Overview and List of Topics


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. Math Hints was developed by Lisa Johnson, who has tutored math for over two 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. And always use “simpler numbers” if a problem’s numbers are complicated. For example, paying \(\$4\) for \(2\) oranges makes it more obvious that you need to divide 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: if you can add \(2+2\), and build with math tools, 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. We need to find that and learn it!
  • Math = Rules + Examples + Practice, Practice, Practice!!!

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

Basic Math

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


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

Beginning Algebra

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

Intermediate Algebra

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

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

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

Pre-Calculus/Even More Advanced Algebra

Conics: Parabolas, Ellipses, and Hyperbolas Parametric Equations Introduction to Limits
Systems of Non-Linear Equations Sequences and Series
Introduction to Vectors Binomial Expansion


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

Differential Calculus

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


Integral Calculus

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


Practice Problems Here: