| The Basics |
| The order of operations |
| Evaluating expressions |
| Simplifying algebraic expressions |
| Equations and Inequalities |
| Solving multi-step equations |
| Work word problems |
| Distance-rate-time word problems |
| Mixture word problems |
| Solving absolute value equations |
| Solving multi-step 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 |
| Half-angle and double-angle identities |
| Trig. equations, neither factoring nor identities required |
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