The Basics 
The order of operations 
Evaluating expressions 
Simplifying algebraic expressions 
Equations and Inequalities 
Solving multistep equations 
Work word problems 
Distanceratetime word problems 
Mixture word problems 
Solving absolute value equations 
Solving multistep inequalities 
Solving compound inequalities 
Solving absolute value inequalities 
Linear Relations and Functions 
Graphing linear equations 
Writing linear equations 
Graphing absolute value equations 
Graphing linear inequalities 
Systems of Equations and Inequalities 
Graphing systems of two linear inequalities 
Solving systems of two linear equations by graphing 
Solving systems of two linear equations by elimination 
Solving systems of two linear equations by substitution 
Systems of two equations word problems 
Points in three dimensions 
Planes 
Solving systems of three linear equations by elimination 
Solving systems of three linear equations by substitution 
Matrices 
Basic matrix operations 
Matrix multiplication 
Determinants 
Matrix inverses 
Cramer's Rule 
Matrix equations 
Geometric transformations with matrices 
Complex Numbers 
Adding / subtracting / multiplying / absolute value of complex numbers 
Graphing complex numbers 
Rationalizing imaginary denominators 
Quadratic Functions and Inequalities 
Graphing quadratic functions 
Solving quadratic equations by graphing 
Factoring quadratic trinomials 
Factoring special case trinomials 
Solving quadratic equations by taking square roots 
Solving quadratic equations by factoring 
Completing the square 
Solving quadratic equations by completing the square 
Solving quadratic equations using the Quadratic Formula 
The discriminant 
Graphing quadratic inequalities 
Polynomial Functions 
Naming polynomials 
Adding / subtracting / multiplying polynomials 
The Binomial Theorem 
Dividing polynomials 
Factoring by grouping 
Factoring sum/difference of cubes 
Factoring quadratic form 
Synthetic division and synthetic substitution 
The Remainder Theorem and The Factor Theorem 
Imaginary Root Theorem and Irrational Root Theorem 
Polynomials, factors, and roots 
Writing polynomial functions 
The Rational Root Theorem 
Descartes' Rule of Signs 
The Fundamental Theorem of Algebra 
Solving polynomial equations, all methods 
End behavior of polynomial functions 
Sketching the general shape of polynomial functions 
Graphing polynomial functions, including minima/maxima 
Solving polynomial functions by graphing 
General Functions 
Evaluating functions 
Function operations 
Inverse functions 
Radical Functions and Rational Exponents 
Simplifying radical expressions 
Operations with radical expressions 
Dividing radical expressions 
Relating rational exponents and radical expressions 
Evaluating rational exponent expressions 
The laws of exponents 
Solving radical equations 
Solving rational exponent equations 
Graphing radical functions 
Domain and range of radical functions 
Conic Sections 
Properties of parabolas 
Writing equations of parabolas 
Properties of circles 
Writing equations of circles 
Properties of ellipses 
Writing equations of ellipses 
Properties of hyperbolas 
Writing equations of hyperbolas 
General conic sections 
Systems of quadratic relations 
Rational Expressions 
Graphing simple rational expressions 
Graphing general rational expressions 
Simplifying rational expressions 
Multiplying / dividing rational expressions 
Adding / subtracting rational expressions 
Complex fractions 
Solving rational equations 
Exponential and Logarithmic Functions 
Graphing exponential functions 
Solving exponential equations not requiring logarithms 
Rewriting logarithms 
Evaluating logarithms 
Logarithms and exponential functions as inverses 
Properties of logarithms 
Common logarithms 
Natural logarithms 
Solving exponential equations requiring logarithms 
Solving logarithmic equations 
Graphing logarithmic functions 
Sequences and Series 
General sequences 
Arithmetic sequences 
Geometric sequences 
Arithmetic and geometric mean 
General series 
Arithmetic series 
Geometric series 
Infinite geometric series 
Trigonometry 
Angles and angle measure 
Radians and degrees 
Coterminal angles 
Arc length and sector area 
Right triangle trig. 
Trig. functions of general angles 
The Law of Sines 
The Law of Cosines 
Heron's Formula 
Graphing trig. functions 
Translations of trig. functions 
Angle sum and angle difference identities 
Halfangle and doubleangle identities 
Trig. equations, neither factoring nor identities required 
Statistics and Probability 
Permutations 
Combinations 
Combinations vs permutations 
Probability using combinations and permutations 
