Unit or Topic Skills:

• I can add, subtract, and multiply polynomials.

• I can recognize and use the structure of an expression to identify ways to rewrite it (factoring all methods, gcf, dops, trinomial, factor by grouping. 

• I can identify common structures of an expression (such as the difference of two squares) and use that structure to rewrite it.

• I can solve a rational equation and check for extraneous roots. 

• I can describe an appropriate domain of a function (include real-world context. 

•  I can identify function transformations using f(x) + k, k f(x), f(kx), and f(x + k): i) identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); ii) find the value of k given the graphs; iii) write a new function using the value of k; and iv) use technology to experiment with cases and explore the effects on the graph.

Unit or Topic Skills:

• I can calculate and interpret the average rate of change of a function over a specified interval. (Functions may be presented by function notation, a table of values, or graphically. • Algebra II tasks have a real-world context and may involve polynomial, square root, cube root, exponential, logarithmic, and trigonometric functions.)

• I can solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. 

• I can i) recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x); ii) find the solutions approximately using technology to graph the functions or make tables of values; iii) find the solution of f(x) < g(x) or f(x) ≤ g(x) graphically.

• Convert between radical expressions and expressions with rational exponents using the properties of exponents. 

• Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.

• I can recognize and use the structure of an expression to identify ways to rewrite it. (includes factoring sum and difference of cubes. )

• I can solve quadratic equations in one variable.  (Solve quadratic equations by: i) inspection, ii) taking square roots, iii) factoring, iv) completing the square, v) the quadratic formula, and vi) graphing. Write complex solutions in a + bi form.)

Unit or Topic Skills:

• I can determine when a quadratic equation has a complex solution.

•  I can determine the complex solutions of a quadratic equation with real coefficients.

• I can define i. 

• I can describe complex numbers in terms of their real and imaginary parts. 

• I can apply the commutative, associative, and distributive properties to complex numbers in order to add, subtract, and multiply.

• I can analyze and interpret the key features of a function (quadratic and polynomial functions) using a graph or table. These key features  include:  intercepts;  intervals where the function is increasing, decreasing, positive or negative;  relative maximums and minimums;  symmetries;  end behavior;  periodicity. I can describe and sketch a graphic representation of a function given a verbal description of the relationship.

• I can interpret algebraic expressions that describe real-world scenarios. This means:  I can interpret the parts of an expression including the factors, coefficients, and terms.  

• I can use grouping strategies to interpret expressions. 

• I can identify common structures of an expression (such as the difference of two squares) and use that structure to rewrite it.

• I can determine the zeros of a polynomial from its factors. I can describe and sketch the graph of a polynomial given its zeros.

• I can use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 

• I can determine the quotient and remainder of rational expressions using inspection, long division, and/or a computer algebra system.

• I can explain the Remainder Theorem. 

• I can apply the Remainder Theorem in order to determine the factors (or zeros) of a polynomial.

• I can explain why the x-coordinates of a point of intersection of two graphs are the solution to the equation f(x)=g(x). I can determine the approximate solutions of a system of equations using technology, tables, or successive approximations. 

• I can find the key features of and then graph the following families of functions:  Linear and Quadratic (intercepts, maxima, minima)  Square root, and cube root.  Polynomial functions (zeros via factorization, and end behavior)  Rational functions (zeros, asymptotes, end behavior)  Exponential and logarithmic functions (intercepts, end behavior).

• I can use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay. Note: Tasks also include real world problems that involve compounding growth/decay (A = P(1 + (r/n))nt) and continuous compounding growth/decay (A = Pert).

Unit or Topic Skills:

• I can find the inverse of a one-to-one function both algebraically and graphically.

• I can solve exponential models using logarithms with base 2, 10, or e. 

• I can evaluate the logarithm to find a real number approximation (using technology).

• I can derive the formula for a finite geometric series and use it to solve problems.

• I can determine the appropriate method for writing a function that describes the relationship between two quantities. This means:  I can determine an explicit expression, a recursive process, or steps for calculation appropriate to the context.  

• I can combine standard function types using arithmetic operations. 

• I can analyze probabilities to make fair decisions. 

• I can analyze decisions and strategies using probability concepts.

• I can determine when a data set warrants a normal distribution. 

• I can determine the mean and standard deviation of a data set and fit it to a normal distribution. 

• I can estimate population percentages based on mean, standard deviation, and distribution. 

• I can estimate the areas under the normal curve using calculators, spreadsheets, and tables. 

• I can define statistics in terms of inferences, population parameters, and random sampling. 

• I can decide if a model is consistent with results, given a data-generating process such as simulation.

• I can compare two treatments using data from a randomized experiment. I can decide if differences are significant by using simulations.

• I can describe the importance of the unit circle and all of its parts.

• I can determine the trigonometric function that best models a situation based on period, amplitude, frequency, and midline.