-
Analyze the features of a graph of a given function or relation
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
differentiate between symmetry about the x-axis, the y-axis, and the origin
determine the domain and range of a relation or function
determine the inverse function of a 1-1 function
specify the relation between the domain and the range of a function and its inverse
apply basic transformations to the elementary functions
differentiate among elementary functions
-
Solve linear and quadratic equations and inequalities
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
relate the solution of an equation to the x-intercept of a graph of the function and to the root (or zero) of the function
use appropriate notation when writing solutions of inequalities
solve quadratic equations using more than one method
use modeling techniques to solve applied problems
-
Analyze the properties of linear and quadratic functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
graph quadratic functions
determine the composition of two functions
create new functions by using function operations
apply transformations as compositions of functions
determine the characteristics of a quadratic function
find zeros of quadratic functions algebraically and graphically
convert between standard and vertex form of a quadratic function
-
Analyze polynomials
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
find zeros of polynomial functions
determine whether a function is increasing or decreasing on an interval
determine the end-behavior of a polynomial function
use graphical methods to estimate the roots of a polynomial equation
identify local and global extrema
apply the intermediate value theorem
determine the number of roots of a polynomial equation using the fundamental theorem of algebra
determine the number of roots of a polynomial function using the fundamental theorem of algebra
determine all solutions to polynomial equations including complex solutions
-
Analyze rational functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
identify removable discontinuities
graph rational functions
perform arithmetic operations with rational expressions
determine the domain of rational functions
determine all asymptotes
solve rational equations
-
Analyze radical functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
solve radical equations
graph radical functions
verify solutions to identify extraneous roots
determine the domain of radical expression
-
Analyze exponential and logarithmic functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
define the exponential function with an arbitrary base
graph an exponential function with an arbitrary base
model exponential functions to real life applications
solve exponential equations
define logarithmic functions with an arbitrary base
identify the inverse relationship between the logarithmic function and the exponential function
graph a logarithmic function with an arbitrary base
solve logarithmic equations
-
Solve algebraic systems
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
solve nonlinear systems of equations
solve systems of linear equations in three or more variables
use systems of three equations to solve applied problems
graph systems of linear inequalities
graph systems of nonlinear equations
-
Analyze conic sections
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
identify all conic sections based on a graph
identify all conic sections based on an equation
analyze the characteristics of all conic sections
sketch the graph of all conic sections given their equations
-
Analyze trigonometric functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
graph angles in standard position given degree measure
solve problems involving special right triangles
use reference angles to find exact values of trigonometric functions in any quadrant
find the exact value of a trigonometric function given a point on the terminal side of an angle
find the exact value of a trigonometric function given a right triangle
use reciprocal identities
use quotient identities
use Pythagorean identities
use even-odd identities
use cofunction identities
-
Evaluate the trigonometric functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
identify exact values of trigonometric functions
find approximate values of trigonometric functions using a calculator
solve right triangles using inverse trigonometric functions
solve right triangles using trigonometric functions
-
Apply the unit circle and radian measure
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use the concept of a reference angle
graph angles in standard position given radian measure
relate radian measures to real numbers
convert between radian measures and degree measures of angles
find exact and approximate values of trigonometric functions given in radian measure
analyze the unit circle
-
Analyze graphs of trigonometric functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
sketch graphs of basic trigonometric functions
apply transformations to the graphs of trigonometric functions
identify domains and ranges given trigonometric functions
identify domains and ranges given graphs of trigonometric functions
find equations from graphs of trigonometric functions
-
Analyze inverse trigonometric functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
define the inverse trigonometric functions
identify domains and ranges of inverse trigonometric functions
evaluate the inverse trigonometric functions
evaluate the composition of trigonometric and inverse trigonometric functions
-
Manipulate trigonometric identities
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use identities to evaluate trigonometric functions
use trigonometric identities to verify other identities
apply sum and difference identities
apply double-angle and half-angle identities
apply sum-to-product and product-to-sum identities
-
Solve trigonometric equations
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
solve equations involving trigonometric expressions of a single angle
solve equations involving trigonometric expressions of multiple angles
use correct notation to express infinite and finite solution sets of trigonometric equations
-
Solve oblique triangles
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use the Law of Sines to solve oblique triangles
use the Law of Cosines to solve oblique triangles
solve application problems involving oblique triangles
-
Complete vector operations
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
define a vector
define unit vectors i and j
identify the horizontal and vertical components of a vector
find the magnitude of a vector
find the direction of a vector
perform vector addition
perform scalar multiplication of vectors
compute dot product of vectors
determine if two vectors are perpendicular
find the angle measure between two vectors
-
Complete operations with complex numbers in trigonometric form
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
convert complex numbers between rectangular form and trigonometric form
graph complex numbers in trigonometric form and rectangular form
find products of complex numbers written in trigonometric form
find quotients of complex numbers written in trigonometric form
-
Analyze the polar coordinate system
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
identify points in the polar coordinate system
translate between rectangular coordinates and polar coordinates for a given point
convert an equation between polar form and rectangular form
explore graphs of equations in polar form