K-12 Mathematics Standards: Precalculus
Skills available for Georgia Precalculus standards
Section
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MM
Mathematical Modeling
PC.MM.1 Apply mathematics to real-life situations; model real-life phenomena using mathematics.
PC.MM.1 Apply mathematics to real-life situations; model real-life phenomena using mathematics.
PC.MM.1.1: Explain contextual, mathematical problems using a mathematical model.
PC.MM.1.1: Explain contextual, mathematical problems using a mathematical model.
PC.MM.1.2: Create mathematical models to explain phenomena that exist in the natural sciences, social sciences, liberal arts, fine and performing arts, and/or humanities contexts.
PC.MM.1.2: Create mathematical models to explain phenomena that exist in the natural sciences, social sciences, liberal arts, fine and performing arts, and/or humanities contexts.
PC.MM.1.3: Using abstract and quantitative reasoning, make decisions about information and data from a contextual situation.
PC.MM.1.3: Using abstract and quantitative reasoning, make decisions about information and data from a contextual situation.
PC.MM.1.4: Use various mathematical representations and structures with this information to represent and solve real-life problems.
PC.MM.1.4: Use various mathematical representations and structures with this information to represent and solve real-life problems.
FGR
Functional & Graphical Reasoning
Functions and their Characteristics
PC.FGR.2 Analyze the behaviors of rational and piecewise functions to model contextual mathematical problems.
PC.FGR.2 Analyze the behaviors of rational and piecewise functions to model contextual mathematical problems.
Analyze piecewise-defined functions using different representations.
Analyze piecewise-defined functions using different representations.
PC.FGR.2.1: Graph piecewise-defined functions, including step functions and absolute value functions.
PC.FGR.2.1: Graph piecewise-defined functions, including step functions and absolute value functions.
PC.FGR.2.2: Describe characteristics by interpreting the algebraic form and graph of a piecewise-defined function.
Domain and range
Continuity
PC.FGR.2.2: Describe characteristics by interpreting the algebraic form and graph of a piecewise-defined function.
Domain and range
Continuity
PC.FGR.2.3: Represent the limit of a function using both the informal definition and the graphical interpretation in the context of piecewise-defined functions; interpret limits expressed in analytic notation.
PC.FGR.2.3: Represent the limit of a function using both the informal definition and the graphical interpretation in the context of piecewise-defined functions; interpret limits expressed in analytic notation.
Analyze rational functions using different representations.
Analyze rational functions using different representations.
PC.FGR.2.4: Divide polynomials using various methods.
PC.FGR.2.4: Divide polynomials using various methods.
PC.FGR.2.5: Graph rational functions and identify key characteristics.
PC.FGR.2.5: Graph rational functions and identify key characteristics.
PC.FGR.2.6: Represent the behavior of a rational function using limit notation for vertical and horizontal asymptotes and end behavior.
PC.FGR.2.6: Represent the behavior of a rational function using limit notation for vertical and horizontal asymptotes and end behavior.
PC.FGR.2.7: Represent the limit of a function using both the informal definition and the graphical interpretation in the context of rational functions; interpret limits expressed in analytic notation.
PC.FGR.2.7: Represent the limit of a function using both the informal definition and the graphical interpretation in the context of rational functions; interpret limits expressed in analytic notation.
PC.FGR.2.8: Solve simple rational equations in one variable, and give examples showing how extraneous solutions may arise.
PC.FGR.2.8: Solve simple rational equations in one variable, and give examples showing how extraneous solutions may arise.
PC.FGR.2.9: Perform partial fraction decomposition of rational functions using non-repeated linear factors.
PC.FGR.2.9: Perform partial fraction decomposition of rational functions using non-repeated linear factors.
Trigonometric Relationships and Functions
PC.FGR.3 Utilize trigonometric expressions to solve problems and model periodic phenomena with trigonometric functions.
PC.FGR.3 Utilize trigonometric expressions to solve problems and model periodic phenomena with trigonometric functions.
Define and analyze trigonometric relationships.
Define and analyze trigonometric relationships.
PC.FGR.3.1: Use the concept of a radian as the ratio of the arc length to the radius of a circle to establish the existence of 2? radians in one revolution.
PC.FGR.3.1: Use the concept of a radian as the ratio of the arc length to the radius of a circle to establish the existence of 2? radians in one revolution.
PC.FGR.3.2: Utilize right triangles on the unit circle to determine the values of the six trigonometric ratios for π⁄6, π⁄4, and π⁄3. Use reflections of the triangles as reference angles to establish known values in all four quadrants of the coordinate plane.
PC.FGR.3.2: Utilize right triangles on the unit circle to determine the values of the six trigonometric ratios for π⁄6, π⁄4, and π⁄3. Use reflections of the triangles as reference angles to establish known values in all four quadrants of the coordinate plane.
PC.FGR.3.3: Define the six trigonometric ratios in terms of x , y , and r using the unit circle centered at the origin of the coordinate plane. Interpret radian measures of angles as a rotation both counterclockwise and clockwise around the unit circle.
PC.FGR.3.3: Define the six trigonometric ratios in terms of x , y , and r using the unit circle centered at the origin of the coordinate plane. Interpret radian measures of angles as a rotation both counterclockwise and clockwise around the unit circle.
PC.FGR.3.4: Derive the fundamental trigonometric identities.
PC.FGR.3.4: Derive the fundamental trigonometric identities.
PC.FGR.3.5: Determine the value(s) of trigonometric functions for a set of given conditions.
PC.FGR.3.5: Determine the value(s) of trigonometric functions for a set of given conditions.
Analyze trigonometric functions and their inverses.
Analyze trigonometric functions and their inverses.
PC.FGR.3.6: Graph and write equations of trigonometric functions using period, phase shift, and amplitude in modeling contexts.
Sine functions
Cosine functions
Sine and cosine functions
PC.FGR.3.6: Graph and write equations of trigonometric functions using period, phase shift, and amplitude in modeling contexts.
Sine functions
Cosine functions
Sine and cosine functions
PC.FGR.3.7: Classify the six trigonometric functions as even or odd and describe the symmetry.
PC.FGR.3.7: Classify the six trigonometric functions as even or odd and describe the symmetry.
PC.FGR.3.8: Restrict the domain of a trigonometric function to create an invertible function and graph the inverse function. Evaluate inverse trigonometric expressions.
PC.FGR.3.8: Restrict the domain of a trigonometric function to create an invertible function and graph the inverse function. Evaluate inverse trigonometric expressions.
AGR
Algebraic & Geometric Reasoning
Trigonometric Identities and Equations
PC.AGR.4 Manipulate, prove, and apply trigonometric identities and equations to solve contextual mathematical problems.
PC.AGR.4 Manipulate, prove, and apply trigonometric identities and equations to solve contextual mathematical problems.
Verify trigonometric identities and solve trigonometric equations.
Verify trigonometric identities and solve trigonometric equations.
PC.AGR.4.1: Apply the fundamental trigonometric identities to simplify expressions and verify other identities.
PC.AGR.4.1: Apply the fundamental trigonometric identities to simplify expressions and verify other identities.
PC.AGR.4.2: Use sum, difference, double-angle, and half-angle formulas for sine, cosine, and tangent to establish other identities and apply them to solve problems.
PC.AGR.4.2: Use sum, difference, double-angle, and half-angle formulas for sine, cosine, and tangent to establish other identities and apply them to solve problems.
PC.AGR.4.3: Solve trigonometric equations arising in modeling contexts.
PC.AGR.4.3: Solve trigonometric equations arising in modeling contexts.
Apply trigonometry to general triangles.
Apply trigonometry to general triangles.
PC.AGR.4.4: Prove and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
PC.AGR.4.4: Prove and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
PC.AGR.4.5: Determine the area of an oblique triangle.
PC.AGR.4.5: Determine the area of an oblique triangle.
GSR
Geometric & Spatial Reasoning
Conic Sections and Polar Equations
PC.GSR.5 Analyze the behaviors of conic sections and polar equations to model contextual mathematical problems.
PC.GSR.5 Analyze the behaviors of conic sections and polar equations to model contextual mathematical problems.
Analyze conic sections using different representations.
Analyze conic sections using different representations.
PC.GSR.5.1: Identify and graph different conic sections given the equations in standard form.
Parabolas
Circles
Ellipses
Hyperbolas
PC.GSR.5.1: Identify and graph different conic sections given the equations in standard form.
Parabolas
Circles
Ellipses
Hyperbolas
PC.GSR.5.2: Identify different conic sections in general form and complete the square to convert the equation of a conic section into standard form.
PC.GSR.5.2: Identify different conic sections in general form and complete the square to convert the equation of a conic section into standard form.
Extend trigonometry to the polar plane.
Extend trigonometry to the polar plane.
PC.GSR.5.3: Define polar coordinates and relate polar coordinates to Cartesian coordinates.
PC.GSR.5.3: Define polar coordinates and relate polar coordinates to Cartesian coordinates.
PC.GSR.5.4: Classify special polar equations and apply to contextual situations.
PC.GSR.5.4: Classify special polar equations and apply to contextual situations.
PC.GSR.5.5: Graph equations in the polar coordinate plane with and without the use of technology.
PC.GSR.5.5: Graph equations in the polar coordinate plane with and without the use of technology.
AGR
Algebraic & Graphical Reasoning
Vectors and Parametric Equations
PC.AGR.6 Represent and model vector quantities to solve problems in contextual situations.
PC.AGR.6 Represent and model vector quantities to solve problems in contextual situations.
Perform operations with vectors in context.
Perform operations with vectors in context.
PC.AGR.6.1: Represent vector quantities as directed line segments; represent magnitude and direction of vectors in component form using appropriate mathematical notation.
PC.AGR.6.1: Represent vector quantities as directed line segments; represent magnitude and direction of vectors in component form using appropriate mathematical notation.
PC.AGR.6.2: Add and subtract vectors and multiply vectors by a scalar to find the resultant vector.
Add and subtract
Multiply
PC.AGR.6.2: Add and subtract vectors and multiply vectors by a scalar to find the resultant vector.
Add and subtract
Multiply
PC.AGR.6.3: Add and subtract vectors on a coordinate plane using different methods.
PC.AGR.6.3: Add and subtract vectors on a coordinate plane using different methods.
PC.AGR.6.4: Solve contextual vector problems, such as those involving velocity, force, and other quantities.
PC.AGR.6.4: Solve contextual vector problems, such as those involving velocity, force, and other quantities.
Model situations with parametric equations.
Model situations with parametric equations.
PC.AGR.6.5: Sketch the graph of a curve represented parametrically, indicating the direction of motion.
PC.AGR.6.5: Sketch the graph of a curve represented parametrically, indicating the direction of motion.
PC.AGR.6.6: Apply parametric equations to contextual problems.
PC.AGR.6.6: Apply parametric equations to contextual problems.
PAR
Patterning & Algebraic Reasoning
Sequences and Series
PC.PAR.7 Demonstrate how sequences and series apply to mathematical models in real-life situations.
PC.PAR.7 Demonstrate how sequences and series apply to mathematical models in real-life situations.
Analyze sequences using multiple representations.
Analyze sequences using multiple representations.
PC.PAR.7.1: Demonstrate that sequences are functions whose domain is the set of natural numbers.
PC.PAR.7.1: Demonstrate that sequences are functions whose domain is the set of natural numbers.
PC.PAR.7.2: Represent sequences graphically, numerically, and symbolically.
Find terms
Identify sequences and formulas
Convert between formulas
PC.PAR.7.2: Represent sequences graphically, numerically, and symbolically.
Find terms
Identify sequences and formulas
Convert between formulas
PC.PAR.7.3: Determine the limit of a sequence if it exists.
PC.PAR.7.3: Determine the limit of a sequence if it exists.
Analyze series using multiple representations.
Analyze series using multiple representations.
PC.PAR.7.4: Demonstrate that a series is the sum of the sequence and represent series graphically, numerically, and symbolically.
PC.PAR.7.4: Demonstrate that a series is the sum of the sequence and represent series graphically, numerically, and symbolically.
PC.PAR.7.5: Describe the behavior of a series in terms of the limit of its partial sums.
PC.PAR.7.5: Describe the behavior of a series in terms of the limit of its partial sums.
PC.PAR.7.6: Derive and use the sum formula of a finite geometric series to solve contextual problems to model real-life situations.
PC.PAR.7.6: Derive and use the sum formula of a finite geometric series to solve contextual problems to model real-life situations.
PC.PAR.7.7: Derive and use the sum formula of an infinite geometric series to solve contextual problems to model real-life situations.
PC.PAR.7.7: Derive and use the sum formula of an infinite geometric series to solve contextual problems to model real-life situations.