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Algebra Review

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Overview

Embark on a comprehensive algebra review covering a wide range of topics from basic equations to advanced concepts. Explore solving equations with grouping symbols, working with various conic sections, analyzing polynomial functions, and mastering matrix operations. Delve into logarithms, complex numbers, and trigonometric ratios while honing skills in factoring, graphing, and applying fundamental theorems. This 5-hour educational journey covers over 200 essential algebraic concepts, providing a solid foundation for further mathematical studies and problem-solving applications.

Syllabus

Solving Equations with Grouping Symbols.
Equations in Two Variables.
Equation of a Parabola.
Equation of a Hyperbola.
Equation of a Circle.
End Behavior of a Polynomial Function.
Ellipses.
Elimination using Subtraction.
Elimination using Multiplication.
Elimination using Addition.
Domain and Range.
Division Property of Equality.
Dividing Rational Expressions.
Dividing Integers.
Dividing Fractions.
The Distributive Property.
Distance Formula.
Direct Variation.
Dimensional Analysis.
Dilations.
Descartes' Rule of Signs.
Depressed Polynomials and Factor Theorem.
Cubic Functions.
Cramer's Rule.
Coordinate (Cartesian) Planes.
Consecutive Integers.
Conjugates, Part Two.
Conjugates.
Congruent Triangles.
Conditional Statements.
Compound Interest.
Compound Inequalities.
Composition of Functions.
Complex Numbers.
Complex Fractions.
Complex Conjugates Theorem.
Complex Conjugates.
Completing the Square.
Commutative Property of Multiplication.
Commutative Property of Addition.
Common Logarithms.
Classifying Line Slopes.
Circumference of a Circle.
Change of Base Formula.
The Binomial Theorem.
Bilateral Symmetry.
Best-Fit Lines.
Solving Basic Equations.
Axis of Symmetry of a Parabola.
Associative Property of Multiplication.
Associative Property of Addition.
Arithmetic Series.
Arithmetic Sequences.
Area of a Rectangle.
Area of a Triangle.
Area of a Trapezoid.
Area of a Parallelogram.
Area of Irregular Figures.
Area of a Circle.
Algebraic Fractions.
Algebraic Expressions.
Addition and Subtraction Properties of Inequalities.
Additive Inverse Property.
Additive Identity.
Addition and Subtraction of Matrices.
Addition Property of Equality.
Adding and Subtracting Radical Expressions.
Adding Polynomials.
Adding Integers.
Absolute Value Inequalities.
Absolute Value.
Zero Product Property.
Prime Factorization with Factor Trees.
Prime Numbers and Composite Numbers.
Precision and Significant Digits.
Powers and Exponents.
Power Property of Logarithms.
Power of a Quotient.
Power of a Product.
Power of a Power.
Polynomials.
Polynomial Functions.
Polygons.
Point-Slope Form.
Planes and Polyhedrons.
Perimeter of a Rectangle.
Percent Proportions.
Percent of Change.
Pascal's Triangle.
Order of Operations.
Ordered Triples.
Definition of nth Roots.
Negative Exponents.
Natural Numbers and Whole Numbers.
Solving Multistep Inequalities.
Multiplying Rational Expressions.
Multiplying Radical Expressions.
Multiplying a Polynomial by a Monomial.
Multiplying Matrices.
Multiplying Integers.
Multiplying Fractions.
Multiplication and Division Properties of Inequalities.
Multiplicative Property of -1.
Multiplicative Identity.
Multiplication Property of Equality.
More Types of Angles.
Monomials.
Mixture Problems.
Mixed Numbers.
Mixed Expressions.
Midpoint Formula.
Matrix Translations.
Matrix Rotations.
Matrix Reflections.
Matrix Dilations.
Matrices.
Logarithms.
Logarithmic Inequalities.
Logarithmic Equations.
The Location Principle.
Parallel Lines and Perpendicular Lines.
Rules for Line Intersections.
Linear Interpolation.
Linear Extrapolation.
Linear Equations.
Like Radical Expressions.
Adding and Subtracting Like Fractions.
Least Common Multiple(LCM).
Least Common Denominator(LCD).
Joint Variation.
Iteration.
Irrational Numbers and Real Numbers.
Inverse Variation.
Inverse of a 2 x 2 Matrix.
Inverse Property of Multiplication.
Inverse of a Relation.
Inverse Functions.
Integers.
Infinite Geometric Series.
Inequalities.
Imaginary Numbers.
Identity Matrix.
Greatest Common Factor(GCF).
Graphing Systems of Inequalities.
Graphing Quadratic Functions.
Graphing Inequalities.
Graphing Cubic Functions.
Geometric Series.
Geometric Sequences.
Geometric Means.
Fundamental Theorem of Algebra.
Fundamental Counting Principle.
Functions.
Function Notation.
Writing Fractions as Decimals.
Formulas.
FOIL Method for Multiplying Binomials.
The Fibonacci Sequence.
Factors.
Factoring Quadratic Trinomials.
Factoring Perfect Square Trinomials.
Factoring Differences of Squares.
Factoring by Grouping.
SPSS - Factorial ANOVA, Two Independent Factors.
Factorials.
Exponential Inequalities.
Exponential Growth.
Exponential Functions.
Exponential Equations.
Exponential Decay.
Solving Equations with Variables.
Zero Exponent.
Volume of a Pyramid.
Volume of a Prism.
Volume of a Cylinder.
Volume of a Cone.
Vertical Line Test.
Vertex Form.
Adding and Subtracting Unlike Fractions.
Uniform Motion Problems.
Types of Angles.
Trigonometric Ratios (Sine, Cosine, Tangent).
Trichotomy Property.
Triangles.
Transitive Property of Equality.
Transformations.
Third-Order Determinants.
The Natural Base (e).
The Discriminant.
Terms, Coefficients, and Constants.
Systems of Equations.
Synthetic Division.
Symmetric Property of Equality.
Surface Area of Rectangular Prisms.
Surface Area of Cylinders.
Surface Area of a Cone.
Subtraction Property of Equality.
Subtracting Polynomials.
Subtracting Integers.
Substitution.

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