pi.
Half Angle Formulas - How to Use.
How to Use Double Angle Formulas.
Solving Rational Inequalities.
Rational Functions Graphing.
Intermediate Value Theorem.
Leading Coefficient Test.
Descartes Rule of Signs.
Rational Root Theorem.
Zeros - How to Find Using Factoring.
Complex Numbers Add, Subtract, Multiply, Divide.
How to Use the Remainder Theorem.
How to do Synthetic Division.
Sum and Difference Formulas.
Parabolas in General Form - How to Graph.
Graphing Parabolas in Intercept Form.
Graphing Parabolas in Vertex Form.
Adding and Subtracting Vectors.
Unit Vectors - How to find.
Vectors Finding the Direction.
Magnitude of a Vector.
Vectors Component Form.
How to Find the Inverse of a Function.
Composition of Functions - How to.
Difference Quotient - What is it? (PreCalculus).
Law of Cosines.
Parent Functions Transformations.
Polynmomial Long Division.
Domain of a Function (Given Equation or Graph) How to Find.
Circle Equation in Standard Form (How to Graph).
How to Test for Symmetry.
Is a Function Even or Odd?.
Vertical Line Test.
What is the Horizontal Line Test?.
Solving Trig Equations.
Unit Circle Finding Trig Values.
Reference Angles.
Coterminal Angles.
Simplifying Trigonometric Expressions (Using Identities).
Arc Length (Formula).
Area of a Sector How to Find (Formula Radians).
Converting Degrees to Radians.
Finding Complement and Supplement of an Angle (Radians & Degrees).
Exponential Functions (How to Graph).
Logarithmic Equations - How to Solve.
Expanding and Condensing Logs.
Logarithms (Logs) How to Graph.
Logarithms Change of Base Formula.
Evaluating Logarithms.
How to Graph Secant and Cosecant.
Graphing Tan and Cot.
Graphing Sin and Cos.
Linear Speed and Angular Speed.
Law of Sines (Trigonometry).

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Mario's Math Tutoring

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