Download North Mac High School -- Pacing Guides

North Mac High School -- Pacing Guides
Title of Course:
Course Textbook:
ISBN#:
Instructor:
Algebra 2/ College Prep Algebra 2
Prentice Hall Algebra 2
978-0-13-366032-6
Katie Humphreys
Major Units of Study:
1st Quarter (August-October)
 Tools of Algebra (Chapter 1)
o Properties of Real Numbers
 Graph a Number on a Number Line including fractions, repeating, positive,
negatives
 2.MD.B.6 represent whole numbers as lengths from 0 on a number line diagram with equally spaced point
corresponding to the number 0,1,2…and represent whole-number sums and differences within 100 on a number
line diagram
 Order all Real Numbers
 Find the Inverse of Real Number
 Find the Absolute Values of all Real Numbers
o Algebraic Expressions
 Evaluate Algebraic expressions including with exponents using the given value
for variables
 Combining like terms for algebraic expressions


A-REI.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
A-REI 2: Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise.
o Solving Equations
 Solve an Algebraic equation using combining like terms, distributing, and other
properties



A-REI.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
A-REI 2: Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise
A-REI.3: Solve linear equations and inequalities in one variable, including equations with coefficient
represented by letters
o Solving inequalities
 Solving linear inequalities and graphing answers
 Solving and Graphing compound inequalities
 A-REI.3: Solve linear equations and inequalities in one variable, including equations with coefficient
represented by letters
o Absolute value equations and Inequalities
 Simplify absolute value numerical problems
 Solving multistep absolute value equations
 Checking absolute value equations for extraneous solutions
 Solving absolute value inequalities
 A-REI 2: Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise

A-REI.3: Solve linear equations and inequalities in one variable, including equations with coefficient
represented by letters
o Probability
 Finding Experimental probability of an event
 Finding theoretical probability of an event
 Finding geometric probability of an event
 S-CP.1: Describe events as subsets of a sample space using characteristics of the outcomes, or as unions,



intersection or complements of other events.
S-CP.2: Understand that 2 events A and B are independent if the probability of A and B occurring together is
the product of their probabilities, and use this characterization to determine if they are independent.
S-CP.3. Understand the condition probability of A given B, and interpret independence of A and B as saying
that the conditional probability of A given B is the same as the probability of A, and the conditional probability
of B given A is the as the probability of B.
S-CP. 5 Recognize and explain the concepts of conditional probability and independence in everyday language
and everyday situations
 Functions, Equations, and Graphs (Chapter 2)
o Relations and Functions
 Graphing a relation including finding the domain and range
 Making a mapping diagram to determine whether a relation is a function
 Using the vertical line test to determine whether a graph represents a function
 Identifying relations as functions
 F_IF.1. Understand that a function from one set to another set assigns to each element of the domain exactly



one element of the range.
F-IF.2 use functions notation, evaluate functions for inputs in their domains, and interpret statements that use
function notation in terms of a context.
F-IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and
table in terms of the quantities and sketch graphs showing key features given a verbal description of the
relations
F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it
describes
o Linear Equations
 Graphing a linear equations
 Identifying, changing form between standard, point-slope, slope-intercept form
 F-IF.7.a. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases
and using technology for more complicated cases. Graph linear and quadratic functions and show intercepts,
maxima, and minima
o Direct Variation
 Identifying direct variation from a table and from an equations
 F-IF.9. Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables or by verbal descriptions.
o Using Linear Models
 Using, identifying and creating a scatter plot
o Absolute Value Functions and Graphs
 Graphing an absolute function using a table
 Graphing an absolute function using two linear equations
 F-IF. 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. Graph square root, cube root and piecewise-defined functions
including step functions and absolute value function
o Families of Functions
 Identifying translations including vertical, horizontal, stretch, shrink, and
reflections of an absolute value functions
 F-IF.9. Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables or by verbal descriptions.
o Two-Variable Inequalities
 Graphing a linear inequality
 Graphing an absolute value inequality

F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and
using technology for more complicated cases
 Linear Systems (Chapter 3)
o Graphing Systems of Equations
 Solving systems of equations by graphing
 A-REI. 6. Solve systems of linear equations exactly and approximately focusing on pairs of linear equations in
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

two variables.
A-REI 7. Solve a simple system consisting of a linear equation and a quadratic equation in two variable
algebraically and graphically
A-REI. 10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a line).
A-REI 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
o Solving Systems Algebraically
 Solving systems of equation by substitution, elimination, equivalent systems
 A-REI. 6. Solve systems of linear equations exactly and approximately focusing on pairs of linear equations in

two variables.
A-REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that
equation and a multiple of the other produces a system with the same solutions.
o Systems of Inequalities
 Solving systems of inequalities by graphing, and using a table
 A-REI.12. Graph the solutions to a linear inequality in two variables as a half plane(excluding the boundary in
the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the
intersection of the corresponding half-planes
o Graphs in Three Dimensions
 Naming the points on a 3d graph
 Graphing points, and a rectangular prism on a 3d graph, sketching a plane
o Systems with Three variables
 Solving systems with three variables by elimination, solving by substitution,
 Matrices (Chapter 4)
o Organizing Data into Matrices
 Writing the dimensions of a matrix, identifying a matrix element

N-VM.6 use matrices to represent and manipulate data to represent payoffs or incidence relationships in a
network
o Adding and Subtracting Matrices
 Using identity and inverse matrices
 N-VM.10. understands that the zero and identity matrices play a role in matrix addition and multiplication
similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if
the matrix has a multiplicative inverse.

Solving matrix equations by adding and subtracting
 N-VM.8 add, subtract and multiply matrices of appropriate dimensions
o Matrix Multiplication
 Multiply matrices by a scalar number
 Multiply matrices using multiplication rules and determining whether a product
matrix exists
 N-VM.7. Multiply matrices by scalars to produce new matrices, eg. As when all of the payoffs in a game are

doubled
N-VM.9 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a
commutative operation, but still satisfies the associate and distributive properties
o Geometric Transformation with Matrices
 Using a matrix to translate, rotate, and reflect a figure
 N-Vm.12 Work with 2x2 matrices as transformation of the plane, and interpret the absolute value of the
determinant in terms of area.
o 2x2 Matrices, Determinants, and Inverses
 Verifying inverse of a 2x2 matrix

Finding the determinants and inverse of 2x2 matrix
 N-Vm.12 Work with 2x2 matrices as transformation of the plane, and interpret the absolute value of the

determinant in terms of area.
N-VM.10. understands that the zero and identity matrices play a role in matrix addition and multiplication
similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if
the matrix has a multiplicative inverse.
o 3x3 Matrices, Determinants, and Inverses
 Finding the determinant of a 3x3 matrix
 Verifying inverse of a 3x3 matrix
 N-Vm.12 Work with 2x2 matrices as transformation of the plane, and interpret the absolute value of the
determinant in terms of area.
o Inverse Matrices and Systems
 Writing a system as a matrix equation

N-VM.6 use matrices to represent and manipulate data to represent payoffs or incidence relationships in a
network

Solving a system of two equations using matrices
 A-REI.8. Represent a system of linear equations as a single matrix equation in a vector variable
 A-REI. 9 find the inverse of a matrix if it exists and use it to solve systems of linear equations
 Solving a system of three equations using matrices
o Augmented matrices and Systems
 Using Cramer’s rule to solve a system of linear equations
 Writing an augmented matrix, and writing a system from an augmented matrix
 Using an augmented matrix to solve a system of equations
nd
2 Quarter (October-December)
Quadratic Equations and Functions (Chapter 5)
o Modeling data with Quadratic Functions
 Classifying functions as either linear or quadratic. Identifying the quadratic, linear
and constant terms
 Classifying/knowing corresponding points, vertex, axis of symmetry of a parabola
 F-LE.1. Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish
between situations that can be modeled with linear functions and with exponential functions.
o Properties of parabolas
 Graphing quadratic functions using any form
 F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases



and using technology for more complicated cases.
F-IF.7a graph linear and quadratic functions and show intercept, maxima, and minima
F-IF.8 write a functions defined by an expression in different but equivalent forms to reveal and explain
different properties of the function.
F-IF8a 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.
o Transforming Parabolas
 Identifying translation of functions
 G-CO.2 Represent transformations in the plane using transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other point as outputs. Compare
transformation that preserves distance and angle to those that do not.

Graphing quadratic functions using vertex form
 F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases



and using technology for more complicated cases.
F-IF.7a graph linear and quadratic functions and show intercept, maxima, and minima
F-IF.8 write a functions defined by an expression in different but equivalent forms to reveal and explain
different properties of the function.
F-IF8a 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
o Factoring Quadratic Expressions
 Factoring expressions
 F-IF8a 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



A-REI.4.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.
A-REI4.b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic
formula and factoring as appropriate to the initial form of the equation. Recognize when the quadratic formula
gives complex solutions and write them as a +bi for real numbers a and b.
Factoring expressions using perfect square trinomials and different of two squares
 A-REI.4.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.
A-REI4.b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic
formula and factoring as appropriate to the initial form of the equation. Recognize when the quadratic formula
gives complex solutions and write them as a +bi for real numbers a and b.
o Quadratic Equations
 Solving quadratic equations using factoring, and finding square roots
 A-REI.4.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.
A-REI4.b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic
formula and factoring as appropriate to the initial form of the equation. Recognize when the quadratic formula
gives complex solutions and write them as a +bi for real numbers a and b.
o Complex Numbers
 Simplifying square roots using imaginary numbers and complex numbers
 Finding absolute value of imaginary numbers
 Adding and multiplying complex numbers
 Finding complex solutions of quadratic equations
 N-CN.7 Solve quadratic equations with real coefficients that have complex solutions
 N-CN.8 extend polynomial identities to the complex numbers
 A-REI4.b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic
formula and factoring as appropriate to the initial form of the equation. Recognize when the quadratic formula
gives complex solutions and write them as a +bi for real numbers a and b.
o Completing the Square
 Solving quadratic equations using completing the square method (including when
‘a’ does not equal 1)
 A-REI.4.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.

Finding complex solutions by completing the square
 N-CN.7 Solve quadratic equations with real coefficients that have complex solutions
 N-CN.8 extend polynomial identities to the complex numbers
 A-REI4.b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic
formula and factoring as appropriate to the initial form of the equation. Recognize when the quadratic formula
gives complex solutions and write them as a +bi for real numbers a and b.
o The Quadratic Formula
 Solving quadratic equations using the quadratic formula
 Solving quadratic equations using the quadratic formula, find complex numbers
 A-REI4.b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic
formula and factoring as appropriate to the initial form of the equation. Recognize when the quadratic formula
gives complex solutions and write them as a +bi for real numbers a and b.
 Polynomials and Polynomial Functions (Chapter 6)
o Polynomial Functions
 Be able to identify a polynomial function and its degree
 Classify polynomials by term and degree
 A-APR. 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.
o Polynomial and Linear Factors
 Writing a polynomial in standard form, and writing a polynomial in factored form
 A-APR. 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.

Finding zeros of a polynomial functions
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

A-APR.2 know and apply the remainder theorem
A-APR. 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
Identifying relative max and mins of the graphs
 F-IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available and showing
end behavior.

Using the zero product property to find zeros of the function, finding multiple
zeros and multiplicity
 A-APR. 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
 A-APR prove polynomial identities and use the m to describe numerical relationships
 Knowing the equivalent statements of solutions, x-intercept, zeros, and factors
o Dividing Polynomials
 Using long division to divide polynomials
 Using synthetic division to divide polynomials
 Using the remainder theorem to check answers
 A-APR.2 now 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)
o Solving Polynomial Equations
 Solve using the sum and difference of cubes theorem
 EE.A2. Use square root and cube root symbols to represent solutions to equations of the form x2 = p, x3 = p
where p is a positive rational numbers. Evaluate square roots of small perfect squares and cube roots of small
perfect cubes.

o
o
o
o
Solve using a polynomial equations and quadratic pattern
 CN-C.7 use complex numbers in polynomial identities and equations
Theorems about Roots of Polynomial Equations
 Finding rational roots using the rational root theorem
 Finding irrational roots using the irrational root theorem, including conjugates
 Finding imaginary roots using the imaginary root theorem
The Fundamental Theorem of Algebra
 Using the fundamental theorem of algebra to find all roots
 N-CN.9 Know the Fundamental theorem of algebra; show that it is true for quadratic polynomials
Permutations and Combinations
 Finding permutations using factorials, the number of permutation definition
 Finding combinations using the number of combinations definition
The Binomial Theorem
 Use the binomial theorem and Pascal’s triangle to expand binomials
 A-APR.5. Know and apply the Binomial Theorem for the expansion of (x+y)n 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.
 Radical Functions and Rational Exponents (Chapter 7)
o Roots and Radical Expressions
 Finding all roots of an expressions
 Simplifying radical expressions
 A-APR.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the for 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
A-APR.7 understand that rational expressions form a system analogous to the rational number, closed under
addition, subtraction, multiplication and division by a nonzero rational expression; add, subtract, multiply, and
divide rational expressions
o Multiplying and Dividing Radical Expressions
 Multiplying radical expressions, and using the multiply radicals theorem to
simplify expressions
 A-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise

dividing radicals, using the dividing radicals theorem to simplify expressions
 Rationalizing the denominator of radical expressions
o Binomial Radical Expressions
 Adding / subtracting radical expressions, including simplifying prior to add/sub
 Multiplying binomial radical expressions, multiplying conjugate expressions
 Rationalizing binomial radical denominators
 N-CN.7 Solve quadratic equations with real coefficients that have complex solutions
 N-CN.8 extend polynomial identities to the complex numbers
 A-REI4.b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic

formula and factoring as appropriate to the initial form of the equation. Recognize when the quadratic formula
gives complex solutions and write them as a +bi for real numbers a and b.
A-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise
o Rational Exponents
 Simplifying expressions with rational exponents
 Using properties of rational exponents to simplify expressions
 A-SSE. 3c. Use the properties of exponents to transform expressions for exponential functions.
 A-REI.2. Solve simple rational radical equations in one variable, and give examples showing how extraneous
solutions may arise.
o Solving Square Roots and other Radical Equations
 Solving square root equations (only one square roots)
 Solving square root equations with two rational exponents
 Checking for extraneous solutions
 A-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise
o Function Operations
 Using function operations to solve expressions including add/sub/multiply/divide
 Finding the composite of functions
 F-BF.4b verify by composition that one function is the inverse of another
 F-bF1c Write a function that models a relationship between two quantities, composite functions
 F-IF1 understand that a function from one set to another set assigns to each element of the domain exactly one

element of the range.
F-IF.2 use function notation, evaluate functions for inputs in their domains, and interpret statements that use
function notation in terms of a context
o Inverse Relations and Functions
 Finding inverse relations of tables and equations
 Graphing relation with its inverse
 Finding the composite of function and its inverse
 F-BF.B.4.Build new functions from existing functions. Find inverse functions
 F-BF.B.4a Build new functions from existing functions. 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.
 F-BF.4b verify by composition that one function is the inverse of another
 F-BF.4c Read values of an inverse function from a graph or a table, given that the function has an inverse
 F-BF.4d. Produce an invertible function from a non-invertible function by restricting the domain
o Graphing Square Root and Other Radical Functions
 Graphing square root functions
 F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases


and using technology for more complicated cases.
F-IF.7b Graph square root, cube root and piecewise –defined functions, including step functions and absolute
value functions
Knowing and identifying the translations of square root functions
 G-CO.2 Represent transformations in the plane using transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other point as outputs. Compare
transformation that preserve distance and angle to those that do not.

Graphing cube root functions
 F-IF.C.7d Graph rational functions identifying zeros and asymptotes when suitable factorization are available
and showing end behavior
3rd Quarter (January-March)
 Exponential and Logarithmic Functions (Chapter 8)
o Exploring Exponential Models
 Graphing exponential functions using a table
 Identifying growth and decay factors and functions
 Using two points to write an exponential function
 F-IF7 graph functions expressed symbolically and show key features of the graph, by hand in simple cases and

using technology for more complicated cases.
F-IF.7e graph exponential and logarithmic functions, showing intercepts and end behavior and trigonometric
functions showing period, midline and amplitude.
 F-IF.8b Use the properties of exponents to interpret expressions for exponential functions
o Properties of Exponential Functions
 Identifying and knowing the translations of an exponential function
 G-CO.2 Represent transformations in the plane using transparencies and geometry software; describe

transformations as functions that take points in the plane as inputs and give other point as outputs. Compare
transformation that preserve distance and angle to those that do not.
F-IF.7e graph exponential and logarithmic functions, showing intercepts and end behavior and trigonometric
functions showing period, midline and amplitude.
o Logarithmic Functions as Inverses
 Writing exponential functions in logarithm form, and writing logarithm functions
in exponential form
 A-SSE 3c. Use the properties of exponents to transform expressions for exponential functions
 Evaluating logarithm functions
 Graphing a logarithm function
 F-IF.7e graph exponential and logarithmic functions, showing intercepts and end behavior and trigonometric
functions showing period, midline and amplitude.

Identifying and knowing the translations of a logarithm function
 G-CO.2 Represent transformations in the plane using transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other point as outputs. Compare
transformation that preserve distance and angle to those that do not.
o Properties of Logarithms
 Using the properties of logarithms to expand and simplify expressions
o Exponential and Logarithmic Equations
 Solving an exponential equation using logarithms
 Using the change of base formula to evaluate logarithms
 Solving logarithm equations using exponential functions
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
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
F-LE1. Distinguish between situations that can be modeled with linear functions and with exponential
functions.
F-LE1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential
functions grow by equal factors over equal intervals.
F-LE1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval
relative to another.
F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity
increasing linearly, quadratically, or (more generally) as a polynomial function.
F-LE.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers
and the base b is 2, 10, or e; evaluate the logarithm using technology.
o Natural Logarithms
 Simplifying and expanding natural logarithms using properties of logarithms
 Solving exponential equations and natural logarithms equations
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




F-LE1. Distinguish between situations that can be modeled with linear functions and with exponential
functions.
F-LE1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential
functions grow by equal factors over equal intervals.
F-LE1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval
relative to another.
F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity
increasing linearly, quadratically, or (more generally) as a polynomial function.
F-LE.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers
and the base b is 2, 10, or e; evaluate the logarithm using technology.
 Rational Functions (Chapter 9)
o Inverse Variation
 Identifying and modeling inverse and direct variation
o The Reciprocal Function Family
 Graphing a reciprocal function
 Knowing and identifying all translations of the reciprocal function
 F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases



and using technology for more complicated cases.
F-IF.7b Graph square root, cube root and piecewise –defined functions, including step functions and absolute
value functions
F-IF.7e graph exponential and logarithmic functions, showing intercepts and end behavior and trigonometric
functions showing period, midline and amplitude.
F-IF.7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available,
and showing end behavior
o Rational Functions and Their Graphs
 Find all points of discontinuity, vertical asymptotes, and horizontal asymptotes
 Graph rational functions including all points of discontinuity, vertical asymptotes,
and horizontal asymptotes and x/y table
 F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases



and using technology for more complicated cases.
F-IF.7b Graph square root, cube root and piecewise –defined functions, including step functions and absolute
value functions
F-IF.7e graph exponential and logarithmic functions, showing intercepts and end behavior and trigonometric
functions showing period, midline and amplitude.
F-IF.7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available,
and showing end behavior
o Rational Expressions
 Simplifying rational expressions by factoring
 Multiplying and dividing rational expressions and giving answer in simplest form
 A-APR.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the for 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
A-APR.7 understand that rational expressions form a system analogous to the rational number, closed under
addition, subtraction, multiplication and division by a nonzero rational expression; add, subtract, multiply, and
divide rational expressions
A-REI.2. Solve simple rational radical equations in one variable, and give examples showing how extraneous
solutions may arise.
o Adding and Subtracting Rational Expressions
 Finding LCM of rational functions
 Adding and subtracting rational expressions including finding and making
common denominators
 Simplifying complex fractions
 A-APR.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the for 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
A-APR.7 understand that rational expressions form a system analogous to the rational number, closed under
addition, subtraction, multiplication and division by a nonzero rational expression; add, subtract, multiply, and
divide rational expressions
o Solving Rational Expressions
 Solving rational equations for all zeros
 A-REI.2. Solve simple rational radical equations in one variable, and give examples showing how extraneous


solutions may arise.
A-APR.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the for 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
A-APR.7 understand that rational expressions form a system analogous to the rational number, closed under
addition, subtraction, multiplication and division by a nonzero rational expression; add, subtract, multiply, and
divide rational expressions
4th Quarter (March-May)
 Quadratic Relations and Conic Sections (Chapter 10)
o Exploring Conic Sections
 Graphing a circle, ellipse, and a hyperbola
 Identifying the conic section of graphs
o Parabolas
 Writing an equation of a parabola using the definition
 Identifying focus and directrix
 Graphing the equation of a parabola
 G-GPE.2 Derive the equation of a parabola given a focus and directrix
o Circles
 Writing the equation of a circle using the standard form
 Using translations to write an equation
 G-CO.2 Represent transformations in the plane using transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other point as outputs.
Compare transformation that preserve distance and angle to those that do not.


Finding the center and radius from the standard form of a circle
Graphing a circle using center and radius



G-C.1Prove that all circles are similar.
G-C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the
relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are
right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
G-C.3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a
quadrilateral inscribed in a circle.
o Ellipses
 Writing the equation of an ellipse
 Finding the foci of an ellipse, and using the foci of an ellipse to write the
equation

G-GPE. 3 (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or
difference of distances from the foci is constant.
o Hyperbolas
 Graphing a hyperbola using foci and vertices
 Finding the foci of a hyperbola


G-GPE. 3 (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or
difference of distances from the foci is constant.
Writing my equation of a hyperbola with given foci and vertices

G-GPE. 3 (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or
difference of distances from the foci is constant.
o Translating Conic Sections
 writing the equation of a translated ellipse, hyperbola, and conic section
 G-CO.2 Represent transformations in the plane using transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other point as outputs.
Compare transformation that preserves distance and angle to those that do not.
 Sequences and Series (Chapter 11)
o Mathematical Patterns
 Determine specific terms, finite sum or a rule that will generate a pattern
 Finding recursive or explicit formula for patterns
o Arithmetic Sequences
 Identifying if a sequence is arithmetic or not
 Finding specific terms of the arithmetic sequence
 Finding arithmetic sequence formulas for recursive or explicit patterns
 Using the arithmetic mean to find missing terms
 F-IF. 3 Recognize that sequences are functions, sometimes defined recursively, whose domain is subset of
the integers.
o Geometric Sequences
 Identifying if a sequence is geometric or not


Finding geometric sequence formulas for recursive or explicit patterns
Using the geometric mean to find missing terms
 F-IF. 3 Recognize that sequences are functions, sometimes defined recursively, whose domain is subset of
the integers.
o Arithmetic Series
 Writing and evaluating a series, finding the sum of a series
 Writing a series in summation notation
o Geometric Series
 Using the geometric series to evaluate the series (finite and infinite series)
 Determining divergence and convergence of a geometric series
 A-SSE.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.
o Area Under a Curve
 Using a sum to estimate area under a curve
Assessments Used:
 Daily/weekly homework
 Homework quizzes
 Quizzes
 Monthly Chapter Tests (approximate)
1st Semester:
8-20-13
Pre-Test Date
10-17-13
1st Quarterly Test Date
12-19-13
2nd Quarterly Test Date
2nd Semester:
1-6-14
Pre-Test Date
3-14-14
3rd Quarterly Test Date
5-28-14
Post Test Date (end of year final)