Gizmos for South Carolina - Mathematics: Pre-Calculus (2025 College- and Career-Ready Standards adopted 2023)

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

PC.MPS: : Mathematical Process Standards

PC.MPS.PS: : PROBLEM SOLVING

PC.MPS.PS.1: : Make sense of problems and persevere in solving them strategically.

PC.MPS.RC: : REPRESENTATION & COMMUNICATION

PC.MPS.RC.1: : Explain ideas using precise and contextually appropriate mathematical language, tools, and models.

PC.MPS.C: : CONNECTIONS

PC.MPS.C.1: : Demonstrate a deep and flexible conceptual understanding of mathematical ideas, operations, and relationships while making real-world connections.

PC.MPS.AJ: : ANALYZE & JUSTIFY

PC.MPS.AJ.1: : Use critical thinking skills to reason both abstractly and quantitatively.

PC.MPS.SP: : STRUCTURE & PATTERNS

PC.MPS.SP.1: : Identify and apply regularity in repeated reasoning to make generalizations.

PC.MGSR: : Measurement, Geometry, and Spatial Reasoning

PC.MGSR.1: : Analyze the behaviors of conic sections and polar coordinates to model mathematical and real-world situations.

PC.MGSR.1.1: : Identify and graph different conic sections given the equations in standard form.

PC.MGSR.1.2: : Identify different conic sections in general form and complete the square to convert the equation of a conic section into standard form.

PC.MGSR.2: : Solve problems and model periodic phenomena with trigonometric expressions and functions.

PC.MGSR.2.3: : Derive the formulas for the length of an arc and the area of a sector in a circle and apply these formulas to solve mathematical and real-world situations.

PC.MGSR.2.4: : Determine geometrically the values of the sine, cosine, and tangent for pi/6, pi/4, and pi/3 by special triangles, and use the unit circle to express the values of sine, cosine, and tangent for pi - x, pi + x, and 2pi - x in terms of their values for x, where x is any real number.

PC.MGSR.2.5: : Define the six trigonometric ratios in terms of x, y, and r using the unit circle centered at the origin of the coordinate plane and interpret radian measures of angles as a rotation both counterclockwise and clockwise around the unit circle.

PC.MGSR.2.6: : Explain symmetry, both odd and even, and periodicity of trigonometric functions.

PC.NR: : Numerical Reasoning

PC.NR.1: : Represent and manipulate data using matrices.

PC.NR.1.1: : Identify the identity and zero matrices for any dimension and add, subtract, and multiply matrices.

PC.NR.1.2: : Find the additive and multiplicative inverses of square matrices.

PC.NR.1.3: : Explain the role of the determinant in determining if a square matrix has a multiplicative inverse.

PC.NR.1.4: : Find the determinant of a square matrix if and only if the matrix has a multiplicative inverse.

PC.NR.2: : Represent and model with vector quantities.

PC.NR.2.1: : Represent vector quantities as directed line segments and represent magnitude and direction of vectors in component form.

PC.NR.2.2: : Find the components of a vector by adding and subtracting vectors on a coordinate plane using a variety of methods.

PC.NR.2.3: : Solve problems, including real-life situations, that can be represented by vectors.

PC.NR.2.4: : Add and subtract vectors and multiply vectors by a scalar to find the resultant vector.

PC.NR.3: : Represent complex numbers and their operations on the complex plane.

PC.NR.3.1: : 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.

PC.NR.3.2: : Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

PC.PAFR: : Patterns, Algebra, and Functional Reasoning

PC.PAFR.1: : Build new functions from existing functions to solve mathematical and real-world situations.

PC.PAFR.1.1: : Combine and compose functions algebraically, tabularly, and graphically.

PC.PAFR.1.2: : Find the inverse of functions and verify algebraically, numerically, and graphically.

PC.PAFR.1.3: : Compare the key features of a function and its inverse function and use the relationship to model real-world situations and solve problems.

PC.PAFR.1.4: : Graph and describe the effect on the graph f(x) of f(x) + k, f(x - k), kf(x), and f(kx), for specific values of both negative and positive values of k.

PC.PAFR.2: : Explore and analyze the behaviors of rational and piecewise functions to model contextual mathematical problems.

PC.PAFR.2.1: : Graph rational functions and describe their key features.

PC.PAFR.2.4: : Graph piecewise-defined functions, including step functions and absolute value functions, and describe their key features.

PC.PAFR.3: : Explore and analyze structures and patterns for radical functions and use radical expressions, equations, and functions to model real-life phenomena.

PC.PAFR.3.2: : Solve radical equations and describe how extraneous solutions may arise.

PC.PAFR.3.3: : Analyze and graph radical functions.

PC.PAFR.4: : Explore and analyze structures and patterns for exponential and logarithmic functions and use exponential and logarithmic expressions, equations, and functions to model real-life phenomena.

PC.PAFR.4.1: : Graph logarithmic functions and describe their key features.

PC.PAFR.4.2: : Use the definition of a logarithm, logarithmic properties, and the inverse relationship between exponential and logarithmic functions to solve problems, including real-life context.

PC.PAFR.4.3: : Model real-life situations and solve problems involving exponential and logarithmic functions.

PC.PAFR.5: : Explore and analyze structures and patterns of trigonometric functions and use trigonometric functions to model real-life phenomena.

PC.PAFR.5.1: : Graph trigonometric functions and their inverses and describe their key features.

PC.PAFR.6: : Manipulate, prove, and apply trigonometric identities and equations to solve contextual mathematical problems.

PC.PAFR.6.1: : Apply the fundamental trigonometric identities to simplify expressions and verify other identities.

PC.PAFR.6.2: : Apply the sum, difference, double-angle, and half-angle formulas for sine, cosine, and tangent and use them to solve problems.

PC.PAFR.6.3: : Model real-life situations and solve problems involving trigonometric equations.

PC.PAFR.7: : Represent data with matrices, perform mathematical operations, and solve systems of linear equations for mathematical problems.

PC.PAFR.7.2: : Solve an equation of the form f(x) = g(x) graphically by identifying the x-coordinate(s) of the point(s) of intersection of the graphs of y = f(x) and y = g(x).

PC.PAFR.7.3: : Represent a system of linear equations as a single matrix equation in a vector variable.

Correlation last revised: 8/22/2024

South Carolina - Mathematics: Pre-Calculus

2025 College- and Career-Ready Standards | Adopted: 2023

PC.MPS: : Mathematical Process Standards

PC.MGSR: : Measurement, Geometry, and Spatial Reasoning

PC.NR: : Numerical Reasoning

PC.PAFR: : Patterns, Algebra, and Functional Reasoning