A: Introduction

A.2: To factor the following over a given set: a difference of squares, a sum or difference of cubes, expressions containing rational coefficients, expressions containing negative exponents, expressions of the form x to the n power - y to the n power (n a positive integer), quadratic and higher order polynomials.

Factoring Special Products
Modeling the Factorization of x²+bx+c

A.4: To solve inequalities by: applying inequality properties, using a sign analysis of factors, using knowledge of the graph of the function.

Absolute Value Equations and Inequalities
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Quadratic Inequalities
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

A.5: To apply the definition of absolute value to rewrite absolute value expressions, to use operations with absolute value, to use properties of absolute value to solve absolute value equations and inequalities, and to draw graphs of functions containing absolute value.

A.5.a: To make and justify decisions based upon understanding of calculus concepts (CCT).

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Rational Numbers, Opposites, and Absolute Values

A.5.b: To represent problems and understandings through a variety of communication modes (COM).

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Rational Numbers, Opposites, and Absolute Values

A.5.c: To interact, co-operate, and collaborate through classroom activities and initiatives (PSVS).

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Rational Numbers, Opposites, and Absolute Values

B: Functions

B.1: To demonstrate a clear understanding of the terms function and relation, and to use function notation.

B.1.a: To discuss ideas using own language and then later incorporating the related mathematical terminology.

Exponential Functions

B.1.b: To identify functions as being polynomial, constant, linear, quadratic, cubic, power, root, reciprocal, rational, algebraic, trigonometric, exponential, logarithmic, or transcendental, and to recognize the basic graph forms thereof.

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
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 Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

B.1.c: To further develop knowledge, skills, and attitudes as lifelong learners.

Exponential Functions

B.1.d: To demonstrate a consistent commitment to understanding their own emotions/feelings and their sources, and the abilities to use this understanding to support decision making, constructive social interactions, and strengthen learning.

Exponential Functions

B.1.e: To engage in activities that require exploration in order to develop understandings of the concept of functions.

Exponential Functions

B.1.f: To represent understandings through a variety of communication modes.

Exponential Functions

B.2: To identify functions as being polynomial, constant, identity, linear, quadratic, cubic, power, root, reciprocal, rational, algebraic, trigonometric, exponential, logarithmic, or transcendental, and to recognize the basic graph forms thereof.

B.2.a: To make and justify decisions based upon understanding of calculus concepts (CCT).

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
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 Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

B.2.b: To further develop knowledge, skills, and attitudes as lifelong learners (IL).

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
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 Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

B.2.c: To demonstrate a consistent commitment to understanding their own emotions/feelings and their sources, and the abilities to use this understanding to support decision making, constructive social interactions, and strengthen learning (PSVS).

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
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 Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

B.2.d: To engage in activities that require exploration in order to develop understandings of the concept of functions (CCT).

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
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 Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

B.2.e: To represent understandings through a variety of communication modes (COM).

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
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 Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

B.3: To determine function values for, and draw the graphs of, piecewise and step functions.

Absolute Value with Linear Functions

B.6: To find the domain and range of a function from the graph of the function and from the equation for the function.

B.6.a: To represent problems and understandings through a variety of communication modes (COM).

Exponential Functions
Radical Functions

B.6.b: To make and justify decisions based upon understanding of calculus concepts (CCT).

Radical Functions

B.7: To build functions from other functions through function addition, subtraction, multiplication, division, and composition.

B.7.a: To use language as a tool for learning and communicating (COM).

Addition and Subtraction of Functions

C: Limits and Continuity

C.4: To identify the location of a discontinuity and the type of discontinuity by examining the graph of a function or just the function.

C.4.a: To engage in activities that require exploration in order to develop understandings of the concept of discontinuities (CCT).

General Form of a Rational Function

C.7: To identify the location of an oscillating discontinuity.

General Form of a Rational Function

D: Differentiation

D.1: To interpret the slope of a line as a rate of change, and to find the equation of a line.

D.1.a: To read graphs for information in order to understand and analyze (NUM).

Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

D.5: To find derivatives of power functions and polynomial functions without the use of limits.

Graphs of Derivative Functions

D.9: To differentiate functions requiring a selection from, or combinations of, the power, product, quotient, and chain rule and to write the answers in required forms.

Graphs of Derivative Functions

E: Applications of Derivatives to Curve Sketching

E.1: To find the second derivative of a function.

E.1.a: To engage in activities that require exploration in order to develop understandings related to derivatives (CCT).

Graphs of Derivative Functions

E.5: To determine the asymptotes (vertical, horizontal) of a function.

Exponential Functions
General Form of a Rational Function