Pre-Calculus Assessable Specifications

PRE-CALCULUS ASSESSABLE SPECIFICATIONS

Target #1:

Students will recognize behavior of the following types of functions:

 Polynomial

 Rational

 Trigonometric

 Exponential/Logarithmic

 Linear

and determine the domain/range, intercepts/roots, asymptotes/end behavior and inverses if they exist.

Assessable Specifications:

Students will:

1)Explain the difference between horizontal and vertical asymptotes and demonstrate in which functions [and under what conditions] they exist.

2)Graphically represent functions of each type – graphically represent the inverse or explain why the inverse does not exist.

3)Solve equations of each type applying inverse operations to isolate variables.

4)Determine intercepts/roots of each function and model the end behavior of each

5)Model each type of function using a graphing calculator, setting an appropriate viewing window using domain and range with proper scaling of axes.

Target #2:

Students will represent complex numbers graphically [using standard and trigonometric forms] and demonstrate operations of addition, subtraction, multiplication, division and exponentiation.

 complex numbers expressed in polar form is optional and at the instructor’s discretion

Assessable Specifications:

Students will:

1)Add, subtract, multiply, divide and exponentiate complex numbers.

2)Re-express complex numbers from standard form to trigonometric form.

3)Demonstrate the graphical representations of complex numbers in standard and trigonometric forms.

4)Apply DeMoivre’s Theorem to determine complex roots of an upper degree function and to graphically display these roots.

Target #3:

Students will:

Graphically represent trigonometric functions [sin, cos, tan, csc, sec, cot] and their inverses determining the appropriate period, amplitude, asymptotes and zeros.

Assessable Specifications:

Students will:

1)Translate and transform graphs of sine and cosine determining the period, amplitude and phase shift.

2)Transform graphs of sine and cosine functions into their respective cosecant and secant functions determining asymptotes and points of tangency.

3)Translate and transform functions of tangent and cotangent determining period, asymptotes, roots and phase shift.

4)Given any trigonometric function, graphically represent its inverse and an appropriate domain interval for which that inverse exists.

Target #4

Students will:

Apply fundamental trigonometric relationships to the unit circle to verify identities, solve equations and simplify expressions.

Assessable Specifications:

Students will:

1)Determine the trigonometric ratios for basic angles [0, /6, /4, /3, /2, ] and their multiples

2)Graphically represent, in the appropriate quadrant, basic trigonometric ratios and relationships

3)Verify trigonometric identities with particular emphasis on the Pythagorean identities

4)Solve trigonometric equations determining all possible solutions 0  2

Target #5

Students will:

Solve two and three variable systems of equations algebraically, numerically, graphically and by using matrices.

Assessable Specifications:

Students will:

1)Use substitution and/or elimination to solve a system or to isolate a variable

2)Justify solutions numerically and/or graphically through the use of a table, inspection or technology

3)Translate any linear system into matrix form and solve by applying the inverse matrix

4)Solve a two or three variable system using matrices and/or Cramer’s Rule

5)Create a solution model given a real-world application using systems of equations

Target #6

Students will:

Graphically represent implicitly defined conic sections [circles, ellipses, parabolas, hyperbolas] and determine the appropriate center/vertex, major/minor axes, axes of symmetry, focal distances and equations of asymptotes.

Assessable Specifications:

Students will:

1)Classify and justify conic sections based on implicitly defined equations.

2)Perform all algebraic manipulations in order to determine the appropriate characteristics [center/vertex, major/minor axes, axes of symmetry, focal distance, equations of asymptotes]

3)Graphically represent each conic section, labeling each appropriate characteristic

Target #7

Students will:

Apply rules of exponents, common and natural logarithms and graphs of exponential/logarithmic functions to solve equations and apply exponential/logarithmic models.

Assessable Specifications:

Students will:

1)Solve exponential and logarithmic equations by applying the appropriate inverse function

2)Apply exponential growth and decay models [A = P(1 + r)t, A = Pekt] to solve for any variable

3)Simplify exponential and logarithmic expressions by applying the appropriate rule

4)Graphically represent exponential/logarithmic functions, expressing one as the inverse of the other

5)Create an exponential/logarithmic solution model given a real-world application

Target #8

Students will:

Graph a function [or system of functions] using a graphing calculator, display the function or system in a appropriate viewing window and calculate roots, extreme points, function values and points of intersection.

Assessable Specifications:

1)Apply concepts of domain and range to set an appropriate viewing window

2)Determine local extreme points and/or changes in direction

3)Determine specific x and y values as solutions using either the TABLE command or VALUE command

4)Locate points of intersection

5)Interpret asymptotic and/or end behavior by examining the graphical representation of a given function