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Math Hints: Easy Mathematical Strategies from Counting Through Calculus

MathHints.com (formerly shelovesmath.com) is a free website that includes hundreds of pages of math, explained in simple terms, with thousands of examples of worked-out problems. Topics cover basic counting through Differential and Integral Calculus! Use Math Hints to homeschool math, or as a supplement to math courses at school. The website was developed by Lisa Johnson, a retired telecom engineer, who has tutored math for over three decades.

My philosophy on teaching math:

You can’t study for math tests without doing problems! A lot of times, I think I know the subject I’m tutoring (by looking at the book), and then when I get in there and start solving problems, I realize that I didn’t know it as well as I thought I did!
Learning math should be an active experience and should relate to the world. For example, use “simpler numbers” if a problem’s numbers are complicated. For example, paying $ \$4$ for $ 2$ oranges makes division more obvious for a unit rate than paying $ \$5.88$ for $ 3$ oranges.
Learning math requires an understanding of what to “memorize” (for example, the tools), and what to “understand”. We don’t need to reinvent the wheel; it’s already been invented. Don’t worry if you have to memorize something with math without “understanding” it!
Learning more advanced math is no more than building on what is already known. For example, if you can add $ 2+2$, and build with mathematical tools that you’ll learn slowly, you can be taught to solve a complicated Calculus problem.
Math books tend to “brag” and try to explain things with difficult words that sometimes don’t make sense! Math can be explained more easily with every-day words.
Sometimes there’s just one little concept that isn’t known or understood that makes a whole new math concept difficult. It maybe required to go backwards and relearn this concept.

Math = Rules + Examples + Practice, Practice, Practice! ENJOY!

Note: Please give me feedback for this site at lisa@mathhints.com. Thanks!

Note: The tools I use to create the graphs and equations are Graph (free!) and MathType, respectively.

Basic Math

Adding and Subtracting	Decimals
Multiplying and Dividing	Fractions
Prime Numbers, GCF and LCM	Metric System

Pre-Algebra

Percentages, Ratios, and Proportions	Powers, Exponents, Radicals, and Scientific Notation
Negative Numbers and Absolute Value	Order of Operations (PEMDAS)

Introduction to Statistics and Probability

Beginning Algebra

Algebra Review	Linear Inequalities
Introduction to Algebra	Coordinate Systems and Graphing Lines, including Inequalities
Types of Numbers and Algebraic Properties	Direct, Inverse, Joint, and Combined Variation
Solving Algebraic (Linear) Equations	Introduction to the Graphing Display Calculator (GDC)

Intermediate Algebra

Algebraic Functions, including Domain and Range	Solving Quadratics by Factoring and Completing the Square
Advanced Functions: Compositions, Even and Odd, and Extrema	Quadratic Inequalities
Algebra Word Problems	Quadratic Applications
Systems of Linear Equations and Word Problems	Imaginary and Complex Numbers
Scatter Plots, Correlation, and Regression	Solving Absolute Value Equations and Inequalities
Exponents and Radicals	Solving Radical Equations and Inequalities
Multiplying Polynomials	Solving Inequalities
Introduction to Quadratics

Advanced Algebra (also check Pre-Calculus below for Advanced Algebra)

Inverses of Functions	Rational Functions, Equations, and Inequalities
Parent Functions and Transformations	Graphing Rational Functions, including Asymptotes
Absolute Value Transformations	Graphing and Finding Roots of Polynomial Functions
Piecewise Functions	Exponential Functions
The Matrix and Solving Systems with Matrices	Logarithmic Functions
Solving Systems Using Reduced Row Echelon Form	Advanced Factoring
Linear Programming

Pre-Calculus/Even More Advanced Algebra

Conics Part 1: Circles and Parabolas	Parametric Equations
Conics Part 2: Ellipses and Hyperbolas	Sequences and Series
Systems of Non-Linear Equations (Nonlinear Equations)	Binomial Expansion
Introduction to Vectors	Introduction to Limits

Trigonometry

Right Triangle Trigonometry	Solving Trigonometric Equations
Angles and the Unit Circle	Trigonometric Identities
Linear and Angular Speeds, Areas of Sectors, and Lengths of Arcs	Law of Sines and Cosines, and Areas of Triangles
Graphs of Trigonometric Functions	Polar Coordinates, Equations, and Graphs
Transformations of Trigonometric Functions	Trigonometry and the Complex Plane
Inverse Trigonometric Functions

Differential Calculus

L’Hopitals (L’Hôpital’s or L’Hospital’s) Rule (in Integrals section)

Introduction to Calculus and Study Guides	Extreme Value Theorem, Rolle’s Theorem, and Mean Value Theorem
Differential Calculus Quick Study Guide	Curve Sketching
Limits and Continuity	Optimization Using Calculus
Definition of the Derivative	Differentials, Linear Approximation, and Error Propagation
Basic Differentiation Rules: Constant, Power, Product, Quotient, and Trig Rules	Exponential and Logarithmic Differentiation
Equation of the Tangent Line, Tangent Line Approximation, and Rates of Change	Derivatives of Inverse Functions
The Chain Rule	Derivatives and Integrals of Inverse Trigonometric Functions
Implicit Differentiation and Related Rates

Integral Calculus

Introduction to Calculus and Study Guides	Integration as Accumulated Change
Integral Calculus Quick Study Guide	Exponential and Logarithmic Integration
Antiderivatives and Indefinite Integration, including Trigonometric Integration	Exponential Growth Using Calculus
U-Substitution Integration	Derivatives and Integrals of Inverse Trigonometric Functions
Differential Equations and Slope Fields	Applications of Integration: Area and Volume
L’Hopitals (L’Hôpital’s or L’Hospital’s) Rule	Integration by Parts
Riemann Sums and Area by Limit Definition	Integration by Partial Fractions
Definite Integration	Trigonometric Substitution for Evaluating Integrals

Practice Problems Here: