Calculus
GENERAL STUDIES
Calculus
Course Description:
The Calculus course is a comprehensive look at the study of differential and integral calculus concepts including limits, derivative and integral computation, linearization, Riemann sums, the Fundamental Theorem of Calculus, and differential equations. Applications include graph analysis, linear motion, average value, area, volume, and growth and decay models.
Course Objectives:

 Evaluate limits, including those involving infinity.
 Define and apply numerical and function derivatives.
 Understand the relationship between continuity and differentiability.
 Differentiate a variety of functions written in explicit and implicit form.
 Analyze the behavior of a function using limits and derivatives.
 Apply differential calculus to linear approximations, motion along a line, related rate problems, and optimization.
 Define and apply ant derivatives and indefinite integrals.
 Define and apply Riemann sums and definite integrals.
 Understand the consequences of the Fundamental Theorem of Calculus.
 Integrate a variety of functions.
 Apply integral calculus to average value, total change, and motion along a line, initial value problems, area, and volume.
 Model and solve problems involving differential equations.
Assessments:
Attendance and participation: 10%
Assignments and homework: 10%
 Nightly homework will be given as a review of what was covered in class
Tests and quizzes: 60%
 Quizzes will be given half way through each unit.
 Tests will be given at the end of each unit.
Midterm or final: 20%
Scope and Sequence:
Exploring Expressions, Equations, and Functions
 Variables and Patterns
 Order of Operations
 Properties
 Identity and Equality
 Distributive
 Associative and Commutative
Exploring Rational Numbers
 Integers and Number Line
 Rational Numbers
 Adding/Subtracting
 Multiplying/Dividing
 Square Roots and Real Numbers
Solving Linear Equations
 With Addition/Subtraction
 With Multiplication/Division
 MultiStep Equations and with Variables on Both Sides
 Formulas
Proportional Reasoning
 Ratios and Proportions
 Percent and Percent Change
 Probability and Odds
 Direct and Inverse Variation
Graphing Relations and Functions
 The Coordinate Plane
 Relations and Functions
 Graphing Linear Equations
 Writing Equations from Patterns
Analyzing Linear Equations
 Slope
 Writing Linear Equations
 Point Slope and Standard Form
 Slope Intercept From
 Graphing Linear Equations
 Midpoints
 Perpendicular and Parallel Lines
Solving Linear Inequalities
 With Addition/Subtraction
 With Multiplication/Division
 MultiStep
 Compound Inqualities
 Absolute Value
 Graphing Inequalities with Two Variables
Solving Systems of Linear Equations and Inequalities
 Using Graphing
 Using Substitution
 With Elimination Using Addition/Subtraction and Multiplication
 Graphing Systems of Inequalities
Exploring Polynomials
 Multiplying and Dividing Monomials
 Scientific Notation
 Polynomials
 Addition/Subtraction
 Multiplying by a Monomial
 Multiplying by another Polynomial
 Special Products
Using Factoring
 GCF and Distributive Property
 Factoring Trinomials
 Difference of Squares and Perfect Squares
 Solving Equations by Factoring
Exploring Quadratic and Exponential Functions
 Graphing Quadratic Functions
 Solving Quadratics by Graphing
 The Quadratic Formula
 Exponential Functions and Growth and Decay
Exploring Rational Expressions and Equations
 Simplifying
 Multiplying/Dividing
 Dividing Polynomials
 Rational Expressions with Like and Unlike Denominators
 Mixed Expressions and Complex Fractions
 Solving Rational Equations
Exploring Radical Expressions and Equations
 Simplifying
 Operations with Radical Expressions
 Radical Equations
 Completing the Square