Students use properties of numbers to demonstrate whether assertions are true or false.
Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
Students explain the difference between inductive and deductive reasoning and identify and provide examples of each.
Students identify the hypothesis and conclusion in logical deduction.
Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.
Read, write, and perform basic operations on complex numbers
Evaluate and perform basic operations on expressions containing rational exponents
Describe the relationship between exponential and logarithmic equations
Translate and show the relationships among non-linear graphs, related tables of values, and algebraic symbolic representations
Factor simple quadratic expressions including general trinomials, perfect squares, difference of two squares, and polynomials with common factors
Analyze functions based on zeros, asymptotes, and local and global characteristics of the function
Explain, using technology, how the graph of a function is affected by change of degree, coefficient, and constants in polynomial, rational, radical, exponential, and logarithmic functions
Categorize non-linear graphs and their equations as quadratic, cubic, exponential, logarithmic, step function, rational, trigonometric, or absolute value
Solve quadratic equations by factoring, completing the square, using the quadratic formula, and graphing
Model and solve problems involving quadratic, polynomial, exponential, logarithmic, step function, rational, and absolute value equations using technology
Calculate angle measures in degrees, minutes, and seconds
Explain the unit circle basis for radian measure and show its relationship to degree measure of angles
Identify and apply the unit circle definition to trigonometric functions and use this definition to solve real-life problems
Use the Law of Sines and the Law of Cosines to solve problems involving triangle measurements
Identify conic sections, including the degenerate conics, and describe the relationship of the plane and double-napped cone that forms each conic
Represent translations, reflections, rotations, and dilations of plane figures using sketches, coordinates, vectors, and matrices
Discuss the differences between samples and populations
Devise and conduct well-designed experiments/surveys involving randomization and considering the effects of sample size and bias
Correlate/match data sets or graphs and their representations and classify them as exponential, logarithmic, or polynomial functions
Interpret and explain, with the use of technology, the regression coefficient and the correlation coefficient for a set of data
Describe and interpret displays of normal and non-normal distributions
Explain the limitations of predictions based on organized sample sets of data
Represent data and solve problems involving Euler and Hamiltonian paths
Model a given set of real-life data with a non-linear function
Apply the concept of a function and function notation to represent and evaluate functions
Represent and solve problems involving nth terms and sums for arithmetic and geometric series
Compare and contrast the properties of families of polynomial, rational, exponential, and logarithmic functions, with and without technology
Represent and solve problems involving the translation of functions in the coordinate plane
Determine the family or families of functions that can be used to represent a given set of real-life data, with and without technology