PreCalculus Objectives

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The student will be able to:

The student will be able to:

The student will be able to:

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The student will be able to:

The student will be able to:

The student will be able to:

The student will be able to:

The student will be able to:

The student will be able to:

The student will be able to:

The student will be able to:

__I. Trigonometry Basics Unit__**Unit Knowledge and Skills (Performance Objectives)**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

__Ii. 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.

__III. Trig Identities Unit__**Unit Knowledge and Skills (Performance Objectives)**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.

__IV. PreCalculus Basics__**Unit Knowledge and Skills (Performance Objectives)**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.

__V. Limits and Derivatives Unit__**Unit Knowledge and Skills (Performance Objectives)**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

__VI. Polynomials Unit__**Unit Enduring Understandings****Unit Knowledge and Skills (Performance Objectives)**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

__VII. Rational Functions Unit__**Unit Knowledge and Skills (Performance Objectives)**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

__VIII. Radical Functions Unit__**Unit Knowledge and Skills (Performance Objectives)**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

__IX. Piece-wise Defined Functions Unit (Honors PreCalculus only)__**Unit Knowledge and Skills (Performance Objectives)**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

__X. Exponential and Log Functions Unit__**Unit Knowledge and Skills (Performance Objectives)**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

__XI. Trigonometric Functions Unit__**Unit Knowledge and Skills (Performance Objectives)**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__**Unit Knowledge and Skills (Performance Objectives)**The student will be able to:

- Find the Second Derivative.
- Apply the Second Derivative Test
- 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.

__XIII. The Integral Unit__**Unit Knowledge and Skills (Performance Objectives)**The student will be able to:

- Find the Indefinite Integral of a polynomial.
- Use Integration to solve rectilinear motion problems.
- Use the Unchain Rule to integrate composite, product expressions.
- Integrate functions involving Transcendental operations.
- Evaluate Definite Integrals.
- Interpret Definite Integrals as area under a curve.
- Relate definite integrals to area under a curve.
- Understand the difference between displacement and total distance.
- Extend that idea to understanding the difference between the two concepts in other contexts.