Numbers and quantity
- Operations with integers, fractions, mixed numbers, decimals, powers, roots and unit measurements
- Comparing integers, fractions, mixed numbers, decimals, powers, roots and unit measurements
- Converting fractions, mixed numbers, decimals, percentages and unit measurements
- Least common multiple of a number, greatest common factor, greatest common denominator
- Scientific notation
Complex numbers
- Operations with complex numbers
- Real and imaginary parts, complex conjugate, reciprocal, modulus, argument
- Complex numbers and midpoints in the complex plane
- Converting complex numbers between standard and polar form
- Equations with complex numbers
Equations and inequalities
- Linear, quadratic, exponential, logarithmic, rational, radical (irrational), trigonometric, 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
- Inequalities in set-builder or interval notation
- Literal and parametric equations
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
- Roots, domain, extrema, inflection points, asymptotes
- Even/odd functions
- x- and y-intercepts
- Various transformations (standard form, implicit form, explicit form)
- Injective/one-to-one functions
- Writing quadratic functions
- Inverse functions
- Testing for symmetry
- Axis of symmetry
- Tangent lines
- Evaluation and approximation of functions
- Converting between rectangular, polar, spherical, and cylindrical coordinates
Algebra
- Simplifying, factoring, and evaluating algebraic expressions
- 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, equation of an angle bisectorequation of an angle bisector
- Collinearity
- Equations of circles and conics
- Discriminant
- Perfect Square Trinomial
- Pascal's triangle, Binomial theorem, factorials, equations with factorials
- Combinations, permutations, and variations
- 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, and between a point and a line, between planes
Vectors
- Drawing vectors
- Operations with vectors (addition, subtraction, dot product, scalar multiplication, cross product, scalar triple product)
- Component form and linear combination of vectors, initial and terminal point
- Magnitude of a vector
- Unit 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
- Linear combination of vectors
Geometry
- Classifying shapes
- Plotting 2D figures
- Perimeter of a triangle, rectangle, quadrilateral, parallelogram
- Area of a rectangle, square, parallelogram, triangle, circle, trapezoid
- Finding lengths of sides of the right triangle using trigonometric ratios
- Finding angle measures of the right triangle using trigonometric ratios
- Finding lengths of sides of the special right triangles
- Finding the value of the variable in angles of a triangle and calculating the angle measures
- Solving a right triangle
- 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
Trigonometry and 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
- Coterminal angles
- Reference angle
- Period of trigonometric functions
- Law of Sines and Cosines
- Verifying trigonometric identities
- Rewriting trigonometric expressions using formulas
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
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