Algebra 2 Honors Curriculum

Students will:

• Solve absolute value linear equations and inequalities.
• Recognize the general shape of the absolute value function family.
• Use knowledge of transformations to convert between equations and the corresponding graphs of absolute value functions.
• Investigate and analyze linear and absolute value function families algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, and end behavior.
• Make connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs.
• Find the inverse of a linear function.
• Investigate and analyze composition of functions, algebraically and graphically.
• Create the graph of a piecewise function. 

Students will:

• Factor polynomials completely in one or two variables.
• Solve quadratic equations over the set of complex numbers.
• Recognize the general shape of the quadratic function family.
• Use knowledge of transformations to convert between equations and the corresponding graphs of quadratic functions.
• Investigate and analyze quadratic function family algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, and end behavior.
• Investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.
• Perform operations on complex numbers and express the results in simplest form using patterns of the powers of i.

Students will:

• Solve systems of linear-quadratic and quadratic-quadratic algebraically and graphically.
• Collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of quadratic functions.
• Make predictions, using data, scatterplots, or the equation of the curve of best fit
  Solve practical problems involving an equation of the curve of best fit.

Students will:

• Recognize the general shape of polynomial function families and identify the graph of a function from the equation.
• Use knowledge of transformations to convert between equations and the corresponding graphs of polynomial functions.
• Investigate and analyze polynomial function families algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, and end behavior.
• Define a polynomial function in factored form, given its zeros.
• 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 and type of solutions.
• Use long division and synthetic division to investigate the behaviors of polynomial and rational functions.

Students will:

• Add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents.
• Solve equations containing radical expressions.
• Recognize the general shape of the square root and cube root function families.
• Use knowledge of transformations to convert between equations and the corresponding graphs of square root and cube root functions.
• Investigate and analyze square root and cube root function families algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, and end behavior.
• Find the inverse of square and cube root functions.

Students will:

• Recognize the general shape of the exponential and logarithmic function families.
• Use knowledge of transformations to convert between equations and the corresponding graphs of exponential and logarithmic functions.
• Investigate and analyze exponential and logarithmic function families algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, vertical and horizontal asymptotes and end behavior.
• Find the inverse of exponential and logarithmic functions.
• Collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of exponential functions.
• Use properties of logarithms to condense and expand logarithmic expressions.
• Solve equations containing logarithmic and exponential expressions.

Students will:

• Add, subtract, multiply, divide, and simplify rational algebraic expressions.
• Solve equations containing rational algebraic expressions.
• Recognize the general shape of the rational function family.
• Use knowledge of transformations to convert between equations and the corresponding graphs of rational functions.
• Investigate and analyze rational function family algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, vertical and horizontal asymptotes and end behavior.
• Represent and solve problems, including practical problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

Students will:

• Distinguish between a sequence and a series.
• Generalize patterns in a sequence using explicit and recursive formulas.
• Use and interpret the notations å, n, nth term, and an.
• Given the formula, determine an (the nth term) for an arithmetic or a geometric sequence.
• Given formulas, write the first n terms and determine the sum, Sn, of the first n terms of an arithmetic or geometric series.
• Given the formula, determine the sum of a convergent infinite series.
• Model practical situations using sequences and series.

Students will:

• Identify and describe properties of a normal distribution
• Interpret and compare z-scores for normally distributed data
• Apply properties of normal distributions to determine probabilities associated with areas under the standard normal curve
• Compute and distinguish between permutations and combinations

Students will:

• Multiply matrices by a scalar.
• Add, subtract, and multiply matrices.
• Model problems with a system of no more than three linear equations.
• Express a system of linear equations as a matrix equation.
• Solve a system of equations using matrices.
• Determine the inverse of a two-by-two or three-by-three matrix using paper and pencil.

Students will:

• Make connections between big ideas learned throughout the course.
• Deepen and extend skills learned during the course.