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Virginia: Mathematical Analysis Math Standards

73 standards · 3 domains

ANALYTIC GEOMETRY

MA.AG.1.a Given a translation or rotation matrix, determine an equation for the transformed function or conic section.
MA.AG.1.b Convert between standard and general forms of conic equations by completing the square.
MA.AG.1.c Graph conic sections from equations written in general or standard form using transformations.
MA.AG.1.d Identify characteristics of conic sections including center, vertices, axes, symmetry, foci, directrix, eccentricity, and asymptotes.
MA.AG.1.e Represent applications of conic sections.
MA.AG.2.a Graph and analyze parametric equations and use the graph to determine solutions.
MA.AG.2.b Use parametric equations to model contextual problems, including motion over time.
MA.AG.3.a Use vector notation.
MA.AG.3.b Perform the operations of addition, subtraction, and scalar multiplication, graphically and algebraically on vectors.
MA.AG.3.c Find the dot (inner) product of two vectors and use it to determine the angle between two vectors.
MA.AG.3.d Determine if two vectors are orthogonal.
MA.AG.3.e Express complex numbers in vector notation.
MA.AG.3.f Verify properties of the dot product.
MA.AG.3.g Determine the components of a vector.
MA.AG.3.h Determine the norm (magnitude) of a vector.
MA.AG.3.i Find a unit vector in the same direction of a given vector.
MA.AG.3.j Apply vectors to problems in context.
MA.AG.4.a Classify polar equations (rose, cardioid, limaçon, lemniscate, spiral, and circle), given the graph or the equation.
MA.AG.4.b Determine the effects of changes in the parameters of polar equations on the graph, using graphing technology.
MA.AG.4.c Convert between polar and rectangular forms of coordinates.
MA.AG.4.d Convert between complex numbers written in rectangular form and polar form.
MA.AG.4.e Convert equations between polar and rectangular forms.
MA.AG.4.f Determine and verify the intersection of the graphs of two polar equations, using graphing technology.
MA.AG.5.a Multiply matrices by a scalar.
MA.AG.5.b Add, subtract, and multiply matrices.
MA.AG.5.c Represent problems with a system of no more than three linear equations.
MA.AG.5.d Express a system of linear equations as a matrix equation.
MA.AG.5.e Solve a system of equations using matrices.
MA.AG.5.f Determine the inverse of a two-by-two or three-by-three matrix using paper and pencil.
MA.AG.5.g Verify two matrices are inverses using matrix multiplication.
MA.AG.5.h Verify the commutative and associative properties for matrix addition and multiplication.

CHARACTERISTICS OF FUNCTIONS

MA.CF.1.a Use mathematical reasoning to identify polynomial, rational, piecewise-defined, absolute value, radical, and step functions, given an equation or graph.
MA.CF.1.b.i domain and range;
MA.CF.1.b.ii roots (including complex roots);
MA.CF.1.b.iii intercepts;
MA.CF.1.b.iv symmetry (including even and odd functions);
MA.CF.1.b.ix relative and/or absolute maximum and minimum points.
MA.CF.1.b.v asymptotes (horizontal, vertical, and oblique/slant;
MA.CF.1.b.vi points of discontinuity;
MA.CF.1.b.vii intervals for which the function is increasing, decreasing or constant;
MA.CF.1.b.viii end behavior; and
MA.CF.1.c Sketch the graph of a polynomial, rational, piecewise-defined, absolute value, radical, and step function.
MA.CF.2.a Verify estimates about the limit of a function using graphing technology.
MA.CF.2.b Determine the limit of a function algebraically and verify with graphing technology.
MA.CF.2.c Determine the limit of a function numerically and verify with graphing technology.
MA.CF.2.d Use proper limit notation, including when describing the end behavior of a function.
MA.CF.2.e.i determine the limit of a function numerically by direct substitution;
MA.CF.2.e.ii determine the limit of a function using algebraic manipulation;
MA.CF.2.e.iii estimate the limit of a function using a table; and
MA.CF.2.e.iv determine the limit of a function from a given graph.
MA.CF.2.f As the variable approaches positive or negative infinity, analyze the limit of a function to describe the end behavior.
MA.CF.3.a Describe continuity of a function.
MA.CF.3.b Use mathematical notation to communicate and describe the continuity of functions including polynomial, rational, piecewise, absolute value, radical, and step function, using graphical and algebraic methods.
MA.CF.3.c Prove continuity at a point, using the definition.
MA.CF.3.d Classify types of discontinuity based on which condition of continuity is violated.

FUNCTIONAL RELATIONSHIPS

MA.FR.1.a Construct the composition of functions algebraically and graphically.
MA.FR.1.b Determine the domain and range of composite functions algebraically and graphically.
MA.FR.1.c Develop the inverse of a function algebraically and graphically.
MA.FR.1.d Compare the domain and range of the inverse of a function with the original function, both algebraically and graphically.
MA.FR.1.e Use mathematical reasoning to generalize and communicate the criteria for an inverse function to exist.
MA.FR.2.a Generalize characteristics of exponential and logarithmic functions from an equation or a graph.
MA.FR.2.b Define 𝑒 and estimate its value.
MA.FR.2.c Convert between equations written in logarithmic and exponential form.
MA.FR.2.d Use laws of exponents and properties of logarithms to solve equations and simplify expressions.
MA.FR.2.e Represent contextual problems, using exponential and logarithmic functions, to include common and natural logarithms.
MA.FR.2.f Sketch the graph of exponential and logarithmic functions and identify asymptotes, end behavior, intercepts, domain, and range.
MA.FR.3.a Use and interpret the notation: ∑, 𝑛, 𝑛ᵗʰ, and 𝑎ₙ.
MA.FR.3.b Derive the formulas associated with arithmetic and geometric sequences and series.
MA.FR.3.c Determine the 𝑛ᵗʰ term, 𝑎ₙ, for an arithmetic or geometric sequence.
MA.FR.3.d Determine the sum, 𝑆ₙ, if it exists, of an arithmetic or geometric series.
MA.FR.3.e Model and solve problems in context, using sequences and series.
MA.FR.3.f Distinguish between a convergent and divergent series.
MA.FR.3.g Describe convergent series in relation to the concept of a limit.