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
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.
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.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
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.
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.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: 5/14/2018