# Course Topics

Our LMS provides pre-built math courses online for your math classroom. These templates for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Trigonometry, Precalc, and Calculus concepts are easily edited to meet any course, syllabus, or calendar. This online math program is always free for educators.

## PREALGEBRA

#### Varsity Learning covers the following topics in our Prealgebra Course Template

 Topic A Whole Numbers A.1 Place Value and Names for Numbers A.2 Addition with Whole Numbers A.3 Rounding and Estimating Answers A.4 Subtraction with Whole Numbers A.5 Multiplication with Whole Numbers A.6 Division with Whole Numbers A.7 Powers and Exponents A.8 Order of Operations
 Topic B Introduction to Algebra B.1 Positive and Negative Numbers B.2 Addition with Negative Numbers B.3 Subtraction with Negative Numbers B.4 Multiplication with Negative Numbers B.5 Division with Negative Numbers B.6 Simplifying Algebraic Expressions
 Topic C Fractions & Mixed Numbers C.1 The Meaning and Properties of Fractions C.2 Prime Numbers, Factors, and Reducing to Lowest Terms C.3 Multiplication with Fractions C.4 Division with Fractions C.5 Addition and Subtraction of Fractions C.6 Mixed-Number Notation C.7 Multiplication and Division with Mixed Numbers C.8 Addition and Subtraction with Mixed Numbers C.9 Order of Operations C.10 Complex Fractions
 Topic D Solving Equations D.1 The Distributive Property and Algebraic Expressions D.2 The Addition Property of Equality D.3 The Multiplication Property of Equality D.4 Linear Equations in One Variable D.5 Applications D.6 Evaluating Formulas
 Topic E Decimals E.1 Decimal Notation, Place Value, and Rounding E.2 Addition and Subtraction with Decimals E.3 Multiplication with Decimals E.4 Division with Decimals E.5 Fractions and Decimals E.6 Square Roots and the Pythagorean Theorem
 Topic F Ratio & Proportion F.1 Ratios F.2 Rates and Unit Pricing F.3 Solving Equations by Division F.4 Proportions F.5 Applications of Proportions F.6 Similar Figures
 Topic G Percent G.1 Percents, Decimals, and Fractions G.2 Basic Percent Problems G.3 General Applications of Percent G.4 Sales Tax and Commission G.5 Percent Increase or Decrease, and Discount G.6 Interest
 Topic H Measurement H.1 Unit Analysis I: Length H.2 Unit Analysis II: Area and Volume H.3 Unit Analysis III: Weight H.4 Converting Between the Two Systems, and Temperature H.5 Operations with Time and Mixed Units

## ALGEBRA 1

#### Varsity Learning covers the following topics in our Algebra 1 Course Template

 Topic A Prealgebra Review A.1 Factors and Simplifying Fractions A.2 Operations with Fractions A.3 Decimal Notation A.4 Operations with Decimals A.5 Percents, Decimals, and Fractions A.6 Exponents and Order of Operations
 Topic B Real Numbers and Algebraic Expressions B.1 Real Numbers B.2 Addition and Subtraction of Real Numbers B.3 Multiplication of Real Numbers B.4 Division of Real Numbers B.5 Properties of Real Numbers B.6 Simplifying Expressions
 Topic C Linear Equations and Inequalities in One Variable C.1 Addition Property of Equality C.2 Multiplication Property of Equality C.3 Solving Linear Equations in One Variable C.4 Formulas C.5 Applications: Number, Age, Perimeter, Coin Problems C.6 Applications: Integer, Interest, Triangle, Miscellaneous Problems C.7 Linear Inequalities in One Variable
 Topic D Graphing Linear Equations and Inequalities in Two Variables D.1 The Rectangular Coordinate System D.2 Solutions and Graphs of Linear Equations D.3 Graphing Linear Equations Using Intercepts D.4 Graphing Linear Equations using Slope D.5 Finding the Equation of a Line D.6 Graphing Linear Inequalities in Two Variables
 Topic E Exponents and Polynomials E.1 Multiplication with Exponents and Scientific Notation E.2 Division with Exponents and Negative Exponents E.3 Operations with Monomials E.4 Addition and Subtraction of Polynomials E.5 Multiplication of Polynomials E.6 Special Products E.7 Dividing a Polynomial by a Monomial E.8 Dividing a Polynomial by a Polynomial
 Topic F Factoring Polynomials F.1 The Greatest Common Factor F.2 Factoring by Grouping F.3 Factoring Trinomials of the Form x2+bx+c F.4 Factoring Trinomials of the Form ax2+bx+c F.5 The Difference of Two Squares and Perfect Square Trinomials F.6 The Sum and Difference of Two Cubes F.7 Factoring: A General Review F.8 Solving Quadratic Equations by Factoring F.9 Applications of Quadratic Equations
 Topic G Rational Expressions and Equations G.1 Simplifying Rational Expressions G.2 Multiplication and Division of Rational Expressions G.3 Unit Analysis with Rational Expressions G.4 Addition and Subtraction of Rational Expressions G.5 Equations Involving Rational Expressions G.6 Complex Fractions G.7 Proportions G.8 Variation
 Topic H Systems of Linear Equations H.1 Solving Linear Systems by Graphing H.2 The Substitution Method H.3 The Elimination Method H.4 Systems of Linear Inequalities H.5 Applications of Systems of Equations

## GEOMETRY

#### Varsity Learning covers the following topics in our Geometry Course Template

 Topic A The Basics A.1 The Ruler Postulate and Absolute Value A.2 Lines and Angles A.3 Midpoint Formula A.4 Angle Pairs A.5 The Distance Formula A.6 Transformations
 Topic B Inductive and Deductive Reasoning B.1 Patterns and Inductive Reasoning B.2 Conditional Statements B.3 Deductive Reasoning B.4 Biconditional Statements B.5 Proofs with Algebra B.6 Proofs with Segments and Angles
 Topic C Parallel and Perpendicular Lines C.1 Lines and Angles C.2 Parallel Lines and Transversals C.3 Proving Lines Parallel C.4 Perpendicular Lines C.5 Parallel and Perpendicular Lines in the Coordinate Plane
 Topic D Congruent Triangles D.1 Angles and Triangles D.2 Congruence with Triangles D.3 Proving Triangles are Congruent D.4 Isosceles, Equilateral and Right Triangles
 Topic E Properties of Triangles E.1 Perpendicular and Angle Bisectors E.2 Bisectors of Triangles E.3 Medians and Altitudes of Triangles E.4 Midsegments of Triangles E.5 Inequalities of Triangles
 Topic F Polygons and Quadrilaterals F.1 Properties and Attributes of Polygons F.2 Properties of Parallelograms F.3 Properties of Special Parallelograms F.4 Properties of Kites and Trapezoids
 Topic G Similarity G.1 Ratios and Proportions G.2 Ratios and Similar Polygons G.3 Triangle Similarity: AA, SSS, and SAS G.4 Applying Properties of Similar Triangles G.5 Using Proportional Relationships G.6 Dialations and Similarity in the Coordinate Plane
 Topic H Right Triangles and Trigonometry I H.1 The Pythagorean Theorem H.2 The Rectangular Coordinate System H.3 Definition I: Trigonometric Functions H.4 Introduction to Identities H.5 More on Identities
 Topic I Right Triangle And Trigonometry II I.1 Definition II: Right Triangle Trigonometry I.2 Calculators and Trigonometric Function of an Acute Angle I.3 Solving Right Triangles I.4 Applications I.5 Vectors: A Geometric Approach
 Topic J Extending Perimeter, Circumference and Area J.1 Developing Formulas for Triangles and Quadrilaterals J.2 Areas of Regular Polygons J.3 Radians and Degrees J.4 Circumference and Arc Length J.5 Area of Circles and Sectors J.6 Geometric Probability
 Topic K Conic Sections K.1 Parabolas K.2 Ellipses K.3 Hyperbolas K.4 Nonlinear Systems of Equations and Inequalities

## ALGEBRA 2

#### Varsity Learning covers the following topics in our Algebra 2 Course Template

 Topic A Real Numbers and Algebraic Expressions A.1 The Real Numbers A.2 Properties of Real Numbers A.3 Arithmetic with Real Numbers A.4 Exponents and Scientific Notation
 Topic B Linear Equations and Inequalities in One Variable B.1 Linear Equations B.2 Formulas B.3 Applications B.4 Interval Notation and Linear Inequalities B.5 Sets and Compound Inequalities B.6 Absolute Value Equations B.7 Absolute Value Inequalities
 Topic C Graphs of Equations, Inequalities, and Functions C.1 Graphs of Equations C.2 Introduction to Functions C.3 Function Notation C.4 Algebra and Composition with Functions C.5 Slope and Average Rate of Change C.6 Linear Functions C.7 Linear Inequalities
 Topic D Systems of Equations D.1 Solving Linear Systems D.2 Systems of Linear Equations in Three Variables D.3 Matrix Solutions to Linear Systems D.4 Determinants and Cramer’s Rule D.5 Applications of Systems of Equations D.6 Systems of Linear Inequalities and Applications
 Topic E Exponents and Polynomials E.1 Sums and Differences of Polynomials E.2 Multiplication of Polynomials E.3 Greatest Common Factor and Factoring by Grouping E.4 Factoring Trinomials E.5 Factoring Special Products E.6 Factoring: A General Review E.7 Solving Equations by Factoring
 Topic F Rational Expressions, Equations, and Functions F.1 Basic Properties and Reducing to Lowest Terms F.2 Multiplication and Division of Rational Expressions F.3 Addition of Rational Expressions F.4 Subtraction of Rational Expressions F.5 Rational Equations F.6 Applications F.7 Complex Rational Expressions F.8 Variation
 Topic G Rational Exponents and Radicals G.1 Rational Exponents G.2 Simplifying Radicals G.3 Addition and Subtraction of Radical Expressions G.4 Multiplication and Division of Radical Expressions G.5 Radical Equations and Functions G.6 Complex Numbers
 Topic H Quadratic Equations and Functions H.1 Completing the Square H.2 The Quadratic Formula H.3 The Discriminant and Multiplicity H.4 Equations Quadratic in Form H.5 Graphing Quadratic Functions H.6 Polynomials and Rational Inequalities
 Topic I Exponential and Logarithmic Functions I.1 Exponential Functions and Applications I.2 Inverse Functions I.3 Logarithmic Functions and Applications I.4 Properties of Logarithms I.5 Common and Natural Logarithms with Applications I.6 Exponential Equations, Change of Base, and Applications
 Topic J Conic Sections J.1 The Distance Formula J.2 Circles J.3 Parabolas J.4 Ellipses J.5 Hyperbolas J.6 Nonlinear Systems of Equations and Inequalities
 Topic K Sequence and Series K.1 Sequences and Recursion Formulas K.2 Arithmetic and Geometric Series K.3 Arithmetic Sequences K.4 Geometric Sequences K.5 The Binomial Expansion

## TRIGONOMETRY

#### Varsity Learning covers the following topics in our Trigonometry Course Template

 Topic A The Six Trigonometric Functions A.1 Angles, Degrees, and Special Triangles A.2 The Rectangular Coordinate System A.3 Definition I: Trigonometric Functions A.4 Introduction to Identities A.5 More on Identities
 Topic B Right Triangle Trigonometry B.1 Definition II: Right Triangle Trigonometry B.2 Calculators and Trigonometric Function of an Acute Angle B.3 Solving Right Triangles B.4 Applications B.5 Vectors: A Geometric Approach
 Topic C Radian Measure C.1 Reference Angle C.2 Radians and Degrees C.3 Definition III: Circular Functions C.4 Arc Length and Area of a Sector C.5 Velocities
 Topic D Graphing and Inverse Functions D.1 Basic Graphs D.2 Amplitude Reflection and Period D.3 Vertical Translation and Phase Shift D.4 The Other Trigonometric Functions D.5 Finding an Equation From its Graph D.6 Inverse Trigonometric Functions
 Topic E Identities and Formulas E.1 Sum and Difference Formulas E.2 Double-Angle Formulas E.3 Half-Angle Formulas E.4 Additional Identities
 Topic F Equations F.1 Solving Trigonometric Equations F.2 More on Trigonometric Equations F.3 Trigonometric Equations Involving Multiple Angles F.4 Parametric Equations
 Topic G Triangles G.1 Law of Sines G.2 The Ambiguous Case G.3 The Law of Cosines G.4 The Area of a Triangle G.5 Vectors: An Algebraic Approach G.6 Vectors: The Dot Product
 Topic H Complex Numbers and Polar Coordinates H.1 Complex Numbers H.2 Trigonometric Form for Complex Numbers H.3 Products and Quotients in Trigonometric Form H.4 Roots of a Complex Number H.5 Polar Coordinates H.6 Equations in Polar Coordinates and Their Graphs
 Topic I Introduction to Functions I.1 Introduction to Functions I.2 The Inverse of a Function
 Topic J Exponential and Logarithmic Functions J.1 Exponential Functions J.2 Logarithms are Exponents J.3 Properties of Logarithms J.4 Common Logarithms and Natural Logarithms J.5 Exponential Equations and Change of Base

## PRECALCULUS

#### Varsity Learning covers the following topics in our Precalculus Course Template

 Topic A Functions A.1 Functions and Function Notation A.2 Domain and Range A.3 Rates of Change and Behavior of Graphs A.4 Composition of Functions A.5 Transformation of Functions A.6 Absolute Value Functions A.7 Inverse Functions
 Topic B Linear Functions B.1 Linear Functions B.2 Graphs of Linear Functions B.3 Modeling with Linear Functions B.4 Fitting Linear Models to Data
 Topic C Polynomial and Rational Functions C.1 Complex Numbers C.2 Quadratic Functions C.3 Power Functions and Polynomial Functions C.4 Graphs of Polynomial Functions C.5 Dividing Polynomials C.6 Zeros of Polynomial Functions C.7 Rational Functions C.8 Inverses and Radical Functions C.9 Modeling Using Variation
 Topic D Exponential and Logarithmic Functions D.1 Exponential Functions D.2 Graphs of Exponential Functions D.3 Logarithmic Functions D.4 Graphs of Logarithmic Functions D.5 Logarithmic Properties D.6 Exponential and Logarithmic Equations D.7 Exponential and Logarithmic Models D.8 Fitting Exponential Models to Data
 Topic E Introduction to Trigonometric Functions E.1 Angles E.2 Unit Circle: Sine and Cosine Functions E.3 The Other Trigonometric Functions E.4 Right Triangle Trigonometry
 Topic F Periodic Functions F.1 Graphs of the Sine and Cosine Functions F.2 Graphs of the Other Trigonometric Functions F.3 Inverse Trigonometric Functions
 Topic G Trigonometric Identities and Equations G.1 Solving Trigonometric Equations with Identities G.2 Sum and Difference Identities G.3 Double-Angle, Half-Angle, and Reduction Formulas G.4 Sum-to-Product and Product-to-Sum Formulas G.5 Solving Trigonometric Equations G.6 Modeling with Trigonometric Equations
 Topic H Further Applications of Trigonometry H.1 Non-right Triangles: Law of Sines H.2 Non-right Triangles: Law of Cosines H.3 Polar Coordinates H.4 Polar Coordinates: Graphs H.5 Polar Form of Complex Numbers H.6 Parametric Equations H.7 Parametric Equations: Graphs H.8 Vectors
 Topic I Systems of Equations and Inequalities I.1 Systems of Linear Equations: Two Variables I.2 Systems of Linear Equations: Three Variables I.3 Systems of Nonlinear Equations and Inequalities: Two Variables I.4 Partial Fractions I.5 Matrices and Matrix Operations I.6 Solving Systems with Gaussian Elimination I.7 Solving Systems with Inverses I.8 Solving Systems with Cramer’s Rule
 Topic J Analytic Geometry J.1 The Ellipse J.2 The Hyperbola J.3 The Parabola J.4 The Rotation of Axes J.5 Conic Sections in Polar Coordinates
 Topic K Sequences, Probability, and Counting Theory K.1 Sequences and Their Notations K.2 Arithmetic Sequences K.3 Geometric Sequences K.4 Series and Their Notations K.5 Counting Principles K.6 Binomial Theorem K.7 Probability
 Topic L Introduction to Calculus L.1 Finding Limits: Numerical and Graphical Approaches L.2 Finding Limits: Properties of Limits L.3 Continuity L.4 Derivatives