Gizmos for Virginia - Mathematics: Mathematical Analysis (Standards of Learning adopted 2023)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

MA.CF: : Characteristics of Functions

MA.CF.1: : The student will identify and analyze the properties of polynomial, rational, piecewise-defined, absolute value, radical, and step functions and sketch the graphs of the 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: : Given multiple representations of a polynomial, rational, piecewise-defined, absolute value, radical, and step function, analyze:

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.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.b.ix: : relative and/or absolute maximum and minimum points.

MA.CF.1.c: : Sketch the graph of a polynomial, rational, piecewise-defined, absolute value, radical, and step function.

MA.CF.3: : The student will analyze and describe the continuity of functions.

MA.CF.3.d: : Classify types of discontinuity based on which condition of continuity is violated.

MA.FR: : Functional Relationships

MA.FR.1: : The student will analyze compositions of functions to determine and verify inverses of functions.

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.2: : The student will analyze the characteristics of exponential and logarithmic functions, and sketch the graphs of the functions.

MA.FR.2.a: : Generalize characteristics of exponential and logarithmic functions from an equation or a graph.

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: : The student will analyze sequences and finite series, and model and solve problems in context using sequences and series.

MA.FR.3.a: : Use and interpret the notation: summation symbol, n, nth, and a sub n.

MA.FR.3.b: : Derive the formulas associated with arithmetic and geometric sequences and series.

MA.FR.3.c: : Determine the nth term, a sub n, for an arithmetic or geometric sequence.

MA.FR.3.e: : Model and solve problems in context, using sequences and series.

MA.AG: : Analytic Geometry

MA.AG.1: : The student will identify and analyze the properties of conic sections and sketch a graph given an equation.

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.3: : The student will perform operations with vectors in the coordinate plane.

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.g: : Determine the components of a vector.

MA.AG.3.h: : Determine the norm (magnitude) of a vector.

MA.AG.3.j: : Apply vectors to problems in context.

MA.AG.5: : The student will use matrices to organize data and will add and subtract matrices, multiply matrices, multiply matrices by a scalar, and use matrices to solve systems of equations.

MA.AG.5.a: : Multiply matrices by a scalar.

MA.AG.5.b: : Add, subtract, and multiply matrices.

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.

Correlation last revised: 4/9/2024

Virginia - Mathematics: Mathematical Analysis

Standards of Learning | Adopted: 2023

MA.CF: : Characteristics of Functions

MA.FR: : Functional Relationships

MA.AG: : Analytic Geometry