Add, subtract, multiply, and divide rational algebraic expressions.

Simplify a rational algebraic expression with common monomial or binomial factors.

Recognize a complex algebraic fraction, and simplify it as a quotient or product of simple algebraic fractions.

Add, subtract, multiply, and divide rational expressions whose denominators are monomials or polynomial expressions in non-factored form.

Simplify radical expressions containing positive rational numbers and variables.

Add and subtract radical expressions.

Multiply and divide radical expressions not requiring rationalizing the denominators.

Rationalize radical expressions in the denominator, with and without conjugates, and simplify.

Simplify expressions containing positive or negative rational exponents. 

Convert from radical notation to exponential notation.

Convert from exponential notation to radical notation.

Factor polynomials by applying general patterns including difference of squares, sum and difference of cubes, and perfect square trinomials.

Factor polynomials completely over the integers.

Verify polynomial identities including the difference of squares, sum and difference of cubes, and perfect square trinomials.

Use properties of logarithms to condense and expand logarithmic expressions.

Distinguish between a sequence and a series.

Generalize patterns in a sequence using explicit and recursive formulas.

Use and interpret the notations Σ , n, n^th term, and a_n.

Given the formula, find a_n (the n^th term) for an arithmetic or a geometric sequence.

Given formulas, write the first n terms and find the sum, S_n, of the first n terms of an arithmetic or geometric series.

Given the formula, find the sum of a convergent infinite series.

Model real-world situations using sequences and series.

Write an explicit formula for an arithmetic or geometric sequence.

Express an arithmetic or geometric series in abbreviated form using sigma notation.

Find the position of a term in an arithmetic sequence, given its value.

Represent sequences and series using a table or graph.

Use the arithmetic mean or the geometric mean to find a missing term in an arithmetic or geometric sequence.

Recognize that the square root of –1 is represented as i.

Determine which field properties apply to the complex number system.

Simplify radical expressions containing negative rational numbers and express in a+bi form.

Simplify powers of i.

Add, subtract, and multiply complex numbers.

Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, and natural.

Write a real number in a+bi form.

Write a pure imaginary number in a+bi form.

Divide complex numbers using complex conjugates.

Solve absolute value equations algebraically and graphically.

Solve absolute value inequalities algebraically and graphically.

Apply an appropriate equation to solve a real-world problem.

Verify possible solutions to absolute value equations.

Verify possible solutions to absolute value inequalities.

Recognize absolute value equations and inequalities that have no solution.

Express solutions to absolute value inequalities in both set and interval notation.

Given the equation, graph a piecewise or step function.

Given a graph, write an equation for a piecewise or step function.

Solve a quadratic equation over the set of complex numbers using an appropriate strategy.

Calculate the discriminant of a quadratic equation to determine the number of real and complex solutions.

Apply an appropriate equation to solve a real-world problem.

Recognize that the quadratic formula can be derived by applying the completion of squares to any quadratic equation in standard form.

Solve equations containing rational algebraic expressions with monomial or binomial denominators algebraically and graphically.

Apply an appropriate equation to solve a real-world problem.

Identify vertical asymptotes and horizontal asymptotes of a rational function from the equation and the graph.

Solve an equation containing a radical expression algebraically and graphically. 

Verify possible solutions to an equation containing rational or radical expressions.

Apply an appropriate equation to solve a real-world problem.

Identify possible extraneous solutions when solving equations.

Solve radical equations involving more than one radical expression.

Solve exponential equations.

Solve logarithmic equations.

Solve exponential and logarithmic equations using properties of logarithms.

Predict the number of solutions to a nonlinear system of two equations.

Solve a linear-quadratic system of two equations algebraically and graphically.

Solve a quadratic-quadratic system of two equations algebraically and graphically.

Solve a circle-linear system of two equations graphically.

Solve a circle-quadratic system of two equations graphically.

Solve a circle-linear system of two equations algebraically.

Solve a circle-quadratic system of two equations algebraically.

Sketch the graph of a conic section (parabola or hyperbola) in (h, k) form.

Write the equation of a conic section (parabola or hyperbola) in (h, k) form from a graph.

Use conic sections to model practical problems.

Recognize graphs of parent functions.

Given a transformation of a parent function, identify the graph of the transformed function.

Given the equation and using a transformational approach, graph a function.

Given the graph of a function, identify the parent function.

Given the graph of a function, identify the transformations that map the preimage to the image in order to determine the equation of the image.

Using a transformational approach, write the equation of a function given its graph.

Write the equation of a linear function in point-slope form.

Use parametric equations to represent a linear or quadratic function.

Identify the domain and range of a function presented algebraically or graphically.

Describe restricted/discontinuous domains and ranges.

Write domain and range of a function using interval notation.

Identify the zeros of a function presented algebraically or graphically.

Use long division to find all zeroes of a polynomial.

Use synthetic division/substitution to find all zeros.

Identify the intercepts of a function presented algebraically or graphically.

Given the graph of a function, identify intervals on which the function is increasing and decreasing.

Find the equations of vertical and horizontal asymptotes of functions.

Graph rational functions showing zeroes, removable discontinuities (holes), and vertical and horizontal asymptotes.

Describe the end behavior of a function.

Describe the end behavior of a function as x approaches positive and negative infinity.

Find the inverse of a function.

Graph the inverse of a function as a reflection across the line, y = x.

Investigate exponential and logarithmic functions, using the graphing calculator.

Convert between logarithmic and exponential forms of an equation with bases consisting of natural numbers.

Find the composition of two functions.

Use composition of functions to verify two functions are inverses.

Find the composition of multiple functions.

Find the value of a composition of multiple functions for a given element from the domain.
 

Find the domain and range of a piecewise function.

Describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.

Define a polynomial function, given its zeros.

Determine a factored form of a polynomial expression from the x-intercepts of the graph of its corresponding function.

For a function, identify zeros of multiplicity greater than 1 and describe the effect of those zeros on the graph of the function.

Given a polynomial equation, determine the number of real solutions and nonreal solutions.

Use long division to find all zeroes of a polynomial function.

Use synthetic division/substitution to find all zeros.

Collect and analyze data. 

Investigate scatterplots to determine if patterns exist, and then identify the patterns.

Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, and logarithmic functions.

Make predictions, using data, scatterplots, or the equation of the curve of best fit.

Given a set of data, determine the model that would best describe the data.

Use the correlation coefficient, r, from the graphing calculator to determine how well a regression curve approximates data points.

Translate "y varies jointly as x and z" as y = k x z .

Translate "y is directly proportional to x" as y = k x .

Translate "y is inversely proportional to x" as y = k x .

Given a situation, determine the value of the constant of proportionality.

Set up and solve problems, including real-world problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

Identify inverse or direct variation given a graph, equation, table, or real-world application.

Identify the properties of a normal probability distribution.

Describe how the standard deviation and the mean affect the graph of the normal distribution.

Compare two sets of normally distributed data using a standard normal distribution and z-scores.

Represent probability as area under the curve of a standard normal probability distribution.

Use the graphing calculator or a standard normal probability table to determine probabilities or percentiles based on z-scores.

Compare and contrast permutations and combinations.

Calculate the number of combinations of n objects taken r at a time.

Calculate the number of permutations of n objects taken r at a time.

Use permutations and combinations as counting techniques to solve real-world problems.

Find the product of two 2 x 2 matrices by hand.

Find the product of two matrices greater than 2 x 2 using a graphing calculator.

Use matrix multiplication to solve practical problems.

Represent and solve a system of no more than three linear equations in matrix form.

Find the inverse of a matrix with a graphing calculator.

Find the determinant of a matrix with a graphing calculator.

Identify the identity matrix and its properties.