1. NUMBERS & QUANTITY

- Operations with integers, fractions, mixed numbers, decimals, powers, roots and unit measurements
- Comparing integers, fractions, mixed numbers, decimals, powers and roots and unit measurements
- Converting fractions, mixed numbers, decimals, and percentages unit measurements
- Least common multiple of a number, greatest common factor, greatest common denominator
- Scientific notation

2. COMPLEX NUMBERS

- Operations with complex numbers
- Finding the real and imaginary parts, complex conjugate, reciprocal, modulus, argument
- Complex numbers and midpoints in the complex plane
- Finding absolute value, complex conjugate, real and imaginary parts
- Converting complex numbers between standard and polar form
- Equations with complex numbers

3. EQUATIONS & INEQUALITIES

- Linear, quadratic, exponential, logarithmic, rational, radical (irrational), absolute value equations
- Linear, quadratic, exponential, logarithmic, rational, radical (irrational), absolute value inequalities
- Systems of linear, quadratic, exponential, logarithmic, rational, radical (irrational), absolute value equations, equations with parameters
- Compound equations and inequalities
- Rewriting inequalities to set-builder or interval notation
- Literal and Parametric equations

4. FUNCTIONS

- Operations with functions (addition, subtraction, multiplication, division, composition) and evaluation at a given point
- Graphs of linear, quadratic, exponential, logarithmic, rational, radical (irrational), trigonometric, and absolute value functions
- Finding roots, domain, extrema, inflection points, asymptotes
- Determining if the function is even, odd, or neither
- x- and y-intercepts
- Various transformations (standard form, implicit form, explicit form)
- Writing quadratic functions
- Converting between rectangular, polar, spherical, and cylindrical coordinates
- Finding inverse functions
- Testing for symmetry
- Axis of symmetry
- Tangent lines
- Evaluation and approximation of functions
- Converting between rectangular, polar, spherical, and cylindrical coordinates

5. ALGEBRA

- Simplifying, factoring, and evaluating algebraic expressions
- Simplifying algebraic fractions and partial-fraction decomposition
- Proportions
- Addition, subtraction, multiplication and division of polynomials
- Midpoint of a line segment
- Distance between two points
- Equation of a line and slope of a line
- Collinearity
- Equations of circles and conics
- Discriminant
- Perfect Square Trinomial
- Polynomial Division
- Pascal's triangle, binomial theorem, factorials, equations with factorials
- Combinations, permutations, and variations
- Matrices and mtrix equations
- Determinants
- Mathematical Induction
- Equation of a sphere
- Operations with matrices (addition, subtraction, multiplication, multiplication by a scalar, exponentiation, transpose)
- Inverse of a matrix
- Matrix identities
- Matrix equations
- Determinants
- Linear programming
- Distance between a point and a plane

6. VECTORS

- Drawing vectors
- Operations with vectors (addition, subtraction, dot product, scalar multiplication, cross product, scalar triple product)
- Component form and linear combination of vectors
- Magnitude of a vector
- Angle between two vectors
- Equality of vectors
- Orthogonality of vectors
- Direction angle of a vector
- Vector equation of a line, in a plane or space

7. GEOMETRY

- Classifying shapes
- Plotting 2D figures
- Perimeter of a triangle, rectangle, quadrilateral, parallelogram
- Area of a rectangle, square, parallelogram, triangle, circle, trapezoid
- Circumference, diameter and radius of a circle
- Area of a circle sector
- Length of a circle arc
- Volume of rectangular prisms
- Surface area of cubes and rectangular prisms

8. TRIGONOMETRY & ANGLES

- Classifying angles according to their measure
- Triangle angle-sum theorem
- Operations with angle measures
- Complementary and supplementary angles
- Construction of angles
- Converting angles between degrees and radians
- Converting angles between decimal and DMS form
- Finding Coterminal angles
- Reference angle
- Period of trigonometric functions
- Law of Sines and Cosines
- Verifying trigonometric identities
- Rewriting trigonometric expressions using formulas

9. SEQUENCES

- Identifying arithmetic and geometric sequences
- Sum of arithmetic and geometric sequences
- Rewriting in recursive or explicit form
- Various tests for convergence or divergence
- Limit of a sequence

10. CALCULUS

- Limits
- Derivatives (various methods)
- Find the tangent line using derivatives or limits
- Antiderivative
- Integrals
- Area below a curve
- Identifying conics
- Rotations of conics
- Parametrization of curves
- Identifying quadratic surfaces
- Rewriting functions as power series
- Differential equations
- Polar coordinates
- Taylor and Maclaurin polynomial
- Radius and interval of convergence of a series
- Operations with power series

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