## Algebra-2 Content & Skills

#### Algebra-2 content/skills

*Pre-Requisite Expectations*

- Graph quadratic functions and show intercepts, maxima, and minima (F-IF.7a)
- Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph (F-IF.8)
- Solve quadratic equations in one variable using factoring, completing the square, and quadratic formula (A-REI.4)

- Evaluate functions for inputs in their domains (F-IF.2)
- Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range (F-IF.1)
- Understand that if
*f*is a function and*x*is an element of its domain, then*f*(*x*) denotes the output of*f*corresponding to the input of*x*(F-IF.1) - Understand that the graph of
*f*is the graph of the equation*y*=*f*(*x*) (F.IF.1) - Use function notation (F-IF.2)

*Quadratic Equations tutorials*

- Solving-quadratic-equations-by-square-roots
- Factoring-quadratic-expressions
- Solving-quadratic-equations-by-completing-the-square
- Using-the-quadratic-formula
- Features-of-quadratic-functions
- Graphing-a-quadratic-function

*Function tutorials*

*Learning Expectations*

- Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions (F-IF.7b)
- Identify the effect on the graph of 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) - Find the value of
*k*given the graphs (F-BF.3) - Experiment with cases and illustrate an explanation of the effects on the graph using technology (F-BF.3)
- Recognizing even and odd functions from their graphs and algebraic expressions for them (F-BF.3)

*Functions Tutorials*

*Learning Expectations*

- Add, subtract, and multiply polynomials (A-APR.1)
- Determine zeros of a polynomial when factorizations are available (A-APR.3)
- Apply the Remainder Theorem (A-APR.2)
- Use the zeros of polynomials to construct a rough graph of a polynomial function (A-APR.3)
- Use long or synthetic division to rewrite rational expressions (A-APR.6)
- Rewrite simple rational expressions in different forms (A-APR.6)
- Solve simple rational equations in one variable, and give examples showing how extraneous solutions may arise (A-REI.2)

*Polynomial and Rational Functions Tutorials:*

- Adding, subtracting, and multiplying-polynomials
- Polynomial-division
- Synthetic-division
- Polynomial-remainder-theorem
- Factoring-higher-degree-polynomials
- Polynomial-end-behavior
- Simplifying-rational-expressions-introduction
- Rational-functions
- Asymptotes-and-graphing-rational-functions

#### Complex Numbers sub-unit

*Learning Expectations*

- Use the relation
*i*^{2}= -1, and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers (N.CN2) - Solve quadratic equations with real coefficients that have complex solutions (N-CN.7)

*Complex Numbers Tutorials*

*Learning Expectations*

- Rewrite expressions involving radicals and rational exponents using the property of exponents (N-RN.2)
- Interpret the parameters in an exponential function in terms of a context (F-LE.5)
- Solve simple radical equations in one variable, and give examples showing how extraneous solutions may arise (A-REI.2)
- Graph exponential and logarithmic functions, showing intercepts and end behavior (F-IF.7e)
- Find inverse functions (F-BF.4)
- Express as a logarithm, the solution to
*ab*, where^{ct}= d*a*,*c*, and*d*are numbers and the base*b*is 2, 10 or*e*; evaluate using technology (F-LE.4)

*Exponential and Logarithmic Functions Tutorials*

*Learning Expectations*

- Interpret pars of an expression, such as terms, factors, and coefficients of geometric and arithmetic sequences and series (A-SSE.1)
- Derive the formula for the sum of finite geometric series (when the common ratio is not 1) and use the formula to solve problems (A-SSE.4
- Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms (F-BF.2)

*Sequences and Series Tutorials*

Learning Expectations:

- Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not") (S-CP.1)
- Find the conditional probability of A given B as the fraction of B’s outcome that also belong to A and interpret the answer in terms of the model (S-CP.6)
- Apply the addition rule (i.e., P(A or B) = P(A) + P(B) – P(A and B) (S-CP.7))
- Interpret two-way frequency tables of data when two categories are associated with each object being classified (S-CP.4)
- Use a two-way table as a sample space to decide if the events are independent and approximate conditional probabilities (S-CP.4)
- Understand that two events
*A*and*B*are independent if the probability of*A*and*B*occurring together is the product of their probabilities, and use this characterization to determine if they are independent (S-CP.3)

Learning Expectations:

- Understand that statistics is a process for making inferences about population parameters based on a random sample from that population (S-IC.1)
- Decide if a specified model is consistent with results from a given data-generated process (S-IC.2)
- Recognize the purposes of and differences among sample surveys, experiments, and observational studies (S-IC.3)
- Explain how randomization applies to sample surveys, experiments, and observational studies (S-IC.3)
- Estimate the population mean or proportion using data from sample surveys, experiments, and observational studies (S-IC.4)
- Develop a margin of error through the use of simulation models for random sampling, sample surveys, experiments, and observational studies (S-IC.4)
- Compare two treatments using data from a randomized experiment (S-IC.5)
- Use simulations to decide if differences between parameters are significant (S-IC.5)
- Evaluate reports based on data (S-IC.5)

*Statistics Tutorials*Learning Expectations

- Understand the relationship between radians and degrees. Convert between radians and degrees (F.TF.1)
- Explain how the unit circle in the coordinate plan enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles transversed counterclockwise around the unit circle (i.e., construct the unit circle for multiples of and ) (F-TF.2)
- Evaluate sine, cosine, and tangent for various angle measures
- Graph simple trigonometric functions showing period, midline, and amplitude (F-IF.7e)
- Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline (F-TF.5)
- Use the Pythagorean identify sin
^{2}Ѳ + cos^{2}Ѳ = 1 to find sin Ѳ, cos Ѳ, or tan Ѳ given sin Ѳ, cos Ѳ, or tan Ѳ and the quadrant of the angle (F-TF.8)