Gizmos for Maryland - Mathematics: Precalculus B (College and Career-Ready Standards adopted 2022)

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

CN: : Complex Numbers

CN.N: : Number and Quantity

CN.N.CN: : The Complex Number System

CN.N.CN.A: : Perform arithmetic operations with complex numbers.

CN.N.CN.A.3: : Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

CN.N.CN.B: : Represent Complex Numbers and their operations on the complex plane.

CN.N.CN.B.4: : Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

CN.N.CN.B.5: : Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

CN.N.CN.B.6: : Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

VM: : Vectors and Matrices

VM.N: : Number and Quantity

VM.N.VM: : Vector and Matrix Quantities

VM.N.VM.A: : Represent and model with vector quantities.

VM.N.VM.A.1: : Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g. v, |v|, ||v||, v).

VM.N.VM.A.2: : Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

VM.N.VM.A.3: : Solve problems involving velocity and other quantities that can be represented by vectors.

VM.N.VM.B: : Perform operations on vectors.

VM.N.VM.B.4: : Add and subtract vectors.

VM.N.VM.B.4.a: : Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

VM.N.VM.B.5: : Multiply a vector by a scalar.

VM.N.VM.B.5.c: : Determine the dot product of two vectors.

VM.N.VM.C: : Perform operations on matrices and use matrices in applications.

VM.N.VM.C.7: : Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

VM.N.VM.C.8: : Add, subtract, and multiply matrices of appropriate dimensions.

VM.N.VM.C.10: : Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

VM.N.VM.C.12: : Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

SS: : Sequences and Series

SS.N: : Number and Quantity

SS.N.OA: : Operations and Algebraic Thinking

SS.N.OA.A: : Write and interpret numerical expressions.

SS.N.OA.A.1: : Use the notation for the factorial of a non-negative integer, n!, to evaluate expressions.

SS.A: : Algebra

SS.A.APR: : Arithmetic with Polynomials and Rational Expression

SS.A.APR.C: : Use polynomial identities to solve problems.

SS.A.APR.C.5: : Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.

SS.F: : Functions

SS.F.IF: : Interpreting Functions

SS.F.IF.A: : Understand the concept of function and use function notation.

SS.F.IF.A.3: : Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

SS.F.IF.C: : Analyze functions using different representations.

SS.F.IF.C.10: : Describe the behavior of a sequence.

SS.F.BF: : Building Functions

SS.F.BF.C: : Build a function that models a relationship between two quantities.

SS.F.BF.A.1: : Write a function that describes a relationship between two quantities.

SS.F.BF.A.1.a: : Determine an explicit expression, a recursive process, or steps for calculation from a context.

SS.F.BF.A.2: : Write sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

CS: : Conic Sections

CS.A: : Algebra

CS.A.SSE: : Seeing Structure in Expressions

CS.A.SSE.A: : Interpret the structure of expressions.

CS.A.SSE.B.3.d: : Choose and produce an equivalent form of a second degree equation, Ax² + Cy² + Dx + Ey + F = 0, to reveal and explain properties of the conic section represented by the equation.

CS.A.SSE.B.3.e: : Translate between the standard and general form, Ax² + Cy² + Dx + Ey + F = 0, of a second degree equation.

CS.G: : Geometry

CS.G.GPE: : Expressing Geometric Properties with Equations

CS.G.GPE.A: : Translate between the geometric description and the equation for a conic section.

CS.G.GPE.A.1: : Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

CS.G.GPE.A.2: : Derive the equation of a parabola given a focus and directrix.

CS.G.GPE.A.3: : Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

Correlation last revised: 4/28/2025

Maryland - Mathematics: Precalculus B

College and Career-Ready Standards | Adopted: 2022

CN: : Complex Numbers

VM: : Vectors and Matrices

SS: : Sequences and Series

CS: : Conic Sections