Supported Math Content

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
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