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Algebra 2 honors

Algebra 2 Honors is a difficult course for a middle school student. This represents the second high school credit since algebra 1 honors is a pre-requisite.

In Volusia county we structure courses according to Common Core State Standards (CCSS).

We used to structure courses by Florida's Next Generation Sunshine State Standards (NGSSS) and associated benchmarks.

We divide the courses by Essential Questions. The Essential Questions are then divided by Measurement Topics which are then outlined with learning targets.

Unit 1: Linear Functions

Essential Question(s): In what ways can the problem be solved, and why should one method be chosen over the other? How can algebra describe the relationship between sets of numbers? How can the relationship between quantities best be represented?

MACC.912.A-REI.1.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.	 apply order of operations and inverse operations to solve equations.  construct an argument to justify my solution process.
MACC.912.A-CED.1.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.	 solve formulas for a specified variable.
MACC.912.F-IF.2.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.	 define interval, rate of change, and average rate of change.  explain the connection between average rate of change and the slope formula.  calculate the average rate of change of a function, represented either by function notation, a graph, or a table, over a specific input interval.  compare the rates of change of two or more functions when they are represented with function notation, with a graph, or with a table.  interpret the meaning of the average rate of change (using units) as it relates to a real-world problem.
MACC.912.F-IF.3.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima.	 identify that the parent function for lines is the line f(x) = x.  identify the point-slope form of a linear function as .  graph a line in point-slope form and use the graph to show where the starting point and the slope (m) are represented on the graph.  identify the slope-intercept form of a linear function as f(x) = mx + b.  graph a line in slope-intercept form and use the graph to show where the y-intercept (b) and the slope (m) are represented on the graph.  identify the standard form of a linear function as Ax + By = C.  use the definitions of x-intercept and y-intercept to find the intercepts of a standard form line and graph the line.  relate the constants A, B, and C to the values of the x-intercepts, y-intercepts, and slope.
MACC.912.F-LE.2.5 Interpret the parameters in a linear or exponential function in terms of a context.	 identify the names and definitions of the parameters m and b in the linear function f(x)=mx + b.  explain the meaning (using appropriate units) of the slope of a line when the line models a real-world relationship.  explain the meaning (using appropriate units) of the y-intercept and other points on the line when the line models a real-world relationship.  compose an original
MACC.912.A-CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.	 identify the variables and quantities represented in a real-world problem.  determine the best models for the real-world problem.  write the system of equations and/or inequalities that best models the problem.  graph the system on coordinate axes with appropriate labels and scales.  interpret solutions in the context of the situation modeled and decide if they are reasonable.
MACC.912.A-REI.3.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.	 define system of linear equations and solution of a system.  explain why some linear systems have no solutions and identify linear systems that have infinitely many solutions.  solve a system of linear equations algebraically (by substitution or elimination) to find an exact solution.  graph a linear equation on a coordinate plane.  determine the approximate solution to a system of linear equations by graphing both equations and estimating the point of intersection.
MACC.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems.	 identify the variables and quantities represented in a real-world problem.  determine the best model for the real-world problem.  write the equation or inequality that best models the problem.  solve the equation or inequality.  interpret the solution in the context of the problem.
MACC.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.	 identify the variables and quantities represented in a real-world problem.  determine the best model for the real-world problem.  write the equation that best models the problem.  determine appropriate scale and label the axes.  graph equations on coordinate axes with appropriate labels and scales.
MACC.912.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.	 explain why f(x) + k translates the original graph of f(x) up k units and why f(x)-k translates the original graph of f(x) down k units.  explain why f(x + k) translates the original graph of f(x) left k units and why f(x-k) translates the original graph of f(x) right k units.  explain why kf(x) vertically stretches or shrinks the graph of f(x) by a factor of k and predict whether a given value of k will cause a stretch or shrink.  explain why f(kx) horizontally stretches or shrinks the graph of f(x) by a factor of 1/k and predict whether a given value of k will cause a stretch or a shrink.  describe the transformation that changed a graph of f(x) into a different graph when given pictures of the pre-image and image.  determine the value of k given the graph of a transformed function.  graph the listed transformations when given a graph of f(x) and a value of k ( f(x) k, f(x k), kf(x), and f(kx).  use a graphing calculator to generate examples of functions with different k values.  analyze similarities and differences between functions with different k values.

Unit 2: Quadratic Functions

Essential Question(s): Can the student model and solve quadratic equations using a variety of algebraic methods? Why structure expressions in different ways?

MACC.912.A-REI.2.4 Solve quadratic equations in one variable.	 solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.  use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions, and derive the quadratic equation from this form.
MACC.912.N-CN.1.1 Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.	 know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.  use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.  solve quadratic equations with real coefficients that have complex solutions.  express the solution of a quadratic equation as a complex number, a + bi.  Write the factors of polynomials using complex numbers.  use complex numbers to rewrite a sum of squares, a2 + b2 as the product of a complex number and its conjugate.  show that factored quadratics have real coefficients when written in standard form.
MACC.912.N-CN.1.2 Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
MACC.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions.
MACC.912.N-CN.3.8 Honors Only Extend polynomial identities to the complex numbers.
MACC.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems.	 determine the best model for the real-world problem, write and solve the equation or inequality, and interpret the solution in the context of the problem.  write the system of equations and/or inequalities that best models the problem.  interpret solutions in the context of the situation modeled and decide if they are reasonable.
MACC.912.A-CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
MACC.912.F-IF.3.7(a,b,c,e) Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.	 graph quadratic functions showing intercepts, maxima, and minima.  use technology to graph a quadratic function and to find precise values for the intercepts, maximum, or minimum.  graph square root, cube root and piecewise-defined functions, including step functions and absolute value functions.  explain that there are three forms of quadratic functions: standard form, vertex form, and factored form.  explain that the graph of all three forms of quadratic functions is a parbola.  find the x-intercepts of a quadratic to find the axis of symmetry.  identify the line of symmetry.  sketch a graph of a parabola written in vertex form.  apply completing the square to rewrite a quadratic function in vertex form.  factor a quadratic expression to find the zeroes of the function it represents.  identify and factor perfect-square trinomials.  define an exponential function.  rewrite exponential functions using the properties of exponents.
MACC.912.F-IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a) 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.
MACC.912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
MACC.912.F-BF.2.3 dentify 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. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.	 explain why f(x) + k translates the original graph of f(x) up k units and why f(x) – k translates the original graph of f(x) down k units.  explain why f(x+k) translates the original graph of f(x) left k units and why f(f-x) translates the original graph of f(x) right k units.  explain why kf(x) vertically stretches or shrinks the graph of f(x) by a factor of k and predict whether a given value of k will cause a stretch or a shrink.  explain why f(fx) horizontally stretches or shrinks the graph of f(x) by a factor of 1/k and predict whether a given value of k will cause a stretch or a shrink.  describe the transformation that changed a graph of f(x) into a different graph when given pictures of the pre-image and image.  determine the value of k given the graph of a transformed functions.  graph the listed transformations when given a graph of f(x) and a value of k (f(x) ±k, f(x±k), k(f(x) and f(kx)).  use a graphing calculator to generate examples of functions with different k values.  analyze the similarities and difference between functions with different k values.  recognize from a graph if the function is even or odd.  explain that a function is even when f(-x) = (fx) and its graph has y-axis symmetry.  explain that a function is odd when f(-x) = -f(x) and its graph has 180° rotational symmetry.  relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
MACC.912.F-IF.2.5 Relate the domain of a function to its graph and where applicable, to the quantitative relationship it describes.
MACC.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.	 identify the variables and quantities represented in a real-world problem.  write the equation that best models the problem.  determine an appropriate scale and label the axes.  graph equations on coordinate axes.
MACC.912.A-REI.3.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.	 determine the approximate solution of a system of equations in which on equation is linear and one equation is quadratic by graphing and estimating the point(s) of intersection.
MACC.912.G-GPE.1.2 Derive the equation of a parabola given a focus and directrix.	 define a parabola.  determine the distance from a point on the parabola to the directrix.  determine the distance from a point on the parabola to the focus using the distance formula (Pythagorean Theorem).  equate the two distance expressions for a parabola to write its equation.  identify the focus and directrix of a parabola when given its equation.

Here are the old essential questions:

Can the student identify and graph different forms for the equation of a line? Can the student solve a linear equation or inequality? Can the student solve real world problems using linear functions? Can the student graph linear inequalities? Can the student solve and graph systems of linear equations and inequalities?
Can the student solve and graph absolute value equations? Can the student solve and graph absolute value inequalities? Can the student identify domain and range of absolute value graphs?
Can the student solve quadratic equations using various methods? Can the student identify the real and imaginary parts of complex numbers and perform basic operations? Can the student graph and identify parts of quadratic equations given various forms?
Can the student solve polynomial functions? Can the student graph and describe the characteristics of a polynomial function? Can the student use polynomials to solve real world applications?
Can the student solve radical functions in various forms? Can the student graph and describe the characteristics of a radical function?
Can the student perform operations of functions? Can the student solve problems involving functions and their inverses?
Can the student define, graph, and solve exponential functions? Can the student define, graph, and solve logarithmic functions? Can the student analyze the relationship between exponential and logarithmic functions? Can the student apply exponential and logarithmic functions to solve real world applications?
Can the student solve rational equations? Can the student graph and analyze the characteristics of a rational function including points of discontinuity?
Can the student define and evaluate arithmetic and geometric sequences and series? Can the student analyze arithmetic and geometric sequences and series to find the nth term?
Can the student analyze and differentiate different intersections of a cone and a plane? How can one identify conic sections based on their equations? How does the equation of a conic section relate to its graph? How can one differentiate between ellipses and hyperbolas algebraically and graphically?

Measurement Topic	Learning Target	NGSSS
Linear Functions	Decide whether a given linear expression, equation, or inequality is always, sometimes, or never true.	MA.912.A.10.3
	Solve literal equations for specified variable.	MA.912.A.3.3
	Solve problems using direct variation.	MA.912.A.2.12
	Identify and graph linear functions including function notation and domain and range.	MA.912.A.2.6
	Write an equation of a line given any of the following information: two points on a line, its slope and one point on a line or its graph.	MA.912.A.3.10
	Find an equation of a new line parallel to a given line or perpendicular to a given line through a given point on the new line.	MA.912.A.3.10
	Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods.	MA.912.A.3.14
	Solve real world problems involving systems of linear equations and inequalities in two and three variables.	MA.912.A.3.15
	Recognize, interpret, and graph functions defined piecewise.	MA.912.A.2.9
Absolute Value	Solve and graph the solutions of absolute value equations with one variable.	MA.912.A.3.6
	Solve and graph the solutions of absolute value inequalities with one variable.	MA.912.A.3.6
	Graph absolute value equations in two variables and identify domain and range.	MA.912.A.2.5
	Describe and graph transformations of absolute value functions and identify domain and range.	MA.912.A.2.10
	Graph absolute value inequalities in two variables and identify domain and range.	MA.912.A.2.5

REVIEW 1 (with answers)

links on this site:

Exponential notation Percent converting fractions and decimals 8th grade FCAT sample test (2.0)

pre algebra sample questions rates and proportions

greatest common factor least common multiple prime factorization

Introduction to rules for using exponents

links off site

7th grade FCAT sample test (2.0)

8th grade FCAT sample test (2.0)

brightstorm.com

khanacademy.org

webmath.com aaamath.com www.mathway.com/ math.com/students/homeworkhelp.html

algebrahelp.com algebra.com www.purplemath.com