SheLovesMath.com is a **free math website** that explains** math** in a simple way, and includes lots of examples, from Counting through Calculus.

Here are the topics that **She Loves Math** covers, as expanded below: **Basic Math**, **Pre-Algebra**, **Beginning Algebra**, **Intermediate Algebra**, **Advanced Algebra**, **Pre-Calculus**, **Trigonometry**, and **Calculus**.

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**Note**: Please let me know if you see any errors or have suggestions for this site at **lisa@shelovesmath.com**. Thanks!

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**Basic Math**

#### Decimals

#### Fractions

- Introduction to Fractions
- Adding Fractions, Simplifying Fractions
- Subtracting Fractions
- Multiplying Fractions
- Dividing Fractions
- Comparing Fractions
- Fractions Used in Cooking

#### Metric System

**Pre-Algebra**

#### Percents, Ratios, and Proportions

- Percentages and Percent Changes
- Ratios and Proportions
- Unit Multipliers
- Using Percentages with Ratios

#### Negative Numbers and Absolute Value

- Negative Numbers
- Absolute Value
- Adding and Subtracting Negative Numbers
- Multiplying and Dividing Negative Numbers

#### Powers, Exponents, Radicals, and Scientific Notation

#### Order of Operations PEMDAS

#### Introduction to Statistics and Probability

#### **Beginning Algebra**

#### Introduction to Algebra

#### Types of Numbers and Algebraic Properties

- Types of Numbers
- Algebraic Properties
- Summary of Algebraic Properties (Chart)
- Proper Algebraic Notation

#### Solving Algebraic Equations

#### Linear Inequalities

- Basic Linear Inequalities
- Inequalities
- Absolute Value and Inequalities
- Graphing Linear Inequalities with Two Variables

#### Coordinate System and Graphing Lines Including Inequalities

#### Coordinate System and Graphing Lines Including Inequalities (cont’d)

- Graphing Lines
- Obtaining an Equation for a Line
- Parallel and Perpendicular Lines
- Distance and Midpoint Formulas
- Graphing Linear Inequalities with Two Variables

#### Direct, Inverse, Joint and Combined Variation

- Direct or Proportional Variation
- Inverse or Indirect Variation
- Joint and Combined Variation
- Partial Variation

#### Introduction to the Graphing Display Calculator (GDC)

#### **Intermediate Algebra**

#### Word Problems in Algebra

- English to Math Translation
- Unit Rate Problem
- “Find the Numbers” Word Problems
- Percent Word Problem
- Percent Increase Word Problem
- Ratio/Proportion Word Problems
- Weighted Average Word Problem
- Consecutive Integer Word Problem
- Age Word Problem
- Money (Coins) Word Problem
- Mixture Word Problem
- Percent Mixture Word Problem
- Rate/Distance Word Problem
- Profit Word Problem
- Converting Repeating Decimal to Fraction Word Problem
- Inequality Word Problems
- Integer Function Problem
- Direct, Inverse, Joint and Combined Variation Word Problems
- Work Word Problems (in Rational Functions and Equations)
- Systems of Equations Word Problems
- More Word Problems using Rational Functions
- Absolute Value Word Problems

#### Systems of Linear Equations and Word Problems

- Introduction to Systems
- Solving Systems by Graphing
- Solving Systems with Substitution
- Solving Systems with Linear Combination or Elimination
- Types of Equations
- Word Problems with Systems

#### Algebraic Functions, including Domain and Range

- Algebraic Functions Versus Relations
- Vertical Line Test
- Domain and Range of Relations and Functions
- Finding the Domain Algebraically

#### Scatter Plots, Correlation, and Regression

#### Exponents and Radicals in Algebra

- Introducing Exponents and Roots (Radicals) with Variables
- Properties of Exponents and Roots
- Putting Exponents and Radicals in the Calculator
- Rationalizing Radicals
- Simplifying Exponential Expressions
- Solving Exponential and Radical Equations
- Solving Simple Radical Inequalities

#### Introduction to Multiplying Polynomials

#### Introduction to Quadratics

- Quadratics and the Parabola
- Graphing Quadratics (Parabolas)
- Standard Form to Vertex Form
- Solving for Roots with Quadratics
- Quadratic Transformations

#### Solving Quadratics by Factoring and Completing the Square

- Factoring Methods
- Completing the Square (Square Root Method)
- Completing the Square to get Vertex Form
- Obtaining Quadratic Equations from a Graph or Points
- Quadratics Review

#### Quadratic Inequalities

- Graphing Quadratic Inequality Functions
- Solving Quadratic Inequalities
- Quadratic Inequality Real World Example

#### Quadratic Applications

- Quadratic Projectile Problem
- Quadratic Trajectory (Path) Problem
- Optimization of Area Problem
- Maximum Profit and Revenue Problems
- Population Problem
- Linear Increase/Decrease Problem
- Pythagorean Theorem Quadratic Application
- Quadratic Inequality Problem
- Finding Quadratic Equations from Points or a Graph

#### Solving Absolute Value Equations and Inequalities

- Solving Absolute Value Equations
- Solving Absolute Value Inequalities
- Graphs of Absolute Value Functions
- Applications of Absolute Value Equations

#### Solving Radical Equations and Inequalities

- Radical Function Graphs
- Solving Radical Equations Algebraically
- Solving Radical Equations Graphically
- Solving Radical Inequalities Algebraically
- Solving Radical Inequalities Graphically

#### Imaginary (Non-Real) and Numbers

**Advanced Algebra**

#### Advanced Functions: Compositions, Even and Odd, and Extrema

- Adding, Subtracting, Multiplying and Dividing Functions
- Increasing, Decreasing and Constant Functions
- Extrema: Minimums and Maximums
- Even and Odd Functions
- Compositions of Functions (Composite Functions)
- Decomposition of Functions
- Domains of Composites
- Applications of Compositions

#### Inverses of Functions

- Introduction to Inverses
- Finding Inverses Graphically
- Finding Inverses Algebraically
- Inverse Functions with Restricted Domains
- Using Compositions of Functions to Determine if Functions are Inverses
- Inverses of Exponential and Logarithmic Functions

#### Parent Functions and Transformations

- Basic Parent Functions
- Generic Transformations of Functions
- Mixed Transformations
- Transformations in Function Notation
- Writing Transformed Equations from Graphs
- Rotational Transformations
- Transformations of Inverse Functions
- Absolute Value Transformations
- Applications of Parent Function Transformations

#### Absolute Value Transformations

- Transformations of the Absolute Value Parent Function
- Absolute Value Transformations of other Parent Functions

#### Piecewise Functions

- Introduction to Piecewise Functions
- Evaluating Piecewise Functions
- Graphing Piecewise Functions
- How to Tell if a Piecewise Function is Continuous or Non-Continuous
- Obtaining Equations from Piecewise Function Graphs
- Absolute Value as a Piecewise Function
- Transformations of Piecewise Functions
- Piecewise Function Word Problems

#### The Matrix and Solving Systems with Matrices

- Introduction to the Matrix
- Adding and Subtracting Matrices
- Multiplying Matrices
- Matrices in the Graphing Calculator
- Determinants, the Matrix Inverse, and the Identity Matrix
- Solving Systems with Matrices
- Solving Systems with Reduced Row Echelon Form
- Solving Matrix Equations
- Cramer’s Rule
- Number of Solutions when Solving Systems with Matrices
- Applications of Matrices

#### Introduction to Linear Programming

- Review of Inequalities
- Bounded and Unbounded Regions
- Inequality Word Problem
- Linear Programming Terms
- Linear Programming Word Problems

#### Advanced Factoring

- Revisiting Factoring Quadratics
- Factoring with Polynomials
- Factoring Sum and Difference of Cubes
- Factoring with Exponents

#### Rational Functions, Equations and Inequalities

#### Graphing Rational Functions, including Asymptotes

- Revisiting Direct and Inverse Variation
- Polynomial Long Division
- Asymptotes of Rationals
- Drawing Rational Graphs — General Rules
- Finding Rational Functions from Graphs or Points
- Applications of Rational Functions

#### Graphing and Finding Roots of Polynomial Functions

- Review of Polynomials
- Polynomial Graph and Roots
- End Behavior of Polynomials and Leading Coefficient Test
- Zeros (Roots) and Multiplicity
- Writing Equations for Polynomials
- Conjugate Zeros Theorem Problem

- Synthetic Division
- Rational Root Test
- Putting it All Together: Finding all Factors and Roots of a Polynomial Function
- Factor and Remainder Theorems
- DesCartes’ Rule of Signs
- Putting it All Together: Finding all Factors and Roots of a Polynomial Function
- Solving Polynomial Inequalities
- Polynomial Applications
- Revisiting Factoring to Solve Polynomial Equations

#### Exponential Functions

- Introduction to Exponential Functions
- Parent Graphs of Exponential Functions
- Transformations of Exponential Functions
- Writing Exponential Equations from Points and Graphs
- Exponential Function Applications
- Exponential Word Problems
- Solving Exponential Functions by Matching Bases
- Factoring to Solve with Exponents
- Exponential Regression
- Inverses of Exponential and Logarithmic Functions
- Exponential Inequalities

#### Logarithmic Functions

- Introduction to Logarithms
- Special Logarithms
- Using Logs (and Exponents) in the Graphing Calculator
- Parent Graphs of Logarithmic Functions
- Transformations of Log Functions
- Basic Log Properties, including Shortcuts
- Expanding and Condensing Logs
- Solving Exponential Equations using Logs
- Solving Log Equations
- Applications of Logs, including Half-Life
- Inverses of Exponential and Logarithmic Functions
- Logarithmic Inequalities

#### Solving Inequalities

- Linear Inequalities
- Inequality Word Problems
- Linear Inequalities in Two Variables
- Quadratic Inequalities
- Absolute Value Equations and Inequalities
- Radical Equations and Inequalities
- Using Inequalities to Find Domains of Composites
- Inequalities in Linear Programming
- Rational Functions Inequalities
- Polynomial Inequalities
- Exponential Inequalities
- Logarithmic Inequalities
- Trigonometry Inequalities

#### Solving Systems using Reduced Row Echelon Form

**Pre-Calculus**

#### Conics: Circles, Parabolas, Ellipses, and Hyperbolas

- Tables of Conics
- Circles
- Applications of Circles
- Parabolas
- Applications of Parabolas
- Ellipses
- Applications of Ellipses
- Hyperbolas
- Applications of Hyperbolas
- Identifying the Conic

#### Systems of Non-Linear Equations

#### Introduction to Vectors

#### Parametric Equations

- Introduction to Parametric Equations
- Parametric Equations in the Graphing Calculator
- Converting Parametric Equations to Rectangular Equations: Eliminating the Parameter
- Finding Parametric Equations from a Rectangular Equation
- Simultaneous Solutions
- Applications of Parametric Equations
- Projectile Motion Applications
- Parametric Form of the Equation of a Line in Space

#### Sequences and Series

- Introduction to Sequences and Series
- Summary of Formulas for Sequences and Series
- Sequences and Series Terms
- Explicit Formulas Versus Recursive Formulas
- Arithmetic Sequences
- Geometric Sequences
- Writing Formulas
- Arithmetic Series
- Summation Notation
- Geometric Series
- Applications of Sequences and Series

#### Binomial Expansion

**Trigonometry**

#### Right Triangle Trigonometry

#### Angles and the Unit Circle

#### Linear and Angular Speeds, Area of Sectors, and Length of Arcs

#### Graphs of Trig Functions

- Table of Trigonometric Parent Functions
- Graphs of the Six Trigonometric Functions
- Trig Functions in the Graphing Calculator

#### Transformations of Trig Functions

- T-Charts for the Six Trigonometric Functions
- Sine and Cosine Transformations
- Cosecant and Secant Transformations
- Tangent and Cotangent Transformations
- Transformations of all Trig Functions without T-Charts

#### The Inverses of Trigonometric Functions

- Introduction to Inverse Trig Functions
- Graphs of Inverse Functions
- Evaluating Inverse Trig Functions – Special Angles
- Trig Inverses in the Calculator
- Transformations of the Inverse Trig Functions
- Composite Inverse Trig Functions with Non-Special Angles

#### Solving Trigonometric Equations

- Solving Trigonometric Equations Using the Unit Circle
- Solving Trigonometric Equations – General Solutions
- Solving Trigonometric Equations with Multiple Angles
- Factoring to Solve Trigonometric Equations
- Solving Trigonometric Equations Using a Calculator
- Solving Trig Systems of Equation
- Trigonometric Inequalities

#### Trigonometric Identities

- Reciprocal and Quotient Identities
- Pythagorean Identities
- Solving with Reciprocal, Quotient and Pythagorean Identities
- Sum and Difference Identities
- Solving with Sum and Difference Identities
- Double Angle and Half Angle Identities
- Solving with Double and Half Angle Identities
- Trig Identity Summary and Mixed Identity Proofs

#### Law of Sines and Cosines and Areas of Triangles

- Review of Right Triangle Trig
- Law of Sines
- Law of Cosines
- Area of Triangles
- Applications/Word Problems

#### Polar Coordinates, Equations and Graphs

- Plotting Points Using Polar Coordinates
- Polar-Rectangular Point Conversions
- Drawing Polar Graphs
- Converting Equations from Polar to Rectangular
- Converting Equations from Rectangular to Polar
- Polar Graph Points of Intersection

#### Trigonometry and the Complex Plane

**Calculus (Differential)**

#### Introduction to Calculus

#### Differential Calculus Quick Study Guide

#### Limits and Continuity

- Introduction to Limits
- Finding Limits Algebraically
- Continuity and One Side Limits
- Continuity of Functions
- Properties of Limits
- Limits with Sine and Cosine
- Intermediate Value Theorem (IVT)
- Infinite Limits
- Limits at Infinity
- Limits of Sequences

#### Definition of the Derivative

- Tangent Line
- Definition of the Derivative
- Equation of a Tangent Line
- Definition of Derivative at a Point (Alternative Form of the Derivative)
- Derivative Feature on a Graphing Calculator
- Determining Differentiability
- Derivatives from the Left and the Right

#### Basic Differentiation Rules: Constant, Power, Product, Quotient and Trig Function Rules

- Constant Rule
- Power Rule
- Product Rule
- Quotient Rule
- List of Rules
- Examples of Constant, Power, Product and Quotient Rules
- Derivatives of Trig Functions
- Higher Order Derivatives

#### Equations of the Tangent Line, Tangent Line Approximation, and Rates of Change

#### The Chain Rule

#### Implicit Differentiation and Related Rates

#### Curve Sketching

- Extreme Value Theorem, Rolle’s Theorem, and Mean Value Theorem
- Relative Extrema and First Derivative Test
- Concavity and the Second Derivative
- Curve Sketching: General Rules

#### Optimization

#### Differentials, Linear Approximation and Error Propagation

#### Exponential and Logarithmic Differentiation

- Introduction to Exponential and Logarithmic Differentiation and Integration
- Differentiation of the Natural Logarithmic Function
- General Logarithmic Differentiation
- Derivative of
*e*^{u} - Derivatives of Inverse Trig Functions

#### Derivatives of Inverse Functions

**Calculus (Integral)**

#### Exponential and Logarithmic Integration

- Introduction to Exponential and Logarithmic Integration
- Review of Logarithms
- The Log Rule for Integration
- Integrals of Trigonometric Functions using “ln”
- Integrals of
*e*and^{u}*a*^{u}

#### Exponential Growth using Calculus

- Introduction to Exponential Growth and Decay
- Solving Exponential Growth Problems Using Differential Equations
- Exponential Growth Word Problems

#### Derivatives and Integrals of Inverse Trig Functions

#### Applications of Integration: Area and Volume

- Area Between Curves
- Volumes of Solids by Cross Sections
- Volumes of Solids: The Disk Method
- Volumes of Solids: The Washer Method
- Volumes of Solids: The Shell Method

#### Integration by Parts

- Introduction to Integration by Parts
- Guidelines for Integration by Parts using LIATE
- Integration by Parts Problems
- Tabular Method for Integration by Parts

#### Integration by Partial Fractions

#### Integral Calculus Quick Study Guide

#### Antiderivatives and Indefinite Integration, including Trig Integration

- Antiderivatives
- Basic Integration Rules
- Trigonometric Integration Rules
- Indefinite Integration Problems
- Initial Conditions and Particular Solutions
- Position, Velocity, and Acceleration

#### U-Substitution Integration

#### Differential Equations and Slope Fields

#### L’Hopital’s Rule

#### Riemann Sums and Area by Limit Definition

- Introduction to Riemann Sums
- Using Upper and Lower Sums to Approximate Areas
- Using Midpoint Rule to Approximate Area
- Upper, Lower, and Midpoint Rule Sums Problems
- Trapezoidal Rule
- Area by Limit Definition Problems

#### Definite Integration

- Introduction to Definite Integrals
- Properties of Definite Integrals
- Fundamental Theorem of Calculus
- Definite Integrals on the Graphing Calculator
- Definite Integration and Area
- Mean Value Theorem (MVT) for Integrals
- Average Value of a Function
- 2nd Fundamental Theorem of Calculus
- Integration as Accumulated Change
- Using U-Substitution with Definite Integration