OCG - Algebra 2

There are no prerequisites for this course.

South Carolina Standards:  (List the standards students are expected to master in this course)

● Standards denoted by an asterisk (*) are SCCCR Graduation Standards.

• Arithmetic with Polynomials and Rational Expressions
  The student will:
  A2.AAPR.1* Add, subtract, and multiply polynomials and understand that polynomials are
  closed under these operations.
  A2.AAPR.3 Graph polynomials identifying zeros when suitable factorizations are available
  and indicating end behavior. Write a polynomial function of least degree
  corresponding to a given graph. (Limit to polynomials with degrees 3 or less.)
  Creating Equations
  The student will:
  A2.ACE.1* Create and solve equations and inequalities in one variable that model
  real-world problems involving linear, quadratic, simple rational, and
  exponential relationships. Interpret the solutions and determine whether they
  are reasonable.
  A2.ACE.2* Create equations in two or more variables to represent relationships between
  quantities. Graph the equations on coordinate axes using appropriate labels,
  units, and scales.
  A2.ACE.3 Use systems of equations and inequalities to represent constraints arising in
  real- world situations. Solve such systems using graphical and analytical
  methods, including linear programing. Interpret the solution within the context
  of the situation. (Limit to linear programming.)
  A2.ACE.4* Solve literal equations and formulas for a specified variable including
  equations and formulas that arise in a variety of disciplines.
  Reasoning with Equations and Inequalities
  The student will:
  A2.AREI.2* Solve simple rational and radical equations in one variable and understand
  how extraneous solutions may arise.
  A2.AREI.4* Solve mathematical and real-world problems involving quadratic equations in
  one variable.
  b. Solve quadratic equations by inspection, taking square roots,
  completing the square, the quadratic formula and factoring, as
  appropriate to the initial form of the equation. Recognize when the
  quadratic formula gives complex solutions and write them as a+ bi for
  real numbers a and b .
  (Note: A2.AREI.4b is not a Graduation Standard.)
  A2.AREI.7 Solve a simple system consisting of a linear equation and a quadratic equation
  in two variables algebraically and graphically. Understand that such systems
  may have zero, one, two, or infinitely many solutions. (Limit to linear equations
  and quadratic functions.)
  A2.AREI.11* Solve an equation of the form f(x) = g(x) graphically by identifying the x
  -coordinate(s) of the point(s) of intersection of the graphs of y = f(x) and
  y = g(x) .
  Structure and Expressions
  The student will:
  A2.ASE.1* Interpret the meanings of coefficients, factors, terms, and expressions based
  on their real-world contexts. Interpret complicated expressions as being
  composed of simpler expressions.
  A2.ASE.2* Analyze the structure of binomials, trinomials, and other polynomials in order
  to rewrite equivalent expressions.
  A2.ASE.3* Choose and produce an equivalent form of an expression to reveal and explain
  properties of the quantity represented by the expression.
  (Note: A2.ASE.3b and 3c are not Graduation Standards.)
  b. Determine the maximum or minimum value of a quadratic
  function by completing the square.
  c. Use the properties of exponents to transform expressions for
  exponential functions.
  Building Functions
  The student will:
  A2.FBF.1* Write a function that describes a relationship between two quantities. (Note:
  IA.FBF.1a is not a Graduation Standard.)
  a. Write a function that models a relationship between two
  quantities using both explicit expressions and a recursive process
  and by combining standard forms using addition, subtraction,
  multiplication and division to build new functions.
  b. Combine functions using the operations addition, subtraction,
  multiplication, and division to build new functions that describe the
  relationship between two quantities in mathematical and real-world
  situations.
  A2.FBF.2* Write arithmetic and geometric sequences both recursively and with an explicit
  formula, use them to model situations, and translate between the two forms.
  A2.FBF.3* Describe the effect of the transformations kf(x), f(x) + k, f(x + k), and
  combinations of such transformations on the graph of y = f(x) for any real
  number k . Find the value of k given the graphs and write the equation of a
  transformed parent function given its graph.
  Interpreting Functions
  The student will:
  A2.FIF.3* Define functions recursively and recognize that sequences are functions,
  sometimes defined recursively, whose domain is a subset of the integers.
  A2.FIF.4* Interpret key features of a function that models the relationship between two
  quantities when given in graphical or tabular form. Sketch the graph of a
  function from a verbal description showing key features. Key features include
  intercepts; intervals where the function is increasing, decreasing, constant,
  positive, or negative; relative maximums and minimums; symmetries; end
  behavior and periodicity.
  A2.FIF.5* Relate the domain and range of a function to its graph and, where applicable,
  to the quantitative relationship it describes.
  A2.FIF.6* Given a function in graphical, symbolic, or tabular form, determine the average
  rate of change of the function over a specified interval. Interpret the meaning
  of the average rate of change in a given context.
  A2.FIF.7* Graph functions from their symbolic representations. Indicate key features
  including intercepts; intervals where the function is increasing, decreasing,
  positive, or negative; relative maximums and minimums; symmetries; end
  behavior and periodicity. Graph simple cases by hand and use technology for
  complicated cases.
  a. Graph rational functions, identifying zeros and asymptotes when
  suitable factorizations are available, and showing end behavior.
  b. Graph radical functions over their domain show end behavior.
  c. Graph exponential showing intercepts and end behavior.
  A2.FIF.8* Translate between different but equivalent forms of a function equation to
  reveal and explain different properties of the function. (Note: A2.FIF.8b is not a
  Graduation Standard.)
  b. Interpret expressions for exponential functions by using the properties
  of exponents.
  A2.FIF.9* Compare properties of two functions given in different representations such as
  algebraic, graphical, tabular, or verbal.
  Linear, Quadratic, and Exponential
  The student will:
  A2.FLQE.1* Distinguish between situations that can be modeled with linear functions or
  exponential functions by recognizing situations in which one quantity changes
  at a constant rate per unit interval as opposed to those in which a quantity
  changes by a constant percent rate per unit interval. (Note: A2.FLQE.1b is not
  a Graduation Standard.)
  b. Recognize situations in which a quantity grows or decays by a
  constant percent rate per unit interval relative to another.
  A2.FLQE.2* Create symbolic representations of linear and exponential functions, including
  arithmetic and geometric sequences, given graphs, verbal descriptions, and
  tables.
  A2.FLQE.5* Interpret the parameters in a linear or exponential function in terms of the
  context.
  Complex Number System
  The student will:
  A2.NCNS.1* Know there is a complex number such that i i2 =− 1 , and every complex
  number has the form a + bi with a and b real.
  A2.NCNS.7* Solve quadratic equations in one variable that have complex solutions.List SC standard by number and description

 South Carolina College- and Career-Ready Mathematical Process Standards
A mathematically literate student can:
1. Make sense of problems and persevere in solving them.
a. Relate a problem to prior knowledge.
b. Recognize there may be multiple entry points to a problem and more than
one path to a solution.
c. Analyze what is given, what is not given, what is being asked, and what
strategies are needed, and make an initial attempt to solve a problem.
d. Evaluate the success of an approach to solve a problem and refine it if
necessary.
2. Reason both contextually and abstractly.
a. Make sense of quantities and their relationships in mathematical and
real-world situations.
b. Describe a given situation using multiple mathematical representations.
c. Translate among multiple mathematical representations and compare the
meanings each representation conveys about the situation.
d. Connect the meaning of mathematical operations to the context of a given
situation.
3. Use critical thinking skills to justify mathematical reasoning and critique the
reasoning of others.
a. Construct and justify a solution to a problem.
b. Compare and discuss the validity of various reasoning strategies.
c. Make conjectures and explore their validity.
d. Reflect on and provide thoughtful responses to the reasoning of others.
4. Connect mathematical ideas and real-world situations through modeling.
a. Identify relevant quantities and develop a model to describe their
relationships.
b. Interpret mathematical models in the context of the situation.
c. Make assumptions and estimates to simplify complicated situations.
d. Evaluate the reasonableness of a model and refine if necessary.
5. Use a variety of mathematical tools effectively and strategically.
a. Select and use appropriate tools when solving a mathematical problem.
b. Use technological tools and other external mathematical resources to
explore and deepen understanding of concepts.
6. Communicate mathematically and approach mathematical situations with
precision.
a. Express numerical answers with the degree of precision appropriate for
the context of a situation.
b. Represent numbers in an appropriate form according to the context of the
situation.
c. Use appropriate and precise mathematical language.
d. Use appropriate units, scales, and labels.
7. Identify and utilize structure and patterns.
a. Recognize complex mathematical objects as being composed of more
than one simple object.
b. Recognize mathematical repetition in order to make generalizations.
c. Look for structures to interpret meaning and develop solution strategies.

Required Materials:

• McGraw-Hill. Glencoe Algebra 2, Student Edition. New ed. New York: Glencoe/McGraw-Hill, 2012. Print.
• Pearson Education. Pearson Algebra 2, Student Edition. New Jersey: Prentice Hall, 2012. Print.
• Student access to a graphing calculator is essential to the full implementation of the SCCCR Standards.