Kevin Quattrin, EdD
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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.

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