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**.

## More Practice:

**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**

**Average, Mean, Median, Mode, and Range****Box and Whisker Plot****Stem and Leaf Plot****Frequency Tables and Graphs****Pie Chart****Probability**

# **Beginning Algebra**

**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**

**Compound Inequalities****Absolute Value and Inequalities****Graphing Linear Inequalities with Two Variables**

**Word Problems in 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**

**Coordinate System and Graphing Lines Including Inequalities**

**Coordinate System****Slope-Intercept Formula****Positive and Negative Slopes****Horizontal and Vertical Line****s****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**

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

# **Intermediate Algebra**

**Intermediate Algebra**

**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 Function, 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**

**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 a Quadratic Equation 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)**

**Inverses of Functions**

**Introduction to Inverses****Finding Inverses Graphically****Finding Inverses Algebraically****Finding Inverses 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**

## 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 Word Problems with Matrices****Cramer’s Rule****Number of Solutions when Solving Systems with 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 and Equations**

**Graphing Rational Functions, including Asymptotes**

**Graphing Rational Functions, including Asymptotes**

**Revisiting Direct and Inverse Variation****Polynomial Long Division****Asymptotes of Rationals****Drawing Rational Graphs — General Rules****Rational Inequalities, including Absolute Values****Applications of Rational Functions**

**Graphing and Finding Roots of Polynomial Functions**

**Review of Polynomials****Polynomial Graphs****Polynomial Characteristics and Sketching Graphs****Factor and Remainder Theorems****DesCartes’ Rule of Signs****Conjugate Zeros Theorem Problem****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**

**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**

# 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**

**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

## 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****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**

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