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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!
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
Coordinate System and Graphing Lines Including Inequalities
- Coordinate System
- Slope-Intercept Formula
- Positive and Negative Slopes
- Horizontal and Vertical Lines
- 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, Increasing and Decreasing
- Adding, Subtracting, Multiplying and Dividing Functions
- Increasing, Decreasing and Constant Functions
- 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
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
- Exponential Functions
- Parent Graphs of Exponential Functions
- Writing Exponential Equations from Points and Graphs
- Exponential Regression
- Exponential Function Applications
- Exponential Word Problems
- Solving Exponential Functions by Matching Bases
- Factoring to Solve with Exponents
Logarithmic Functions
- Introduction to Logarithms
- Special Logarithms
- Using Logs (and Exponents) in the Graphing Calculator
- Parent Graphs of Logarithmic Functions
- Basic Log Properties, including Shortcuts
- Expanding and Condensing Logs
- Solving Exponential Equations using Logs
- Solving Log Equations
- Applications of Logs, including Half-Life
Transformations, Inverses, Compositions, and Inequalities of Exponents/Logs
- Transformations of Exponential and Log Functions
- Writing Exponential and Logarithmic Functions from a Graph
- Inverses and Compositions of Exponential and Logarithmic Functions
- Exponential and 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 and Log 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
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
- Transformations of the Inverse Trig Functions
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 on the Calculator
- Solving Trig Systems of Equations
- 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 eu
- 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 eu and au
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
- 1st 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
- Integration as Accumulated Change and Average Value Applications
- 2nd Fundamental Theorem of Calculus
- Using U-Substitution with Definite Integration