Curriculum Frameworks

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.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

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.

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

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.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.

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

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.

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.

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.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.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

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.

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

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.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.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.

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.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.

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.

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.

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

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.

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.

Correlation last revised: 1/20/2017

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