12: Mathematics

12.N: Number Sense and Operations

12.N.1: Define complex numbers (e.g., a + bi) and operations on them, in particular, addition, subtraction, multiplication, and division. Relate the system of complex numbers to the systems of real and rational numbers.

 Points in the Complex Plane
 Roots of a Quadratic

12.N.2: Simplify numerical expressions with powers and roots, including fractional and negative exponents.

 Dividing Exponential Expressions
 Exponents and Power Rules
 Multiplying Exponential Expressions
 Operations with Radical Expressions

12.P: Patterns, Relations, and Algebra

12.P.4: Demonstrate an understanding of the trigonometric, exponential, and logarithmic functions.

 Compound Interest
 Cosine Function
 Exponential Functions
 Introduction to Exponential Functions
 Logarithmic Functions
 Sine Function
 Sine, Cosine, and Tangent Ratios
 Tangent Function
 Translating and Scaling Functions

12.P.5: Perform operations on functions, including composition. Find inverses of functions.

 Addition and Subtraction of Functions
 Logarithmic Functions

12.P.6: Given algebraic, numeric and/or graphical representations, recognize functions as polynomial, rational, logarithmic, exponential, or trigonometric.

 Compound Interest
 Exponential Functions
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Introduction to Exponential Functions
 Logarithmic Functions
 Polynomials and Linear Factors
 Quadratics in Factored Form
 Quadratics in Vertex Form
 Rational Functions
 Translating and Scaling Functions

12.P.7: Find solutions to quadratic equations (with real coefficients and real or complex roots) and apply to the solutions of problems.

 Quadratics in Factored Form

12.P.8: Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula; use technology where appropriate. Include polynomial, exponential, logarithmic, and trigonometric functions; expressions involving absolute values; trigonometric relations; and simple rational expressions.

 Absolute Value Equations and Inequalities
 Compound Inequalities
 Compound Interest
 Exponential Functions
 Polynomials and Linear Factors
 Quadratics in Vertex Form

12.P.11: Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, trigonometric, and step functions, absolute values, and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include growth and decay; joint (e.g., I = Prt, y = k(w log 1 + w log 2)) and combined (F = G(m log 1 x m log 2)/d²) variation, and periodic processes.

 Compound Interest
 General Form of a Rational Function
 Introduction to Exponential Functions
 Rational Functions

12.P.13: Describe the translations and scale changes of a given function f(x) resulting from substitutions for the various parameters a, b, c, and d in y = af (b(x + c/b)) + d. In particular, describe the effect of such changes on polynomial, rational, exponential, logarithmic, and trigonometric functions.

 Introduction to Exponential Functions
 Rational Functions
 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions
 Zap It! Game

12.G: Geometry

12.G.1: Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.

 Sine, Cosine, and Tangent Ratios

12.G.3: Use the notion of vectors to solve problems. Describe addition of vectors and multiplication of a vector by a scalar, both symbolically and geometrically. Use vector methods to obtain geometric results.

 Adding Vectors
 Vectors

12.G.4: Relate geometric and algebraic representations of lines, simple curves, and conic sections.

 Absolute Value with Linear Functions
 Circles
 Ellipses
 Hyperbolas
 Slope

12.G.5: Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.

 Chords and Arcs
 Constructing Congruent Segments and Angles
 Inscribed Angles
 Parallel, Intersecting, and Skew Lines

12.M: Measurement

12.M.1: Describe the relationship between degree and radian measures, and use radian measure in the solution of problems, in particular, problems involving angular velocity and acceleration.

 Cosine Function
 Sine Function
 Tangent Function

12.D: Data Analysis, Statistics, and Probability

12.D.1: Design surveys and apply random sampling techniques to avoid bias in the data collection.

 Polling: Neighborhood

12.D.2: Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data.

 Box-and-Whisker Plots

12.D.3: Apply regression results and curve fitting to make predictions from data.

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots

12.D.4: Apply uniform, normal, and binomial distributions to the solutions of problems.

 Binomial Probabilities
 Polling: City

12.D.5: Describe a set of frequency distribution data by spread (i.e., variance and standard deviation), skewness, symmetry, number of modes, or other characteristics. Use these concepts in everyday applications.

 Populations and Samples

12.D.6: Use combinatorics (e.g., "fundamental counting principle," permutations, and combinations) to solve problems, in particular, to compute probabilities of compound events. Use technology as appropriate.

 Binomial Probabilities
 Permutations and Combinations

12.D.7: Compare the results of simulations (e.g., random number tables, random functions, and area models) with predicted probabilities.

 Independent and Dependent Events

AII: Algebra II

AII.N: Number Sense and Operations

AII.N.1: Define complex numbers (e.g., a + bi) and operations on them, in particular, addition, subtraction, multiplication, and division. Relate the system of complex numbers to the systems of real and rational numbers.

 Points in the Complex Plane
 Roots of a Quadratic

AII.N.2: Simplify numerical expressions with powers and roots, including fractional and negative exponents.

 Dividing Exponential Expressions
 Exponents and Power Rules
 Multiplying Exponential Expressions
 Operations with Radical Expressions

AII.P: Patterns, Relations, and Algebra

AII.P.4: Demonstrate an understanding of the exponential and logarithmic functions.

 Compound Interest
 Exponential Functions
 Introduction to Exponential Functions
 Logarithmic Functions

AII.P.5: Perform operations on functions, including composition. Find inverses of functions.

 Addition and Subtraction of Functions
 Logarithmic Functions

AII.P.6: Given algebraic, numeric and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential.

 Compound Interest
 Exponential Functions
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Introduction to Exponential Functions
 Logarithmic Functions
 Polynomials and Linear Factors
 Quadratics in Factored Form
 Quadratics in Vertex Form
 Rational Functions

AII.P.7: Find solutions to quadratic equations (with real coefficients and real or complex roots) and apply to the solutions of problems.

 Quadratics in Factored Form

AII.P.8: Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula; use technology where appropriate. Include polynomial, exponential, and logarithmic functions; expressions involving the absolute values; and simple rational expressions.

 Absolute Value Equations and Inequalities
 Compound Inequalities
 Compound Interest
 Exponential Functions
 Polynomials and Linear Factors
 Quadratics in Vertex Form

AII.P.9: Use matrices to solve systems of linear equations. Apply to the solution of everyday problems.

 Solving Linear Systems (Matrices and Special Solutions)

AII.P.11: Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, and step functions, absolute values and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include growth and decay; logistic growth; joint (e.g., I = Prt, y = k(w log 1 + w log 2)), and combined (F = G(m log 1 x m log 2)/d²) variation.

 Compound Interest
 General Form of a Rational Function
 Introduction to Exponential Functions
 Rational Functions

AII.P.13: Describe the translations and scale changes of a given function f(x) resulting from substitutions for the various parameters a, b, c, and d in y = af (b(x + c/b)) + d. In particular, describe the effect of such changes on polynomial, rational, exponential, and logarithmic functions.

 Introduction to Exponential Functions
 Rational Functions
 Zap It! Game

AII.G: Geometry

AII.G.1: Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.

 Sine, Cosine, and Tangent Ratios

AII.G.3: Relate geometric and algebraic representations of lines, simple curves, and conic sections.

 Absolute Value with Linear Functions
 Circles
 Ellipses
 Hyperbolas
 Slope

AII.D: Data Analysis, Statistics, and Probability

AII.D.1: Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data.

 Box-and-Whisker Plots

AII.D.2: Use combinatorics (e.g., "fundamental counting principle," permutations, and combinations) to solve problems, in particular, to compute probabilities of compound events. Use technology as appropriate.

 Binomial Probabilities
 Permutations and Combinations

PC: Precalculus

PC.N: Number Sense and Operations

PC.N.1: Plot complex numbers using both rectangular and polar coordinates systems. Represent complex numbers using polar coordinates, i.e., a + bi = r (cos theta + i sin theta). Apply DeMoivre's theorem to multiply, take roots, and raise complex numbers to a power.

 Points in the Complex Plane

PC.P: Patterns, Relations, and Algebra

PC.P.2: Relate the number of roots of a polynomial to its degree. Solve quadratic equations with complex coefficients.

 Points in the Complex Plane
 Polynomials and Linear Factors
 Roots of a Quadratic

PC.P.3: Demonstrate an understanding of the trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent). Relate the functions to their geometric definitions.

 Cosine Function
 Simplifying Trigonometric Expressions
 Sine Function
 Sine, Cosine, and Tangent Ratios
 Sum and Difference Identities for Sine and Cosine
 Tangent Function

PC.P.8: Identify and discuss features of conic sections: axes, foci, asymptotes, and tangents. Convert between different algebraic representations of conic sections.

 Circles
 Ellipses
 Hyperbolas
 Parabolas
 Rational Functions

PC.P.9: Relate the slope of a tangent line at a specific point on a curve to the instantaneous rate of change. Explain the significance of a horizontal tangent line. Apply these concepts to the solution of problems.

 Logarithmic Functions

PC.G: Geometry

PC.G.2: Use the notion of vectors to solve problems. Describe addition of vectors, multiplication of a vector by a scalar, and the dot product of two vectors, both symbolically and geometrically. Use vector methods to obtain geometric results.

 Adding Vectors
 Vectors

PC.G.3: Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.

 Chords and Arcs
 Constructing Congruent Segments and Angles
 Inscribed Angles
 Parallel, Intersecting, and Skew Lines

PC.M: Measurement

PC.M.1: Describe the relationship between degree and radian measures, and use radian measure in the solution of problems, in particular problems involving angular velocity and acceleration.

 Cosine Function
 Sine Function
 Tangent Function

PC.D: Data Analysis, Statistics, and Probability

PC.D.1: Design surveys and apply random sampling techniques to avoid bias in the data collection.

 Polling: Neighborhood

PC.D.2: Apply regression results and curve fitting to make predictions from data.

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots

PC.D.3: Apply uniform, normal, and binomial distributions to the solutions of problems.

 Polling: City

PC.D.4: Describe a set of frequency distribution data by spread (variance and standard deviation), skewness, symmetry, number of modes, or other characteristics. Use these concepts in everyday applications.

 Populations and Samples

Correlation last revised: 4/4/2018

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