Radnor High School
Course Syllabus
Modified 09/01/2011
Advanced Algebra 2 (College Prep)
0434
General Information
Credits: 1.0 Credits
Weighted: Unweighted
Prerequisite: Advanced Geometry
Length: Full Year
Format: Meets Daily
Grade: 10, 11
Course Description
This course reviews and extends an understanding of the number system, formulas, equations
and graphs. Subject matter includes quadratics, radicals, exponents, complex numbers and
the mathematical concept of function. Logarithms, exponential functions and theory of
equations are introduced during the course. This course involves the use of a graphing
calculator to develop and practice concepts, rather than the theoretical approach used in
Honors Algebra 2. Students are expected to handle an appropriate workload at a moderate
pace.
MARKING PERIOD ONE



EQUATIONS AND INEQUALITIES
LINEAR EQUATIONS AND FUNCTIONS
SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES
Common Core Standards
Common Core Standards
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.
A-APR.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.
A-APR.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.
A-APR.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.
A-CED.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 and
exponential functions.
A-CED.2. Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.
A-CED.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.
A-CED.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.
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.6. Solve systems of linear equations exactly and approximately (e.g., with graphs),
focusing on pairs of linear equations in two variables.
A-REI.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
F-LE.2. Construct linear and exponential functions, including arithmetic and geometric
sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
F-LE.5. Interpret the parameters in a linear or exponential function in terms of a context.
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.★
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.
Keystone Connections:
Student Objectives:
At the end of the first marking period, students should be able to successfully manage the
following skills:




Solve linear equations by using the addition and/or multiplication properties of equality
Solve linear equations by using the distributive property
Solve linear inequalities by using the addition and/or multiplication properties of equality
Solve linear inequalities by using the distributive property












Solve linear inequality a  x  b
Solve application problems with inequalities
Define absolute value
Solve various absolute value problems, including special cases of absolute value and
inequalities
Distinguish between independent and dependent variables
Define and identify relations and functions
Find domain and range for specific functions and/or relations
Use function notation, and identify functions defined by graphs and equations
Solve 2 equation linear systems by graphing, substitution and elimination
Solve special systems (dependent and inconsistent)
Use a graphing calculator to assist in solving systems of equations
Solve an inequality in the form of ax  b  c and ax  b  c
Materials & Texts
Larson, Boswell, Kanold, Stiff (2001). Algebra 2. Evanston, IL: McDougal Littell Inc.
ISBN 789-DWO-03 02
Activities, Assignments, & Assessments
ACTIVITIES
 Use properties of equality to solve linear equations
 Use the distributive property to solve linear equations
 Solve linear equations with fractions and decimals
 Use properties of equality to solve linear inequalities
 Use the distributive property to solve linear inequalities
 Use all properties to solve a  x  b
 Use all properties to solve applications problems with inequalities
 Define absolute value
 Solve an absolute value equation
 Solve one-way absolute value inequalities, such as 2 x  1  7 and/or 2 x  1  7


Solve an absolute value equation that requires rewriting
Solve an equation with 2 absolute values, such as ax  b  cx  d








Define and use the definitions of relation and function
Determine whether relations are functions
Find domain and range of relations and functions from various sources
Use the 'vertical line test'
Identify functions from their equations
Write equations using function notation
Graph linear and constant functions, using function notation to express the graphs
Decide whether an ordered pair is a solution to a system of equations
 Solve a system of equations by graphing, substitution and elimination
 Determine the number of solutions a system of equations has
 Define Dependent and Inconsistent systems, and solve those types of systems
ASSIGNMENTS
Assignments for this and all marking periods can be found at the High School Math
Department website under Advanced Algebra 2 HW.
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the
Mathematics Department page of Radnor High School’s web site.
ASSESSMENTS
Grades will be based on quizzes and tests. In addition, teachers may use homework, group
activities, and/or projects for grading purposes. All students will take departmental midyear
and final exams. The Radnor High School grading system and scale will be used to determine
letter grades.
Terminology
Whole numbers, integers, rational numbers, irrational numbers, origin, graph, coordinate,
dimensional analysis, numerical expression, base, exponent, power, order of operations,
variable,
algebraic expression, term, coefficient, like terms, equation, solution, equivalent, formulas,
verbal model, algebraic model, linear inequalities, graph, compound inequalities, absolute
value.
Relation, domain, range, function, ordered pair, coordinate plane, equation, solution,
independent variable, dependent variable, graph, linear function, function notation, slope,
parallel, perpendicular, y-intercept, slope-intercept form, standard form, x-intercept, direct
variation, constant of variation, scatterplot, positive correlation, negative correlation, no
correlation,
linear inequalities, compound functions, linear functions as models
Media, Technology, Web Resources
 Teacher-developed documents
 Calculator based documents
 http://www.mcdougallittell.com
MARKING PERIOD TWO

QUADRATIC FUNCTIONS


COMPLEX NUMBERS
PROPERTIES OF EXPONENTS
Common Core Standards
N-RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
N-CN.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.
N-CN.2. Use the relation i2 = –1 and the commutative, associative, and distributive properties to add,
subtract, and multiply complex numbers.
A-SSE.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).
A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
A-APR.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.
A-REI.4. Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x2 = 49),
taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial
form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi
for real numbers a and b.
A-REI.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.
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.★
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end
behavior.
F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential
functions.
Keystone Connections:
Student Objectives:
At the end of the second marking period, students should be able to successfully manage the
following skills:
 Recognize quadratic functions and their corresponding graphs
 Locate, calculate, recognize, and use the vertex, axis of symmetry, and x-intercepts
(zeros)
 Manipulate quadratic equations in all three forms—standard, vertex, and intercept
 Factor trinomials and special cases—difference of squares and perfect square trinomial
 Graph quadratics by hand and using technology
 Locate a maximum or minimum
 Use a quadratic model to predict an outcome
 Solve quadratic equations with single, multiple, and complex solutions
 Define, use, and manipulate “i”
 Use complex conjugates
 Graph and solve quadratic inequalities
 Solve systems of inequalities involving quadratics
 Use regression to find a model
 Use the quadratic formula
 Use the discriminant to determine the number of real solutions
Activities, Assignments, & Assessments
ACTIVITIES











Explore how an “a-value” effects a standard graph
Use patterns, calculations (zpp, -b/2a), and calculators to find the zeros and vertex of a
graph
Use the same calculations to rewrite equations in different forms
Find the greatest common factor of a polynomial
Use logic to limit the possible factors of a trinomial
Factor trinomials with an a-value.
Add, subtract, multiply, and divide using “i”
Distribute and use complex conjugates
Find the intersection point(s) of a linear equation and a quadratic equation
Use a set of data to create a quadratic model and predict further outcomes
Determine what happens if the discriminant of a quadratic equation is positive,
negative, or zero.
ASSIGNMENTS
See Marking Period One for location of assignment sheets.
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the
Mathematics Department page of Radnor High School’s web site.
ASSESSMENTS
Grades will be based on quizzes and tests. In addition, teachers may use homework, group
activities, and/or projects for grading purposes. All students will take departmental midyear and
final exams. The Radnor High School grading system and scale will be used to determine letter
grades.
Terminology
Quadratic function, parabola, vertex, axis of symmetry, standard form, vertex form, intercept
form , binomials, trinomials, factoring, monomial, zeros, radical sign, radicand and radical,
rationalizing the denominator, conjugate, complex number, real part, imaginary part, quadratic
formula, real solutions, discriminant , quadratic inequalities in one and two variables, best
fitting quadratic model, quadratic regression
Media, Technology, Web Resources
 Teacher-developed documents
 Calculator based documents
 http://www.mcdougallittell.com
MARKING PERIOD 3
 POLYNOMIAL FUNCTIONS
 POWERS, ROOTS AND RADICALS
 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Common Core Standards
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.
A-APR.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.
A-APR.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.
A-APR.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.
A-CED.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 and
exponential functions.
A-CED.2. Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.
A-CED.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.
A-CED.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.
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.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
F-LE.2. Construct linear and exponential functions, including arithmetic and geometric
sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
F-LE.5. Interpret the parameters in a linear or exponential function in terms of a context.
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.★
N-CN.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.
N-CN.2. Use the relation i2 = –1 and the commutative, associative, and distributive properties
to add, subtract, and multiply complex numbers.
N-CN.3. (+) Find the conjugate of a complex number; use conjugates to find moduli and
quotients of complex numbers.
N-CN.5. (+) Represent addition, subtraction, multiplication, and conjugation of complex
numbers geometrically on the complex plane; use properties of this representation
for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and
argument 120°.
N-CN.7. Solve quadratic equations with real coefficients that have complex solutions.
N-CN.8. (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4
as (x + 2i)(x – 2i).
N-CN.9. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic
polynomials.
Student Objectives:
At the end of the third marking period, students should be able to successfully manage the
following skills:
 Evaluate and simplify polynomial functions
 Add, subtract, and multiply polynomial functions
 Recognize and factor certain polynomials
 Solve equations using the zero-product property
 Add, subtract, multiply, divide and simplify rational expressions
 Define rational functions and describe their domains
 Write rational expressions is lowest terms
 Find a least common denominator
 Perform standard operations with rational expressions
 Determine the domain of the variable in a rational equation
 Solve rational equations
 Recognize the graph of a rational function
 Find roots of numbers
 Solve radical equations
 Simplify the square root of negative numbers
 Manipulate and use “i”
Activities, Assignments, & Assessments
ACTIVITIES
 Evaluate polynomial expressions
 Use a greatest common factor to factor polynomial expressions
 Use the distributive property
 Remove parentheses from polynomial expressions
 Simplify expressions with integer exponents
 Solve equations in factored form using the zero-product property
 Evaluate and simplify polynomial functions
 Add, subtract, and multiply polynomials
 Recognize and factor certain polynomials
 Solve equations using the zero-product property
 Add, subtract, multiply, divide, and simplify rational expressions
 Simplify expressions using rules of exponents
 Add, subtract and multiply rational numbers
 Find numbers that are not in the domains of rational functions
 Write rational expressions in lowest terms
 Use multiplication and division to combine rational expressions
 Add and subtract rational expressions that have common denominators












Find least common denominators
Add and subtract rational expressions that have different denominators
Use the distributive property when subtracting rational expressions
Determine the domains of the variables in rational equations
Solve rational equations
Find square roots
Identify the graph of a radical function
Use the power rule to solve radical equations
Use the power rule to square a binomial
Simplify square roots of negative numbers
Perform operations using “i”
Use “i” when raised to a power
ASSIGNMENTS
See Marking Period One for location of assignment sheets.
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the
Mathematics Department page of Radnor High School’s web site.
ASSESSMENTS
Grades will be based on quizzes and tests. In addition, teachers may use homework, group
activities, and/or projects for grading purposes. All students will take departmental midyear and
final exams. The Radnor High School grading system and scale will be used to determine letter
grades.
Terminology
Rational expression, rational function, least common denominator (LCD), rational equation,
domain of the variable, asymptote, radicand, index, radical, root, radical expression, radical
equation, extraneous solution, imaginary numbers, “i”
Media, Technology, Web Resources
 Teacher-developed documents
 Calculator based documents
 http://www.mcdougallittell.com
MARKING PERIOD FOUR



EXPONENTIAL AND LOGARITHMIC FUNCTIONS
RATIONAL EQUATIONS AND FUNCTIONS
SEQUENCES AND SERIES
Common Core Standards
A-APR.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.
A-APR.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
F-IF.1. Understand that a function from one set (called the domain) to another set (called the
range) assigns to each element of the domain exactly one element of the range. If f is a
function and x is an element of its domain, then f(x) denotes the output of f
corresponding to the input x. The graph of f is the graph of the equation y = f(x).
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.
F-IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is
a subset of the integers.
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.
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.
d. (+) Graph rational functions, identifying zeros and asymptotes when suitable
factorizations are available, and showing end behavior.
e. Graph exponential and logarithmic functions, showing intercepts and end behavior,
and trigonometric functions, showing period, midline, and amplitude.
F-IF.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.
b. Use the properties of exponents to interpret expressions for exponential functions.
For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t,
y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or
decay.
F-IF.9. Compare properties of two functions each represented in a different way (either
algebraically, graphically, numerically in tables, or by verbal descriptions).
F-LE.1. Distinguish between situations that can be modeled with linear functions and with
exponential functions.
Prove that linear functions grow by equal differences over equal intervals, and that
exponential functions grow by equal factors over equal intervals.
Recognize situations in which one quantity changes at a constant rate per unit interval
relative to another.
Recognize situations in which a quantity grows or decays by a constant percent rate per
unit interval relative to another.
F-LE.2. Construct linear and exponential functions, including arithmetic and geometric
sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
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.
F-LE.5. Interpret the parameters in a linear or exponential function in terms of a context.
A-SSE.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.
b. Complete the square in a quadratic expression to reveal the maximum or minimum
value of the function it defines.
c. Use the properties of exponents to transform expressions for exponential functions.
For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the
approximate equivalent monthly interest rate if the annual rate is 15%.
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.
Student Objectives
At the end of the fourth marking period, students should be able to successfully manage the
following skills:
 Define rational functions and describe their domains
 Write rational expressions is lowest terms
 Find a least common denominator
 Perform standard operations with rational expressions
 Determine the domain of the variable in a rational equation
 Solve rational equations
 Recognize the graph of a rational function
 Find roots of numbers
 Solve radical equations
 Define an exponential function
 Graph an exponential function
 Solve exponential equations
 Use exponential functions with growth and decay
 Define a logarithm
 Convert between exponential and logarithmic forms






Evaluate logarithms
Solve logarithmic equations
Identify sequences
Evaluate sequences
Recognize and use sigma notation
Identify arithmetic and geometric sequences and series
Activities, Assignments, & Assessments
ACTIVITIES





















Add and subtract rational expressions that have common denominators
Find least common denominators
Add and subtract rational expressions that have different denominators
Use the distributive property when subtracting rational expressions
Determine the domains of the variables in rational equations
Solve rational equations
Graph an exponential function with a > 1
Graph an exponential function with 0 < a < 1
Solve exponential equations
Explore the difference between growth and decay
Apply growth and decay to real world problems
Graph logarithmic functions both by hand and on the calculator
Explore how and why the graphs shift
Solve logarithmic functions
Write equations in both logarithmic form and exponential form
Identify which form will provide the solution in the simplest way
Identify patterns and sequences
Explore the difference between an arithmetic sequence and a geometric sequence
Solve series’ in sigma notation
Explore the difference between an arithmetic series and a geometric series
Identify an infinite geometric series
ASSIGNMENTS
See Marking Period One for location of assignment sheets.
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the
Mathematics Department page of Radnor High School’s web site.
ASSESSMENTS
Grades will be based on quizzes and tests. In addition, teachers may use homework, group
activities, and/or projects for grading purposes. All students will take departmental midyear and
final exams. The Radnor High School grading system and scale will be used to determine letter
grades.