Course Topics

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

Topic I	Radical Expressions and Equations
I.1	Radical Expressions
I.2	Simplifying Radicals
I.3	Addition and Subtraction of Radicals
I.4	Multiplication and Division of Radicals
I.5	Radical Equations
I.6	Rational Exponents
I.7	Graphs of Radical 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

CALCULUS

Varsity Learning covers the following topics in our Calculus Course Template

Topic A	Functions, Limits and Rates of Change
A.1	Introduction to Functions and Relations
A.2	Algebra and Composition with Functions
A.3	Slope, Rares of Change, and Linear Functions
A.4	Introduction to Limits
A.5	Functions and Continuity
A.6	Average and Instantaneous Rates of Change

Topic B	Differentiation: The Language of Change
B.1	Derivative of a Function and Two Interpretations
B.2	Differentiating Products and Quotients
B.3	Higher Order Derivatives
B.4	The Chain Rule and General Power Rule
B.5	Implicit Differentiation

Topic C	Applying the Derivative
C.1	The First Derivative and the Behavior of Functions
C.2	The Second Derivative and the Behavior of Functions
C.3	Applications of the Derivative: Optimization
C.4	Applications of the Derivative in Business and Economics

Topic D	Derivatives of Exponential and Logarithmic Functions
D.1	The Exponential Functions
D.2	The Natural Logarithm Function
D.3	Differentiating the Natural Logarithm Function
D.4	Differentiating the Natural Exponential Function

Topic E	Integration: The Language of Accumulation
E.1	Antidiffernetiation and the Indefinite Integral
E.2	Integration by Substitutions
E.3	The Definite Integral
E.4	The Definite Integral and Area
E.5	Improper Intergrals
E.6	Integration by Parts

Topic F	Applications of Integration
F.1	Area of Regions in the Plane
F.2	Consumer’s and Producer’s Surplus
F.3	Annuities and Money Streams
F.4	Differential Equations
F.5	Applications of Differential Equations
F.6	Probability

Topic G	Calculus of Functions of Several Variables
G.1	Functions of Several Variables
G.2	Partial Derivatives
G.3	Optimization of Functions of Two Variables
G.4	Constrained Maxima and Minima
G.5	The Total Differential
G.6	Double Intergrals as Volume
G.7	The Average Value of a Function