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Algebra 2 2018 - 2019

Curriculum Guide Algebra 2 (1200330)

Algebra 2 Honors (#1200340)

Clay County Public Schools 900 Walnut Street

Green Cove Springs, FL 32043 U.OneClay.net

Clay County Schools 1 Algebra 2

Course Description:Algebra II - (1200330) Algebra II Honors - (1200340)

Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include polynomial, rational, and radical functions. Students work closely with the expressions that define the functions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, prescribe

that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

How to use this guide:

Each unit has a topic, essential question(s), suggested pacing, vocabulary, a set of standards, and resources to align with the topic. Item specifications and content limits are provided within each unit that are linked directly to the standard being taught within the unit. The Number and Quantity standards are in all units: they require students to define appropriate quantities for the purpose of modeling, choose an appropriate level of accuracy, and to choose and interpret units. The list of suggested resources is not exhaustive and additional high quality standards based resources exist. This is a working document and, as new resources and additional EOC information becomes available, the guide is subject to updates.

Suggested ResourcesCarnegie Learning Series for Algebra 2Math NationKahn AcademyCommon Core Flip BookAlgebra 2 EOC Item SpecificationsTest Design Summary and BlueprintHigh School Flip Book - Common Core State Standards for Mathematics

Mathematical Practices


The Mathematical Practices are a part of each course description for Grades 3-8, Algebra 1, Geometry, and Algebra 2. These practices are an important part of the curriculum and should be assessed in every unit.1

1. Make sense of problems and persevere in solving them. (MAFS.K12.MP.1)Solving a mathematical problem involves making sense of what is known and applying a thoughtful and logical process which sometimes requires perseverance, flexibility, and a bit of ingenuity.

2. Reason abstractly and quantitatively. (MAFS.K12.MP.2)The concrete and the abstract can complement each other in the development of mathematical understanding: representing a concrete situation with symbols can make the solution process more efficient, while reverting to a concrete context can help make sense of abstract symbols.

3. Construct viable arguments and critique the reasoning of others. (MAFS.K12.MP.3)A well-crafted argument/critique requires a thoughtful and logical progression of mathematically sound statements and supporting evidence.

4. Model with mathematics. (MAFS.K12.MP.4)Many everyday problems can be solved by modeling the situation with mathematics.

5. Use appropriate tools strategically. (MAFS.K12.MP.5)Strategic choice and use of tools can increase reliability and precision of results, enhance arguments, and deepen mathematical understanding.

6. Attend to precision. (MAFS.K12.MP.6)Attending to precise detail increases reliability of mathematical results and minimizes miscommunication of mathematical explanations.

7. Look for and make use of structure. (MAFS.K12.MP.7)Recognizing a structure or pattern can be the key to solving a problem or making sense of a mathematical idea.

8. Look for and express regularity in repeated reasoning. (MAFS.K12.MP.8)Recognizing repetition or regularity in the course of solving problems can lead to results more quickly and efficiently.

1 Note also that Number and Quantity standards should be assessed in all units. These standards require students to define appropriate quantities for the purpose of modeling, choose an appropriate level of accuracy, and to choose / interpret units.Clay County Schools 3 Algebra 2

ALGEBRA 2 CONCEPTS YEAR AT A GLANCENote: All Literacy Standards and Mathematical Practices listed in the course description should be incorporated throughout

each unit.

Quarter 1 (37 days)● Unit 1: Functions (14 days)● Unit 2: Linear Functions, Equations, and Inequalities (15 days)● Unit 3: Piecewise-Defined Functions (5 days)

Extra days: First Day (1 day), remediation (2 days)

Quarter 2 (44 + 3 days)● Unit 4: Quadratics -- Part 1 (15 days)● Unit 5: Quadratics -- Part 2 (12 days)● Unit 6: Polynomial Functions (14 days)

Extra Days: Remediation (2 days), Review (1 day)

Quarter 3 (47 days)● Unit 7: Rational Expressions and Equations (7 days)● Unit 8: Expressions and Equations with Radicals and Rational Exponents (14 days)● Unit 9: Exponential and Logarithmic Functions and Transformations (15 days)● Unit 10: Sequences and Series (10 days)

Extra Days: Remediation (2 days)

Quarter 4 (46 + 3 days)● Unit 11: Probability (10 days)● Unit 12: Statistics (10 days)● Unit 13: Trigonometry -- Part 1 (10 days)● Unit 14: Trigonometry -- Part 2 (13 days)

Extra Days: Remediation (2 days), Review (1 day)


Quarter 1Course: Algebra 2 Time: 14 daysUnit 1: Functions

Presumed knowledge● Students should have a functional knowledge of basic

operations and order of operations with integers and fractions

Vocabulary for Functionsdomain, range, relation, function, polynomial, polynomial long division, inverse, composition, even function, odd function, solutions, y-intercepts, increasing/decreasing, maximum, minimum, transformations of functions

Unit 1: Functions

Objectives Carnegie Math Nation Standards

1.A Students will add, subtract, and multiply polynomials with rational coefficients.

1.2 1.11.2

MAFS.912.A-APR.1.1 Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

1.B Students will rewrite a rational expression as the quotient in the form of a polynomial added to the remainder divided by the divisor. Students will use polynomial long division to divide a polynomial by a polynomial.

4.2 1.3 MAFS.912.A-APR.4.6 Rewrite simple rational expressions in different forms; write a (x)/b(x) in the form q(x) + r(x)/b(x) , where a(x) , b(x) , q(x) , and r(x) are polynomials with the degree of r(x) less than the degree of b(x) , using inspection, long division, or, for the more complicated examples, a computer algebra system.

1.C Students will understand key features of linear functions and find the inverse of a linear function.

1.4 MAFS.912.F-BF.2.4 Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function, f, that has an inverse and write an expression for the inverse. For example, f(x) = 2 x3 or f(x) = (x+1)/(x–1) for x = 1.



1.D Students will write a function to model a real-world context by composing functions and the information within the context.

1.5 1.5 MAFS.912.F-BF.1.1c Write a function that describes a relationship between two quantities.c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

1.E Students will use a graph or a table of a function to determine values of the function’s inverse. Students will find the inverse of a function.

1.6 MAFS.912.F-BF.2.4a,c Find inverse functions.a. Solve an equation of the form f(x) = c for a simple function,f , that has an inverse and write an expression for the inverse.For example,f(x) = 2 x3or f(x) = (x+1/x-1) for x ≠ 1 .c. Read values of an inverse function from a graph or a table, given that the function has an inverse.

1.F Students will find the inverse of a function. Students will use composition of functions to determine if two functions are inverses. Students will use a graph or a table of a function to determine values of the function’s inverse. Students will restrict the domain of a function whose inverse is not a function so that the inverse will be a function.

1.7 MAFS.912.F-BF.2.4a,b,c,d Find inverse functions.a. Solve an equation of the form f(x) = c for a simple function,f , that has an inverse and write an expression for the inverse.For example, f(x) = 2 x3 or f(x) = (x+1/x-1) for x ≠ 1 .b. Verify by composition that one function is the inverse of another.c. Read values of an inverse function from a graph or a table, given that the function has an inverse.d. Produce an invertible function from a non-invertible function by restricting the domain.

1.G Students will recognize even and odd functions from their graphs and equations.

3.2 1.8 MAFS.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 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.

1.H Students will identify key features of the graphs of functions (solutions, y-intercepts,increasing/decreasing, maximum, minimum).

3.4 1.9

MAFS.912.F-IF.2.5:Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble engines in a factory, then the positive integers would be an appropriate domain for the function.

MAFS.912.F-IF.2.4:For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

MAFS.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.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

MAFS.912.F-IF.2.6: Calculate and interpret the average rate of


change of function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

1.I To discover the effect of the transformation of the graph when you add and multiply by another number.

1.10 MAFS.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 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.


Course: Algebra 2 Time: 15 daysUnit 2: Linear Functions, Equations, and Inequalities

Presumed Knowledge● Students can use order of operations, inverse

operations with integers and fractions, and understand how to graph on an xy coordinate plane

Vocabulary for Linear Functions, Equations, and InequalitiesFactors, coefficients, equation, expression, coordinate axis, function notation, domain, literal equation, intercepts, system of equations, linear function, even function, odd function, inverse, inequalities, system of inequalities

Unit 2: Linear Functions, Equations, and Inequalities


2.A Students will write and solve an equation in one variable that represents a real-world context. Students will complete an algebraic proof to explain steps for solving a simple equation. Students will construct a viable argument to justify a solution method.

2.1 MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. MAFS.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.

2.B Students will solve multi-variable formulas or literalequations for a specific variable. Create equations and inequalities in one variable and using them to solveproblems. Students will write and solve an equation with one variable that represents a real-world context.

2.2 MAFS.912.A-CED.1.4 Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. For example, rearrange Ohm’s law, V = IR, to highlight resistance, R.

MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems.

2.C Students will identify the quantities in a real-world 2.3 MAFS.912.A-CED.1.2 Create equations in two or more


situation that should be represented by distinct variables. Students will write constraints for a real-world context using equations, inequalities

variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

MAFS.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.

2.D Students will understand key features of linear functions and find the inverse of a linear function. They will also investigate whether linear functions are even, odd or neither.

2.4 MAFS.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.

MAFS.912.A.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.

MAFS.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 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.

2.E Students will solve systems of linear equations. Students will find a solution or an approximate solution for using a graph.Students will demonstrate why the intersection of two

2.5 MAFS.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.


functions is a solution to . MAFS.912.A-REI.4.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x)intersect are the solutions of the equation f(x) = g(x) ; find the solutions approximately (e.g., using technology to graph the functions, make tables of values, or find successive approximations). Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

2.F Students will identify the quantities in a real-worldsituation that should be represented by distinct variables. Students will write a system of equations given a situation. Students will write a system of equations for a modeling context that is best represented by a system of equations. Students will solve systems of linear equations. Students will write constraints for a real-world context using equations, inequalities, a system of equations, or a system of inequalities. Students will interpret the solution of a real-world context as viable or not viable.


MAFS.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.

MAFS.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.

2.G Students will solve systems of linear equations. Students will identify the quantities in a real-world situation that \should be represented by distinct variables. Students will write a system of equations given a real-world situation. Students will write a system of equations for a modeling context that is best represented by a system of equations.


MAFS.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



2.H Students will solve systems of linear equations with 3 variables..


2.I Students will identify the quantities in a real-worldsituation that should be represented by distinct variables. Students will write a system of equations given a real-world situation. Students will write a system of equations for a modeling context that is best represented by a system of equations.


2.J Students will write constraints for a real-world context using equations, inequalities, a system of equations, or a system of inequalities.

2.10 MAFS.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.


Course: Algebra 2 Time: 5 daysUnit 3: Piecewise-Defined Functions

● Presumed Knowledge: Students understand the relationship between domain and range of a function, students understand intervals on a graph, students can evaluate functions for a given domain.

Vocabulary for Piecewise-Defined FunctionsPiecewise function, discontinuity, absolute value function

Unit 3: Piecewise-Defined Functions

Objectives Carnegie Math Nation Florida Math Standards

3.A The student will consider a piecewise function and make observations about the graph.

5.3 3.13.2

MAFS.912.A.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.

3.B Students will be able to graph a piecewisefunction, taking restrictions into consideration.

5.3 3.3 MAFS.912.F-IF.3.7b Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.

3.C Students will be able to write a piecewise -defined function from a graph.

5.3 3.4 MAFS.912.A.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.

3.D Students will be able to write a piecewise-definedfunction that represents a real-life situation.

5.3 3,5 MAFS.912.F-IF.3.7b Graph functions expressed symbolically and show key features of the graph by hand in simple cases and


using technology for more complicated cases.

3.E Students will be able to graph absolute value functions and write an absolute value function as a piecewise-defined function.

3.6 MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems.

MAFS.912.F-IF.3.7b Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.

3.F Students will determine the value of k when given a graph of the function and its transformation. Students will identify a graph of a function given a graph or a table of a transformation and the type of transformation that is represented.



Course: Algebra 2 Time: 15 daysUnit 4 : Quadratics-Part 1

Presumed Knowledge: Students can evaluate exponents, understand a zero of a function is an x-intercept, and can identify maxima and minima

Vocabulary for Quadratics - Part 1Quadratic, factors, zeros, intercepts, extrema values, maximum, minimum, coefficients, complex numbers, completing the square, quadratic formula, inequalities, exponential functions, symmetry

Unit 4: Quadratics (Part 1)


4.A Students will determine and relate the key features of a function within a real-world context by examining the function’s graph. Students will write an equation in one variable that represents a real-world context.

2.1 4.1 MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.

MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational, absolute, and exponential functions.

4.B Students will use equivalent forms of a quadratic expression to interpret the expression’s terms, factors, zeros, maximum, minimum, coefficients, or parts in terms of the real-world situation the expression represents. Students will rewrite algebraic expressions in different equivalent forms by recognizing the expression’s structure. Students will rewrite algebraic expressions in different

2.1 4.2 MAFS.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.a. Factor a quadratic expression to reveal the zeros of the function it defines.


equivalent forms using factoring techniques (Common Factors).

4.C Students will use equivalent forms of a quadratic expression to interpret the expression’s terms, factors, zeros, maximum, minimum, coefficients, or parts in terms of the real-world situation the expression represents. Students will rewrite algebraic expressions in different equivalent forms by recognizing the expression’s structure. Students will rewrite algebraic expressions in different equivalent forms using factoring techniques (difference of 2 squares).

2.1 4.34.4

MAFS.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.a. Factor a quadratic expression to reveal the zeros of the function it defines.

4.D Students will add, subtract, and multiply complex numbers and use to write the answer as a complex number.

2.6 4.54.6

MAFS.912.N-CN.1.2 Use the relation and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.MAFS.912.N-CN1.1 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.

4.F Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.a. Factor a quadratic expression to reveal the zeros of the function it defines.Solve quadratic equations with real coefficients that have complex solutions. Solve quadratic equations in one variable.

1. Use completing the square to transform any quadratic equation in x into an equation of

2.7 4.7 MAFS.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.

a. Factor a quadratic expression to reveal the zeros of the function it defines.

MAFS.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions.MAFS.912.A-REI.2.4 Solve quadratic equations in one variable.


the form that has the same solutions. Derive the quadratic formula from this form.

2. Solve quadratric equations by inspection (e.g., for 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. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

a. 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. Derive the quadratic formula from this form.b. 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. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

4.G Students will solve a quadratic equation by choosing an appropriate method (i.e., completing the square, the quadratic formula, or factoring). Students will solve a quadratic equation by choosing an appropriate method (i.e., completing the square, the quadratic formula, or factoring).

4.8 MAFS.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions.MAFS.912.A-REI.2.4 Solve quadratic equations in one variable.a.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. Derive the quadratic formula from this form.

b. 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. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.



4.H Solve quadratic equations with real coefficients that have complex solutions. Solve quadratic equations in one variable.

4.9 MAFS.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions.MAFS.912.A-REI.2.4 Solve quadratic equations in one variable.a. 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. Derive the quadratic formula from this form.

b. 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. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.


Course: Algebra 2 Quarter: 2 Time: 12 daysUnit 5 : Quadratics-Part 2

Presumed knowledge● Students should understand how to graph

points, identify intercepts and maxima and minima, students can solve by factoring, and students can evaluate functions for a given set of values

Vocabulary for Quadratics - Part 2Directrix, transformation, axis of symmetry

Unit 5: Quadratics - Part 2


5.A Students will graph a function using key features.Students will compare properties of two functions using a variety of function representations (e.g., algebraic, graphical, numerical in tables, or verbal descriptions).

2.1, 2.5

5.1 MAFS.912.F-IF.3.7a Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.

MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

5.B Students will identify zeros, extreme values, and symmetry of the graph of a quadratic function symbolically.

2.1,2.4

5.2 MAFS.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.


5.C Students will graph a function using key features. 2.5 5.3 MAFS.912.F-IF.3.7a 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.

5.D Students will graph a function using key features.Students will compare properties of two functions using a variety of function representations (e.g., algebraic, graphical, numerical in tables, or verbal descriptions).

2.5 5.4 MAFS.912.F-IF.3.7a 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.


5.E Students will identify zeros, extreme values, and symmetry of the graph of a quadratic function symbolically.

2.1 5.5 MAFS.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.

5.F Students will use equivalent forms of a quadratic expression to interpret the expression’s terms, factors, zeros, maximum, minimum, coefficients, or parts in terms of the real-world situation the

2.1 5.6 MAFS.912.A-SSE.2.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.


expression represents.


5.G Student should write the quadratic equation given the focus and directrix.

2.1 5.7 MAFS.912.G-GPE.1.2. Derive the equation of a parabola given a focus and directrix.

5.H Student will solve a simple system of a linear equation and a quadratic equation in two variables graphically. Students will find a solution or an approximate solution for using a graph. Students will find a solution or an approximate solution for using a table of values. Students will demonstrate why the intersection of two functions is a solution to.

p68 and p75

5.8 MAFS.A-REI.3.7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example,

find the points of intersection between the line y = -3x and the circle x2❑+ y2❑= 3.

5.I Students will solve a simple system of a linear equation and a quadratic equation in two variables graphically. Students will find a solution or an approximate solution for using a graph or a table of values. Students will find a solution or an approximate solution for using successive approximations that gives the solution to a given place value. Students will demonstrate why the intersection of two functions is a solution.

p68 and p75

5.9 MAFS.A-REI.3.7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2❑+ y2❑= 3.MAFS.912.A-REI.4.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x)intersect are the solutions of the equation f(x) = g(x) ; find the solutions approximately (e.g., using technology to graph the functions, make tables of values, or find successive approximations). Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.


5.J Students will determine the value of when given a graph of the function and its transformation. Students will identify differences and similarities between a function and its transformation. Students will identify a graph of a function given a graph or a table of a transformation and the type of transformation that is represented. Students will graph by applying a given transformation to a function. Students will identify ordered pairs of a transformed graph. Students will complete a table for a transformed function.

2.22.32.4



Course: Algebra 2 Quarter: 2 Time: 14 daysUnit 6: Polynomial Functions

Prerequisite SkillsGraphing square root and cube root functions, Using properties of exponents, Graphing quadratics and linear functions, Fractional operations, Simplifying rational expressions, Long division

Vocabulary for Polynomial Functions*

Closure, average rate of change, zeros, x-intercepts, end behavior, grouping, the difference of two squares, the sum or difference of two cubes

Unit 6: Polynomial Functions


6.A Students will apply their understanding of closure to adding, subtracting, and multiplying polynomials.

3.6 6.16.2

MAFS.912.A-APR.1.1 Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

6.B Students will rewrite algebraic expressions in different equivalent forms by recognizing the expression’s structure. Students will use the structure of algebra to complete an algebraic proof of a polynomial identity. Students will use polynomial identities to describe numerical relationships.

4.6 6.36.4

MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – ( y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2+ y2).

MAFS.912.A-APR.3.4 Prove polynomial identities and use them to describe numerical relationships.

6.C Students will differentiate between different types of functions using a variety of descriptors (e.g., graphical, verbal, numerical, and algebraic).

3.2 6.5 MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.

6.D Students will differentiate between different types of functions using a variety of descriptors (e.g., graphical, verbal, numerical, and algebraic).Students will calculate and interpret the average

4.1p322

6.6 MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.


rate of change of a continuous function that is represented algebraically, in a table of values, on a graph, or as a set of data with a real-world context.

MAFS.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.

6.E Students will determine and relate the key features of a function within a real-world context by examining the function’s graph. Students will use a given verbal description of the relationship between two quantities to label key features of a graph of a function that models the relationship. Students will interpret statements that use function notation within the real-world context given. Students will find the zeros of a polynomial function when the polynomial is in factored form.Students will identify a rough graph of a polynomial function in factored form by examining the zeros of the function. Students will use the x-intercepts of a polynomial function and end behavior to graph the function. Students will identify and interpret key features of a graph within the real-world context that the function represents.

4.1 6.7 MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

MAFS.912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.

6.F Students will rewrite algebraic expressions in different equivalent forms using factoring techniques (e.g., common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely) or simplifying expressions (i.e., combining like terms, using the distributive property, and using other operations with polynomials). Students will rewrite algebraic expressions in different equivalent forms by recognizing the expression’s structure.

4.4 6.8 MAFS.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.

MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – ( y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2+ y2).

6.G Students will use the x-intercepts of a polynomial function and end behavior to graph the function.Students will rewrite algebraic expressions in

3.4 6.9 MAFS.912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.


different equivalent forms using factoring techniques (e.g., common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely) or simplifying expressions (i.e., combining like terms, using the distributive property, and using other operations with polynomials). Students will rewrite algebraic expressions in different equivalent forms by recognizing the expression’s structure.

MAFS.912.F-IF.3.7c Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.

MAFS.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.

MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. For example, seex4 – y4 as (x2)2 – ( y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2+ y2).

MAFS.912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.


Course: Algebra 2 Time: 7 daysUnit 7: Rational Expressions and Equations

Presumed knowledge: Vocabulary for Rational Expressions and EquationsRemainder Theorem, extraneous solution

Unit 7: Rational Expressions and Equations


7.A Students will use the Remainder Theorem to determine if (x – a) is a factor of a polynomial.Students will use the Remainder Theorem to determine the remainder of p(x )/(x – a).

4.3 7.1 MAFS.912.A-APR.2.2 Know and apply the Remainder Theorem: For a polynomial p(x ) and a number a, the remainder on division by x – a is p(a), so p(a)=0 if and only if (x – a) is a factor of p(x ).

7.B Students will solve a rational equation in one variable. Students will justify algebraically why a solution is extraneous.

8.3 7.2 MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

7.C

Students will demonstrate why the intersection of two functions is a solution to f (x)=g (x). Students will solve a rational equation in one variable. Students will justify algebraically why a solution is extraneous.

7.3 MAFS.912.A-REI.4.11 Explain why the x-coordinates of the points where the graphs of the equations y=f (x ) and y=g (x) intersect are the solutions of the equation f (x)=g (x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values, or find successive approximations). Include cases where f (x) and/or g(x ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

7.D Students will write an equation in one variable that represents a real-world context. Students will write

8.4 7.4 MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. Include equations


and solve an equation in one variable that represents a real-world context.

arising from linear and quadratic functions and simple rational, absolute, and exponential functions.

7.E

Students will graph a function using key features.

7.1 7.5 MAFS.912.F-IF.3.7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior.



Course: Algebra 2 Time: 14 daysUnit 8: Expressions and Equations with Radicals and Rational Exponents

Presumed Knowledge: Vocabulary for Expressions and Equations with Radical and Rational Exponentsfunction, radical, rational exponents, rational function, vertical asymptote, horizontal asymptote, extraneous solution, composition of functions, inverse function, square root, cube root, removable discontinuity, non-removable discontinuity, average rate of change, end behavior, radicand

Unit 8: Expressions and Equations with Radicals and Rational Exponents


8.A

Students will explain how the definition of the meaning of rational exponents follows from the properties of integer exponents.

9.4 8.1 MAFS.912.N-RN.1.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51 /3to be the cube root of 5 because we want (5¿¿1/3)3¿ =5(1 /3 )3, to hold, so 5(1 /3 )3must equal 5.

8.B Students will use the properties of exponents to rewrite a radical expression as an expression with a rational exponent. Students will use the properties of exponents to rewrite an expression with a rational exponent to a radical expression. Students will apply the properties of operations of integer exponents to expressions with rational exponents.Students will apply the properties of operations of integer exponents to radical expressions

9.4 8.2 MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

8.C Students will solve a radical equation in one variable. Students will justify algebraically why a solution is extraneous.

9.6 8.3 MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

8.D Students will write an equation in one variable that 9.6 8.4 MAFS.912.A-CED.1.1 Create equations and inequalities in one


represents a real-world context. Students will write and solve an equation in one variable that represents a real-world context. Students will solve a radical equation in one variable. Students will justify algebraically why a solution is extraneous. Students will solve multi-variable formulas or literal equations for a specific variable.

variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational, absolute, and exponential functions.

MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

MAFS.912.A-CED.1.4 Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. For example, rearrange Ohm’s law, V=IR, to highlight resistance, R.

8.E Students will graph a function using key features. 9.29.3

8.5 MAFS.912.F-IF.3.7 b Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.


MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the


positive integers would be an appropriate domain for the function.MAFS.912.F-BF.2.3 Identify the effect on the graph of replacing f (x) byf (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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.


Course: Algebra 2 Quarter: 3 Time: 15 daysUnit 9: Exponential and Logarithmic Functions and Transformations

Presumed knowledge: Students can evaluate exponents, graph functions using a table of values, and find the inverse of a function

Vocabulary for Exponential and Logarithmic Functions and Transformationsexponential functions, inverse, natural base, logarithm, common logarithm, natural logarithm, initial value, exponential growth, exponential decay

Unit 9: Exponential and Logarithmic Functions


9.A Students will write an equation in one variable that represents a real-world context. Students will write and solve an equation in one variable that represents a real-world context. Students will identify the quantities in a real-world situation that should be represented by distinct variables.Students will write constraints for a real-world context using equations, inequalities, a system of equations, or a system of inequalities.

10.1 9.19,2


MAFS.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.

MAFS.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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

MAFS.912.F-BF.1.1b Write a function that describes a relationship between two quantities.Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

9.B Students will classify the exponential function as 10.2 9.3 MAFS.912.F-IF.3.8b Write a function defined by an expression


exponential growth or decay by examining the base, and students will give the rate of growth or decay. Students will use the properties of exponents to write an exponential function defined by an expression in different but equivalent forms to reveal and explain different properties of the function, and students will determine which form of the function is the most appropriate for interpretation for a real-world context. Students will write an equation in one variable that represents a real-world context. Students will rewrite algebraic expressions in different equivalent forms by recognizing the expression’s structure. Students will use equivalent forms of an exponential expression to interpret the expression’s terms, factors, coefficients, or parts in terms of the real-world situation the expression represents.

in different but equivalent forms to reveal and explain different properties of the function.b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in function such asy = (1.02)t , y = (0.97)t , y = (1.01)12t, and y =(1.2)t /10and classify them as representing exponential growth or decay.


MAFS.912.A-SSE.2.3c Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.15¿¿1/12)❑12 t ≈(1.012)❑12t ¿ to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

MAFS.912.A-SSE.1.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpretP(1+r )❑n as the product of P and a factor not depending on P.

9.C Students will understand Euler’s number. 9.4

9.D Students will find a solution or an approximate solution for f (x)=g (x) using a graph.Students will find a solution or an approximate solution for f (x)=g (x) using a table of values.

10.3 9.59.6

MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

MAFS.912.A-REI.4.11 Explain why the x-coordinates of the


points where the graphs of the equations y=f (x ) and y=g (x) intersect are the solutions of the equation f (x)=g (x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values, or find successive approximations). Include cases where f (x) and/org(x ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

9.E Students will find the inverse of a function 10.4 9.7 MAFS.912.F-BF.2.4 Find inverse functions.a. Solve an equation of the form f (x)=c for a simple function, f , that has an inverse and write an expression for the inverse.For example, f (x)=2 x3 or f (x)=(x+1) /(x – 1) for x ≠ 1.

9.F Students will find the inverse of a function. Students will use the properties of exponents to write an exponential function defined by an expression in different but equivalent forms to reveal and explain different properties of the function, and students will determine which form of the function is the most appropriate for interpretation for a real-world context.

10.4 9.8 AFS.912.F-BF.2.4 Find inverse functions.a. Solve an equation of the formf (x)=c for a simple function, f , that has an inverse and write an expression for the inverse.For example, f (x)=2x3 or f (x)=(x+1) /(x – 1) for x ≠ 1.

MAFS.912.F-IF.3.7e. Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude and using phase shift.

9.G Students will use logarithms to solve exponential functions with a base of 2, 10, or e

10.4 9.9 MAFS.912.F-LE.1.4 For exponential models, express as a logarithm the solution to ab❑ct=d, where a, c, and d are numbers and the base, b, is 2, 10, or e; evaluate the logarithm using technology.

9.H Students will use transformations to graph logarithmic and exponential functions

10.5 9.10


Course: Algebra 2 Time: 10 daysUnit 10: Sequences and Series

Presumed knowledge: Students can evaluate a function given values, students can use a formula to find a value, and students can use order of operations

Vocabulary for Sequences and SeriesArithmetic sequences, geometric sequences, geometric series, finite geometric series

Unit 10: Sequence and Series


10A

Students will write an explicit function, define a recursive process, or complete a table of calculations that can be used to mathematically define a real-world context.

6.16.2

10.110.2

MAFS.912.F-BF.1.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

MAFS.912.F-BF.1.1a Write a function that describes a relationship between two quantities.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

10B Students will write an explicit function, define a recursive process, or complete a table of calculations that can be used to mathematically define a real-world context.

6.16.36.4

10.310.4

MAFS.912.F-BF.1.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

MAFS.912.F-BF.1.1a Write a function that describes a relationship between two quantities.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

10CStudents will use the formula for a sum of a finite geometric series to solve real-world problems.

6.5 10.5 MAFS.912.A-SSE.2.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.


10DStudents will derive the formula for a sum of a finite geometric series where r is not equal to 1.


10EStudents will use the formula for a sum of a finite geometric series to solve real-world problems.

10.7 MAFS.912.A-SSE.2.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.

10FStudents will use the formula for a sum of a finite geometric series to solve real-world problems.



Course: Algebra 2 Time: 10 daysUnit 11: Probability

Presumed Knowledge: Students know how to use a Venn Diagram

Vocabulary for ProbabilitySample space, outcomes, unions, intersections, complement, addition rule, independent, conditional probability, two-way frequency table, random sample

Unit 11: Probability **Not covered in Carnegie**


11A Students will find characteristics of sets and subsets using Venn Diagrams (union, intersection, and complement)

11.111.2

MAFS.912.S-CP.1.1 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”).

11B Students will be able to apply the Addition Rule and interpret the answer.

11.311.4

MAFS.912.S-CP.2.7 Apply the Addition Rule, P( A∨B)=P (A )+P (B) – P( A∧B), and interpret the answer in terms of the model.

11C Students will recognize and explain probability and independence.

11.5 MAFS.912.S-CP.1.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

MAFS.912.S-CP.1.2 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.

11D Students will understand conditional probability. 11.6 MAFS.912.S-CP.1.3 Understand the conditional probability of A given B as P( A∧B)/ P(B), and interpret independence of A and B as saying that the conditional probability of A givenB is the same as the probability of A and the conditional


probability of B given A is the same as the probability of B. MAFS.912.S-CP.2.6 Find the conditional probability ofA givenB as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

11E Students will construct and interpret two way frequency tables of data.

11.7 MAFS.912.S-CP.1.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.


Course: Algebra 2 Quarter: 4 April 17-May 5 testing window Time: 10 daysUnit 12: Statistics

Prerequisite Skills: Rational powers, Identify patterns, Simplify expressions

Vocabulary: Random sample, sample survey, experiment, observational study, characteristic of interest, population, sample, randomization, treatment, statistically significant, normal distribution, standard deviation, area under the curve

Unit 12: Statistics *** Carnegie Chpt 15 and 16 are really good resources for these standards***


12A Students will develop an understanding of statistics as a process for making inferences using parameters.

16.116.216.316.4

12.1 MAFS.912.S-IC.1.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.MAFS.912.S-IC.1.2 Decide if a specified model is consistent with results from a given data- generating process (e.g., using simulation).MAFS.912.S-IC.2.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.MAFS.912.S-IC.2.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

12B Students will decide if a specified model is consistent with results from given data.

Recognize the purpose and differences among sample surveys.Use data to compare and evaluate data.

16.116.216.316.4

12.212.3

MAFS.912.S-IC.1.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.MAFS.912.S-IC.1.2 Decide if a specified model is consistent with results from a given data- generating process (e.g., using simulation).MAFS.912.S-IC.2.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.MAFS.912.S-IC.2.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if


differences between parameters are significant.MAFS.912.S-IC.2.6 Evaluate reports based on data.

12C Students will use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate and to recognize that there are data sets for which such a procedure is not appropriate.

15.115.2

12.412.512.6

MAFS.912.S-ID.1.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.


Course: Algebra 2 Time: 10 daysUnit 13: Trigonometry - Part 1Prerequisite Skills: Students know how to use sine, cosine, and tangent with right triangles, students can multiply fractions

Vocabulary: radian, degree, negative angle, arc length

Unit 13: Trigonometry - Part 1


13A Students will extend right triangle trigonometry to the unit circle to determine an ordered pair that lies on the unit circle.

13.2 13.1 MAFS.912.F-TF.1.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

13B Students will extend right triangle trigonometry to the unit circle to determine an ordered pair that lies on the unit circle

13.2 MAFS.912.F-TF.1.3 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

13C Students will convert the degree measure to radian measure. Students will convert the radian measure to degree measure.

13.3 MAFS.912.F-TF.1.3 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

13D Students will convert the degree measure to radian measure. Students will convert the radian measure to degree measure. Students will extend right triangle trigonometry to the unit circle to determine an ordered pair that lies on the unit circle.

13.2 13.4 MAFS.912.F-TF.1.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; convert between degrees and radians.MAFS.912.F-TF.1.3 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

13E Students will convert the radian measure to degree measure.

13.2 13.5 MAFS.912.F-TF.1.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; convert


between degrees and radians.

13F Student will understand how the radian measure of an angle is the length of the arc on the unit circle subtended by the angle.

13.2 13.6 MAFS.912.F-TF.1.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; convert between degrees and radians.


Course: Algebra 2 Time: 13 daysUnit 14: Trigonometry - Part 2Prerequisite Skills: Students know how to use sine, cosine, and tangent with right triangles, students can convert from degrees to radians, students need to factor

Vocabulary: Pythagorean Identity, amplitude, frequency, midline, periodic function,

Unit 14: Trigonometry - Part 2


14A Use the Pythagorean Identity to calculate trigonometric ratios.

14.1 14.1 MAFS.912.F-TF.3.8 Prove the Pythagorean identity

14B Real-world context of trigonometric functions and choosing the correct trigonometric function to model the situation.

14.214.314.4

14.214.314.414.5

MAFS.912.F-TF.2.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.


APPENDIX: Algebra 2 HONORS standards**This list gives the HONORS standards broken down by unit. It is at the teacher’s discretion to fit them into the section that best suits the students in the classroom.

Quarter 2

Unit 5● MAFS.912.N-CN.3.8: Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x + 2i)(x – 2i).

Unit 6● MAFS.912.N-CN.3.9: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

● MAFS.912.A-APR.3.5: Know and apply the Binomial Theorem for the expansion of (x in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

Unit 7● MAFS.912.A-APR.4.7: Understand that rational expressions form a system analogous to the rational numbers, closed under addition,

subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Quarter 3

Unit 11● MAFS.912.S-CP.2.8: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret

the answer in terms of the model. ★● MAFS.912.S-CP.2.9: Use permutations and combinations to compute probabilities of compound events and solve problems. ● MAFS.912.S-MD.2.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). ★● MAFS.912.S-MD.2.7: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey

goalie at the end of a game).


Snapshot of Item Specification Features

Standard number and Objectives

MAFS.912.F-BF.2.4 Find inverse functions.a. Solve an equation of the form f(x) = c for a simple function, f, that has an inverse and write an expression for

the inverse. For example, f(x) =2x³ or f(x) = (x+1)/(x–1) forossible Question Types x ≠ 1.b. Verify by composition that one function is the inverse of another.c. Read values of an inverse function from a graph or a table, given that the function has an inverse.d. Produce an invertible function from a non-invertible function by restricting the domain.

Possible Question Types Item Types MAFS.912.F-BF.2.4

Editing Task Choice – May require choosing a domain that can be used to produce an invertible function from a non-invertible function.

Equation Editor – May require expressing a function or showing steps to find the inverse of a function.

GRID – May require plotting points on a coordinate plane.

Hot Text – May require dragging steps in a verification of an inverse by composition.

Multiple Choice – May require selecting a choice from a set of possible choices.

Table Item – May require completing a table of values for an inverse function.

Depth of Knowledge


These areas are quite helpful for understanding the depth of knowledge required to meet the standard. They also include information letting you know what is, or is not, included on the EOC test.

ClarificationsMAFS.912.F-BF.2.4

Students will find the inverse of a function.

Students will use composition of functions to determine if two functions are inverses.

Students will use a graph or a table of a function to determine values of the function’s inverse.

Students will restrict the domain of a function whose inverse is not a function so that the inverse will be a function.

Assessment LimitMAFS.912.F-BF.2.4

In items that require the student to find the inverse of a function, functions may consist of linear functions, quadratics of the formf(x) = ax2 + c, radical functions with a linear function as the radicand,and rational functions whose numerator is a integer and whose denominator is a linear function.

Stimulus AttributesMAFS.912.F-BF.2.4

Items may be set in a real-world or mathematical context.

Items may use function notation.Response Attribute

MAFS.912.F-BF.2.4Items may require the student to use inequalities or interval notation to represent the domain.

Sample EOC problem for MAFS.912.F-BF.2.4


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