PreCalculus Objectives

 I.           PreCalculus Basics Unit

The student will be able to:

• Find equations of lines from points, slopes, and parallel or perpendicular lines.
• Find the intercepts of lines.
• Find zeros of parabolas.
• Find vertex and range of a parabola.
• Find equations of parabolas.
• Find complete graphs on the calculator
• Find Zeros and extremes by grapher.
• Factor Polynomials to find zeros algebraically and graphically.
• Find the equation of a polynomial from its zeros.                                           
• Factor Polynomials to find zeros algebraically.
• Find the equation of a polynomial from its zeros.
• Find sign patterns to solve polynomial inequalities.

II.           Limits and Derivatives Unit

The student will be able to:

• Evaluate Limits                                             
• Use the Limit Definition to find the Derivative.
• Find the equation of tangent and normal lines to a given curve at a  
• Find the Derivative of a polynomial quickly.
• Find the equation of tangent and normal lines to a given curve at a  given point.
• Use the equation of a tangent line to approximate function values.          
• Given a distance function of an object in rectilinear or parametric motion, find the velocity and acceleration functions or vectors.
• Use the velocity and acceleration functions to describe the motion of an object.
• Interpret sign patterns in context of motion

III.           Polynomials Unit          

The student will be able to:

• Solve maximum and minimum polynomial word problems with or without a calculator                                                        
• Use the derivative to find the critical values, extremes, and range of a polynomial.
• Use the First Derivative Test to identify the type of extreme represented by a particular critical value.                                                           
• Find all the Traits and sketch a fairly accurate polynomial curve algebraically

IV.            Rational Functions Unit

The student will be able to:

• Find Zeros, Points of Exclusion and Vertical Asymptotes of a Rational Function and distinguish them from one another.
• Determine the End Behavior of a Rational Function from a model, from polynomial Long Division, or from Infinite
• Find the Derivative of a Rational Function.
• Find the Extremes of a Rational Function.
• Find sign patterns to solve rational inequalities.
• Apply sign patterns to velocity.
• Apply sign patterns to the First Derivative.
• Find all the Traits and sketch a fairly accurate rational curve algebraically

V.           Radical Functions Unit

The student will be able to:

• Find sign patterns to find the Domain of Radical Functions.
• Find Zeros of Radical Functions.
• Find the Derivative of Radical Functions.
• Find the critical values and extremes of Radical Functions.
• Find all the Traits and sketch a fairly accurate radical curve algebraically
• Take derivatives of relations implicitly.
• Solve related rates problems

VI.           Piece-wise Defined Functions Unit

The student will be able to:

• Evaluate one-sided limits graphically, numerically, and algebraically.
• Interpret Vertical Asymptotes in terms of one-sided limits.
• Evaluate two-sided limits in terms of one-sided limits.
• Prove continuity or discontinuity of a given function.
• Determine if a function is differentiable or not.
• Demonstrate understanding of the connections and differences between differentiability and continuity.
• Find all the Traits and sketch a fairly accurate polynomial curve algebraically

VII.           Exponential and Log Functions Unit

The student will be able to:

• Solve equations involving Exponential and/or Log functions
• Solve real-world financial problems involving Exponential and Logarithmic operations.
• Find derivatives and extremes of Log and Exponential functions.
• Use Logarithms to simplify the derivative process.
• Find the Derivative of a product of two functions.
• Find Traits and sketch exponential functions and functions involving Products
• Find Traits and sketch Log functions

VIII.           Analytic Trigonometry Unit

The student will be able to:

• Draw angles that are negative or are larger that 180°.
• Find quadrant and reference angles of a given angle.
• Given a point on the terminal side, find the six exact trig values.
• Given a trig value and the quadrant, find the other five exact trig values. 
• Convert between radians and degrees.
• Use exact values from the special triangles.
• Use a calculator to find approximate trig values for a given angle.
• Use a calculator to find approximate angle values for a given trig value.
• Find a vector from one point to another
• Find a unit vector in the direction of another vector.
• Find the resultant vector.
• Convert between the Component form and Polar form of a vector

X.           Trig Identities Unit

The student will be able to:

• Transform basic trig expressions.
• Prove basic trig identities.
• Find exact trig values of composite arguments.
• Prove identities involving composite and cofunction rules.
• Solve equations involving composite argument rules.
• Find exact trig values of double and half angles.
• Prove identities involving double and half angle rules.
• Solve equations involving double and half angle rules.
• Solve equations involving the Trigonometric Identities.

IX.           Sinusoidal Unit

The student will be able to:
·            Explore the relationship between the equation and the graph of a sinusoidal.
·            Use a graphing calculator to find the graph of a trigonometric equation.
·            Given a sinusoidal equation, find values of y from x and vice versa.
·            Model and solve sinusoidal situations.
·            Find the graph from the equation of tangent, cotangent, secant, and cosecant functions.

XI.           Trigonometric Functions Unit

The student will be able to:

• Explore the relation between the equation and the graph of a sinusoidal.     
• Use a grapher to find the graph of a trig equation.
• Given a sinusoidal equation, find values of y from x and vice versa
• Model and solve sinusoidal situations
• Find the graph from the equation of tangent, cotangent, secant, and cosecant functions.
• Find the equation from the graph of tangent, cotangent, secant, and cosecant functions.
• Find Derivatives involving Trig Functions.
• Find the Derivative of a product or quotient of two functions.
• Find the derivatives and extrema of inverse trig functions.
• Find the Traits and sketch composite functions involving trig operations

XII.           The 2nd Derivative Unit

The student will be able to:

• Find the Second Derivative.
• Find Points of Inflection and Intervals of Concavity.
• Find the Key Traits and a more complete sketch of any function
• Find Traits of a function from its derivative.