Radnor High School
Course Syllabus
Revised 9/1/2011
Algebra 2 (Academic)
0436
Credits:
Weighted:
1.0
No
Length:
Format :
Year
Meets daily
Grades: 10/11
Prerequisite: Algebra 1, Geometry and/or teacher
recommendation
Overall Description of Course
Algebra 2 is designed to reinforce and to extend the skills and concepts from previous algebra
courses. Topics will include, but are not limited to, solutions of linear equations and inequalities,
solutions of quadratic equations, rules for exponents, radicals and rational expressions, and graphs of
linear, absolute value, and quadratic functions. Where appropriate, applications using geometric
concepts will be included. Students are required to have a graphing calculator (TI-83 or TI-84
preferred) for this course.
Quarter 1

Common Core Standards
N-Q.1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose
and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data
displays.

N-Q.2. Define appropriate quantities for the purpose of descriptive modeling.

A-SSE.1. Interpret expressions that represent a quantity in terms of its context.★
o
Interpret parts of an expression, such as terms, factors, and coefficients.

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.

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 y = –3x and the
circle x2 + y2 = 3.

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 (using
technology for matrices of dimension 3 × 3 or greater).

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.★

F-BF.1. Write a function that describes a relationship between two quantities.★

S-ID.7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of
the data.

S-ID.8. Compute (using technology) and interpret the correlation coefficient of a linear fit.
Keystone Connections:
Student Objectives:
Overall:
1. To utilize technology using graphing calculators and computers.
2. To make connections between mathematics and the real world.
3. To explore mathematical functions and their relationship to real world applications.
4. To strengthen algebraic skills for standardized tests.
5. To explore number systems and computations.
6. To develop the ability to think critically.
7. To represent situations that involve variable quantities with expressions, equations, and
inequalities.
By the end of Quarter 1, students should be able to demonstrate an understanding of:
8. Evaluating and simplifying algebraic expressions
9. Solving linear equations and rewriting formulas
10. Using verbal and algebraic models to solve real-life problems
11. Analyzing and representing data
12. Graphing and using relations and functions
13. Writing and graphing equations of lines using points, slopes and intercepts
14. Writing and graphing direct variation equations
15. Using scatter plots to identify correlation and find best-fitting lines
16. Graphing a system of linear equations in two variables
17. Solving a system of linear equations in two variables
Materials & Texts
MATERIALS
Graphing calculator
Supplemental work, practice sheets
TEXTS
Algebra 2: Concepts and Skills, Holt McDougal
Activities, Assignments, & Assessments
ACTIVITIES
Tools of Algebra
 Real Numbers and Number Operations
 Algebraic Expressions and Models
 Simplifying Algebraic Expressions
 Solving Linear Equations
 Rewriting Equations and Formulas
 Problem Solving Using Algebraic Models
 Analyzing and Displaying Data
Linear Equations and Functions
 Functions and Their Graphs
 Linear Functions and Function Notation
 Slope and Rate of Change
 Quick Graphs of Linear Equations
 Writing Equations of Lines
 Direct Variation
 Scatter Plots and Correlation
Systems of Linear Equations
 Solving Linear Systems of Graphing
 Solving Linear Systems by Substitution
 Solving Linear Systems by Linear Combinations
ASSIGNMENTS
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 mid-year and final exams.
The Radnor High School grading system and scale will be used to determine letter grades.
Terminology
origin, graph, coordinate
opposite, reciprocal
base, exponent, power
numerical expression
variable
algebraic expression
term, coefficient
like terms, constant term
simplified expression
equation, linear equation
solution
mean, median, mode
range
box-and-whisker plot
lower quartile
upper quartile
relation, function
domain, range
equation in two variables
independent variable
dependent variable
linear function
function notation
slope
y-intercept
slope-intercept form
x-intercept
standard form of a linear
equation
direct variation
constant of variation
scatter plot
correlation
best-fitting line
system of linear equations
solution of a system
substitution method
linear combination method
Media, Technology, Web Resources
Graphing Calculator
Quarter 2

Common Core Standards
N-RN.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 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so
(51/3)3 must equal 5.

N-RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

N-CN.7. Solve quadratic equations with real coefficients that have complex solutions.

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.7. Solve quadratic equations with real coefficients that have complex solutions.

A-SSE.1. Interpret expressions that represent a quantity in terms of its context.★
o
Interpret parts of an expression, such as terms, factors, and coefficients.

A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.★
o
a. Factor a quadratic expression to reveal the zeros of the function it defines.

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-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.

A-REI.4. Solve quadratic equations in one variable.
o
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.
o
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.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.

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.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.★

F-IF.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.★

F-IF.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.★
Keystone Connections:
Student Objectives:
Overall:
1.
2.
3.
4.
5.
6.
7.
To utilize technology using graphing calculators and computers.
To make connections between mathematics and the real world.
To explore mathematical functions and their relationship to real world applications.
To strengthen algebraic skills for standardized tests.
To explore number systems and computations.
To develop the ability to think critically.
To represent situations that involve variable quantities with expressions, equations, and
inequalities.
By the end of Quarter 2, students should be able to demonstrate an understanding of:
8. Solving and graphing linear inequalities in one or two variables
9. Solving, graphing and using systems on linear inequalities
10. Solving and graphing absolute value equations and inequalities
11. Graphing absolute value functions
12. Graphing quadratic functions written in standard form, vertex form, and intercept form
13. Solving quadratic equations by factoring
14. Solving quadratic equations by taking square roots and using the quadratic formula
Materials & Texts
MATERIALS
Graphing calculator
Supplemental work, practice sheets
TEXTS
Algebra 2: Concepts and Skills, Holt McDougal
Activities, Assignments, & Assessments
ACTIVITIES
Inequalities and Absolute Value
 Solving Linear Inequalities
 Linear Inequalities in 2 Variables
 Systems of Linear Inequalities
 Solving Absolute Value Equations
 Solving Absolute Value Inequalities
 Absolute Value Functions
Quadratic Functions and Factoring
 Graphing Quadratic Functions in Standard Form
 Graphing Quadratic Functions in Vertex or Intercept Form
 Factoring x2 + bx + c
 Factoring ax2 + bx + c
 Factoring Using Special Patterns
 Solving Quadratic Equations by Finding Square Roots
 Complex Numbers


Completing the Square
The Quadratic Formula and the Discriminant
ASSIGNMENTS
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 mid-year and final exams.
The Radnor High School grading system and scale will be used to determine letter grades.
Terminology
linear inequality in one variable
compound inequality
linear inequality in two variables
half-plane
system of linear inequalities in two variables
absolute value
absolute value equation
absolute value inequality
vertex
quadratic function
parabola
axis of symmetry
trinomial
quadratic equation
zeros of a function
square root
imaginary unit, i
complex number
imaginary number
quadratic formula
discriminant
Media, Technology, Web Resources
Graphing Calculator
Quarter 3

Common Core Standards
N-RN.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 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so
(51/3)3 must equal 5.

N-RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

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.

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.★
o
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
o
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value
functions.
o
c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end
behavior.
o
d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available,
and showing end behavior.

F-BF.1. Write a function that describes a relationship between two quantities.★

F-BF.5. (+) Understand the inverse relationship between exponents and logarithms and use this relationship to
solve problems involving logarithms and exponents.
o
Keystone Connections:
Student Objectives:
Overall:
1. To utilize technology using graphing calculators and computers.
2. To make connections between mathematics and the real world.
3. To explore mathematical functions and their relationship to real world applications.
4. To strengthen algebraic skills for standardized tests.
5. To explore number systems and computations.
6. To develop the ability to think critically.
7. To represent situations that involve variable quantities with expressions, equations, and
inequalities.
By the end of Quarter 3, students should be able to demonstrate an understanding of:
8. Using properties of exponents to evaluate and simplify expressions
9. Defining, graphing and using polynomial functions
10. Adding, subtracting, multiplying and dividing polynomials
11. Factoring polynomial expressions and solving polynomial equations
12. Evaluating nth roots of real numbers using radicals and rational exponents
13. Solving equations containing radicals or rational exponents
14. Finding inverse functions for both linear and nonlinear functions
15. Graphing square root and cube root functions
16. Finding and comparing standard deviations of data sets
Materials & Texts
MATERIALS
Graphing calculator
Supplemental work, practice sheets
TEXTS
Algebra 2: Concepts and Skills, Holt McDougal
Activities, Assignments, & Assessments
ACTIVITIES
Polynomials and Polynomial Functions
 Properties of Exponents
 Polynomial Functions and Their Graphs
 Adding and Subtracting Polynomials
 Multiplying and Dividing Polynomials
 Polynomials of Greater Degree
 Modeling with Polynomial Functions
Powers, Roots, and Radicals
 nth Roots and Rational Exponents
 Properties of Rational Exponents
 Solving Radical Equations
 Function Operations and Composition of Functions
 Inverse Functions
 Graphing Square Root and Cube Root Functions
ASSIGNMENTS
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 mid-year and final exams.
The Radnor High School grading system and scale will be used to determine letter grades.
Terminology
scientific notation
polynomial
standard form of a polynomial function
leading coefficient
degree of a polynomial
constant term
end behavior
polynomial long division
quadratic form
nth root of a real number
index
simplest form of a radical
like radicals
radical equation
extraneous solution
composition of functions
inverse relation
repeated solution
local maximum
local minimum
inverse functions
radical function
Media, Technology, Web Resources
Graphing Calculator
Quarter 4

Common Core Standards
N-Q.1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose
and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data
displays.

N-Q.2. Define appropriate quantities for the purpose of descriptive modeling.

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.

S-IC.1. Understand statistics as a process for making inferences about population parameters based on a
random sample from that population.

S-CP.9. (+) Use permutations and combinations to compute probabilities of compound events and solve
problems.

S-MD.6. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

S-MD.7. (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing,
pulling a hockey goalie at the end of a game).
Keystone Connections:
Student Objectives:
Overall:
1. To utilize technology using graphing calculators and computers.
2. To make connections between mathematics and the real world.
3. To explore mathematical functions and their relationship to real world applications.
4. To strengthen algebraic skills for standardized tests.
5. To explore number systems and computations.
6. To develop the ability to think critically.
7. To represent situations that involve variable quantities with expressions, equations, and
inequalities.
By the end of Quarter 4, students should be able to demonstrate an understanding of:
8. Writing and using inverse variation and joint variation models
9. Graphing rational functions and identifying asymptotes
10. Simplifying rational expressions
11. Solving rational equations
12. Identifying sources of bias in samples and survey questions
13. Choosing random samples and finding the margin of error for a sample
14. Using permutations and combinations to count the ways an event can happen
15. Calculating and using probabilities
Materials & Texts
MATERIALS
Graphing calculator
Supplemental work, practice sheets
TEXTS
Algebra 2: Concepts and Skills, Holt McDougal
Activities, Assignments, & Assessments
ACTIVITIES
Rational Equations and Functions
 Inverse and Joint Variation
 Graphing Rational Functions
 Simplifying and Multiplying Rational Expressions
 Dividing Rational Expressions
 Adding and Subtracting Rational Expressions
 Solving Rational Equations
Data Analysis and Probability
 Populations and Surveys
 Samples and Margin of Error
 Transformations of Data
 The Fundamental Counting Principle and Permuations
 Combinations and Pascal’s Triangle
 Introduction to Probability
 Probability and Compound Events
 Probability of Independent and Dependent Events
ASSIGNMENTS
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 mid-year and final exams.
The Radnor High School grading system and scale will be used to determine letter grades.
Terminology
inverse variation
constant of variation
joint variation
rational function
rational expression
simplified form
complex fraction
least common denominator
rational equation
cross multiply
Media, Technology, Web Resources
Graphing Calculator
Enduring Understandings
Essential Questions
population
unbiased, biased sample
random sample
margin of error
permutation
factorial
combination
geometric probability
compound event
overlapping, disjoint events
complement of an event
independent, dependent events
conditional probability