Download Advanced Algebra 3

Radnor High School
Course Syllabus
Advanced Algebra 3 with Trigonometry
0445
Credits: 1.0
Unweighted:
Length: 1 year
Format: Meets Daily
Grades: 11, 12
Prerequisite: Advanced Algebra 2 or teacher rec.
Overall Description of Course
Advanced Algebra 3 is a college-preparatory course.
Advanced Algebra 3 is a College Preparatory level which features moderate pacing and
workload with teacher guidance to assist in the mastery of the material. Students enrolled on
this level should be seeking to satisfy college requirements/expectations of mathematics course
but not necessarily have an interest in pursuing math related college majors.
This course is designed for the students who need to strengthen their knowledge and skill sets
of Advanced Algebra 2 before taking a full year course in Trigonometry. Time will be spent
reviewing, strengthening and reinforcing skills and concepts involving functions, equations,
inequalities and applications. Additional topics will include exponential and logarithmic
functions, sequences and series and complex and imaginary numbers. Trigonometry will be
introduced through the unit circle and extended to include solving triangles.
MARKING PERIOD ONE



SYSTEMS OF LINEAR EQUATIONS
POLYNOMIALS – EXPRESSIONS AND EQUATIONS
RATIONAL EXPRESSIONS AND EQUATIONS
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.
Modified: 06/28/2011
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 halfplanes.
Keystone Connections
2.8.A2.B: Evaluate and simplify algebraic expressions, for example: products/quotients of
polynomials, logarithmic expressions and complex fractions; and solve and graph
linear, quadratic, exponential and logarithmic equations and inequalities, and solve
Modified: 06/28/2011
and graph systems of equations and inequalities.
2.8.11.B: Evaluate and simplify algebraic expressions and solve and graph linear, quadratic,
exponential and logarithmic equations and inequalities, and solve and graphic
systems of equations and inequalities.
2.8.A2.D: Demonstrate an understanding and apply properties of functions (domain, range,
inverses) and characteristics of families of functions (linear, polynomial, rational,
trigonometric, exponential, logarithmic).
2.8.A2.E: Use combinations of symbols and numbers to create expressions, equations and
inequalities in two or more variables, systems of equations and inequalities, and
functional relationships that model problem situations.
2.8.A2.F: Interpret the results of solving equations, inequalities, systems of equations and
inequalities in the context of the situation that motivated the model.
2.5.11.A: Develop a plan to analyze a problem, identify the information needed to solve the
problem, carry out the plan, check whether an answer makes sense, and explain how
the problem was solved in grade appropriate contexts.
2.5.11.B: Use symbols, mathematical terminology, standard notation, mathematical rules,
graphing and other types of mathematical representations to communicate
observations, predictions, concepts, procedures, generalizations, ideas and results.
Student Objectives
At the end of the first marking period, students should be able to successfully manage the
following skills:
 Solve systems of equations in two variables by graphing, substitution and linear
combination
 Solve problems by translating them to a system of equations
 Determine whether a system of equations has 0, 1 or infinite number of solutions, and
whether lines are parallel or perpendicular
 Graph and solve systems of inequalities
 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
Activities, Assignments, & Assessments
ACTIVITIES
 Solve systems of equations in two variables by graphing and by substitution
 Solve systems of equations in two or three variables by linear combinations
 Solve problems by translating to a system of equations
 Determine whether a system of equations has a solution and whether that solution is
Modified: 06/28/2011
























unique
Determine whether a system of equations is perpendicular
Graph and solve systems of inequalities (shading)
Find the additive inverse of a number
Add, subtract and multiply rational numbers
Graph linear equations in two variables
Graph linear inequalities and absolute value inequalities in two variables
Determine whether two lines are parallel
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
Add and subtract signed fractions
Multiply and divide signed fractions
Evaluate algebraic expressions
Factor a GCF
Simplify expressions using rules of exponents
Solve linear equations
ASSIGNMENTS
Chapter 4
0
n/a
Algebra Review
Quizaroo!
1
4.1
Graphing Systems of Equations
Page 161 #1 -15odd, 18-21
all, 25
2
4.1
Graphing Systems of Equations
Page 161 #2 -14 evens, 2224 all, 26,28
3
4.2
Solving systems of equations by
substitution or by linear
combination
Page 166 #1 -4 all, 7-19
odds, 28, 30, 33, 35
4
4.2
Solving systems of equations by
substitution or by linear
combination
Worksheet
Modified: 06/28/2011
5
4.3
Applications of systems of
equations
Page 171 #1 -7 odds, 13, 17,
19, 25, 40, 42, 43
6
4.3
Applications of systems of
equations
Page 171 #2 - 6 evens, 14,
18, 20, 26, 41
7
4.4
Systems of equations in three
variables
Page 178 #14 -20 all , 23
8
4.5
Applications of systems of
equations in three variables
Page 181 #1 - 13 odds
9
4.6
Independent/Dependent Systems
Worksheet
10
4.6
Independent/Dependent Systems
Page 186 #1 – 19 odds, 20
11
4.7
Systems of Linear Inequalities
Page 192 #1, 5, 9, 15, 17, 23,
27, 30
12
4.7
Systems of Linear Inequalities
Page 192 #3, 7, 11, 13, 19,
21, 25, 29
13
Ch 4
Chapter 4 Review
Page 200 #1-12 all
Page 203 #56-66 all
HW #
Section
Topic
Assignment
14
5.1, 5.2
Polynomials, Adding and
Subtracting
Page 208 #1, 2, 9, 11, 13
Page 212 #3, 5, 7, 11, 15, 17,
19, 28
15
5.3
Multiplying Polynomials
Page 218 #5, 6, 7, 8, 13, 14,
17, 18, 19, 21, 25, 27, 33, 35,
37
16
5.4
Factoring: GCF, Difference of
Squares, Perfect Square
Trinomials, Grouping
Page 222 #9 -17 odds, 19-29
odds, 37-43 odds, 55-59
odds
17
5.4
Factoring: GCF, Difference of
Squares, Perfect Square
Trinomials, Grouping
Page 222 #8 -18 evens, 2030 evens, 36-42 evens, 54-58
evens
18
5.5
Factoring: Difference or Sum of
Cubes, Trinomials
Page 227 #5 -13 odds, 23-35
odds, 43-53 odds, 71, 77, 83
19
5.5
Factoring: Difference or Sum of
Cubes, Trinomials
Page 227 #4 -12 evens, 2234 evens, 42-52 evens, 70,
76, 82
Chapter 5
Modified: 06/28/2011
20
5.6
Factoring: A general strategy
Page 231 #1-7 odds, 11, 13,
19, 23,24, 25, 27, 33, 35
21
5.7
Solving Polynomials (ZPP)
Page 233 #1-33 odds, 36, 47
22
5.8
Applications of Polynomials
Page 235 #1 - 11 odds, 15
23
Ch 5
Chapter 5 Review
Page 241 #1 – 41 odds
HW #
Section
Topic
Assignment
24
6.1
Multiplying and Simplifying
Rational Expressions
Page 248 #5-31 odds
25
6.1
Multiplying and Simplifying
Rational Expressions
Worksheet
26
6.2
Adding and Subtracting Rational
Expressions
Page 253 #1 -29 odds
27
6.2
Adding and Subtracting Rational
Expressions
Page 253 #2 -30 evens
28
6.2
Adding and Subtracting Rational
Expressions
Worksheet
Chapter 6
ASSESSMENTS
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.
Grades will be based on quizzes, tests, homework, group activities and projects. The Radnor
High School grading system and scale will be used to determine letter grades.
Terminology
Boundary, consistent systems, constraints, dependent systems, half-plane, inconsistent
systems, linear combinations, linear inequality, method of elimination, ordered triple,
perpendicular systems, substitution method, systems of equations, triangular form, unique
form. (Chapter 4)
Ascending order, binomial coefficients, degree of a polynomial, degree of a term, descending
order, factor, greatest common factor, like terms, monomial, polynomial function, polynomial
Modified: 06/28/2011
in x, prime factors, prime polynomial, terms, trinomial, trinomial square. (Chapter 5)
Rational expressions, rational equations, multiplication of rational expressions, least common
multiple (LCM), least common denominator (LCD), complex rational expression, addition of
rational expressions. (Chapter 6.1 – 6.3)
Materials & Texts
Smith, Stanley A., Randall, Charles I., Dossey, John A., Bittinger, Marvin L. (2001). Algebra 2
with Trigonometry. Upper Saddle River, NJ: Prentice-Hall, Inc.
ISBN 0-13-051968-5
Media, Technology, Web Resources



Prentice Hall Algebra 2 With Trigonometry Home Page
Teacher-developed smart-board documents
Calculator based documents
Modified: 06/28/2011
MARKING PERIOD TWO



RATIONAL EXPRESSIONS – SOLVING, COMPLEX AND VARIATION
POWERS, ROOTS AND COMPLEX NUMBERS
QUADRATIC FUNCTIONS AND TRANSFORMATIONS
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-LE.1
F-IF.7
F-IF.8,
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.
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.
Keystone Connections
2.8.A2.B: Evaluate and simplify algebraic expressions, for example: products/quotients of
polynomials, logarithmic expressions and complex fractions; and solve and graph
linear, quadratic, exponential and logarithmic equations and inequalities, and solve
and graph systems of equations and inequalities.
2.8.11.B: Evaluate and simplify algebraic expressions and solve and graph linear, quadratic,
exponential and logarithmic equations and inequalities, and solve and graphic
systems of equations and inequalities.
Modified: 06/28/2011
2.8.A2.D: Demonstrate an understanding and apply properties of functions (domain, range,
inverses) and characteristics of families of functions (linear, polynomial, rational,
trigonometric, exponential, logarithmic).
2.8.A2.E: Use combinations of symbols and numbers to create expressions, equations and
inequalities in two or more variables, systems of equations and inequalities, and
functional relationships that model problem situations.
2.8.A2.F: Interpret the results of solving equations, inequalities, systems of equations and
inequalities in the context of the situation that motivated the model.
2.5.11.A: Develop a plan to analyze a problem, identify the information needed to solve the
problem, carry out the plan, check whether an answer makes sense, and explain how
the problem was solved in grade appropriate contexts.
2.5.11.B: Use symbols, mathematical terminology, standard notation, mathematical rules,
graphing and other types of mathematical representations to communicate
observations, predictions, concepts, procedures, generalizations, ideas and results.
Student Objectives
At the end of the second marking period, students should be able to successfully manage the
following skills:
 How to add, subtract, multiply and divide complex rational expressions
 How to factor and rationalize radical expressions
 Ability to solve rational equations
 Ability to solve work and motion problems using rational equations
 Find the constant of variation and an equation of variation for direct and inverse
variation problems given certain information, and then solve the problem
 How to add, subtract, multiply, simplify (by factoring) and rationalize radical expressions
 Will be able to find principal square roots and find odd/even nth roots
 Will write expressions with rational exponents as radical expressions, and vice versa.
 Will simplify expressions containing negative rational exponents
 Will be able to use rational exponents to simplify radical expressions
 Will be able to solve problems with radicals and radical equations
 How to add, subtract, multiply and find the conjugate of imaginary and complex
numbers
 Ability to transform a graph given either coordinates or a function
 Problem-solve using quadratic functions
Activities, Assignments, & Assessments
ACTIVITIES
 Solve complex rational expressions
 Solve a formula for a specified variable
 Solve work, motion, and variation problems
Modified: 06/28/2011


















Simplify absolute value expressions
Use the product, quotient, and power rules for integer exponents
Solve linear equations and quadratic equations in factored form
Multiply binomial expressions
Add, subtract, multiply, simplify (by factoring) and rationalize radical expressions
Find principal square roots and find odd/even nth roots
Use rational exponents
Define, add, subtract, multiply and find the conjugate of imaginary and complex numbers
Solve equations using radicals, imaginary numbers, and complex numbers
Factor binomials and trinomials
Identify the graph of a function
Find x- and y-intercepts of linear equations
Determine whether a function is even, odd, or neither
Sketch or graph quadratic functions
Find a standard form for a quadratic equation
Determine maximum or minimum values and x-intercepts of the graph of a quadratic
function, if they exist
Fit a quadratic function to a graph or data points
Solve problems using quadratic functions
ASSIGNMENTS
Chapter 6
HW #
Section
Topic
Assignment
29
6.3
Complex Rational Expressions
Page 258 #1 -15 odds
30
6.3
Complex Rational Expressions
Page 258 #2 -16 evens
31
6.6
Solving Rational Equations
Page 269 #5-25 odds
32
6.6
Solving Rational Equations
Worksheet
33
6.6
Solving Rational Equations
Worksheet
34
6.7
Applications of Rational Equations
Page 273 #1,3,6,8,11,13,19
35
6.7
Applications of Rational Equations
Page 273 #2, 4, 7, 9, 12,14,18
36
6.9
Variation
Page 283 #1, 3, 5, 9, 11, 13,
17, 19, 21, 25, 30
Modified: 06/28/2011
37
Ch 6
Chapter 6 Review
Page 289 #1-10 all, 15-18all,
20-23all
Chapter 7
HW #
Section
Topic
Assignment
38
7.1-7.4
Radicals and their Operations
Worksheet
39
7.5
Rational Exponents
Page 315 #1-63 every other odd.
(Ex: 1, 5, 9…)
40
7.6
Solving Radical Equations
Page 319 #1 -31 odds
41
7.6
Solving Radical Equations
Page 319 #6 -34 evens
42
7.7, 7.9
Complex Numbers
Page 323 #1-9 odds, 25-33 odds,
35-39 all
Page 329 #12-15 all, 19-22 all
43
Ch 7
Chapter 7 Review
Worksheet
HW #
Section
Topic
Assignment
44
9.2
Translations
Page 393 #1-21 odds
45
9.3
Stretching and Shrinking
Page 398 #1-25 odds
46
9.3
Transformations
Page 99 #27-36 all
47
9.4
Graphs of Quadratic Functions
Page 402 #5 -17 odds, 19-24 all
48
9.5
Graphs of f(x)=a(x-h)2 + k
Page 406 #1 -21 odds
49
9.6
Standard Form of Quadratic
Functions
Page 410 #1 -17 odds, 21, 22
50
9.7
Graphs and x-intercepts
Page 413 #1 -15 odds, 26-28 all
51
9.8
Modeling with quadratic
functions
Page 418 #1 -13 odds, 23, 25, 27
52
9.8
Modeling with quadratic
functions
Page 418 #2 -12 evens, 22, 24,
26, 28
53
Ch 9
Chapter 9 Review
Page 424 #13_38 all
page 426 #10-22 all
Chapter 9
ASSESSMENTS
Assignment sheets will be distributed periodically throughout the school year. Homework will be
Modified: 06/28/2011
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.
Grades will be based on quizzes, tests, homework, group activities and projects. The Radnor
High School grading system and scale will be used to determine letter grades.
Terminology
Rational expressions, rational equations, complex rational expression, constant of variation,
direct variation, graphing rational functions, inverse variation, rational equation, rational
expression, reciprocal, vary directly, vary inversely, solving rational equations (Chapter 6).
Complex numbers, complex conjugate, conjugate, cube root, even root, extraneous roots,
imaginary axis, imaginary numbers, index, kth root, odd root, principal square root, radical
equation, radical expressions, radical sign, radicand, rational exponents, rationalizing the
denominator, real axis, square root. (Chapter7).
Data points, maximum value of a quadratic function, minimum value of a quadratic function,
odd and even functions, parabola, quadratic function, standard form, vertex form, vertex of a
parabola, step sequence, -b/2a, line of symmetry of a quadratic (Chapter 9).
Materials & Texts
Smith, Stanley A., Randall, Charles I., Dossey, John A., Bittinger, Marvin L. (2001). Algebra 2
with Trigonometry. Upper Saddle River, NJ: Prentice-Hall, Inc.
ISBN 0-13-051968-5
Media, Technology, Web Resources



Prentice Hall Algebra 2 With Trigonometry Home Page
Teacher-developed smart-board documents
Calculator based documents
Modified: 06/28/2011
MARKING PERIOD THREE



CONIC SECTIONS
TRIGONOMETRIC FUNCTIONS
TRIGONOMETRIC GRAPHS
Common Core Standards
F-TF.1. Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle.
F-TF.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.
F-TF.3. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent
for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and
tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real
number.
F-TF.4. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of
trigonometric functions.
F-TF.5. Choose trigonometric functions to model periodic phenomena with specified
amplitude, period, and sinusoidal axis.
Keystone Connections
2.8.A2.B: Evaluate and simplify algebraic expressions, for example: products/quotients of
polynomials, logarithmic expressions and complex fractions; and solve and graph
linear, quadratic, exponential and logarithmic equations and inequalities, and solve
and graph systems of equations and inequalities.
2.10.11.A Identify, create and solve practical problems involving right triangles using the
trigonometric functions and the Pythagorean Theorem.
2.10.11.B Graph periodic and circular functions; describe properties of the graphs.
2.8.A2.D: Demonstrate an understanding and apply properties of functions (domain, range,
inverses) and characteristics of families of functions (linear, polynomial, rational,
trigonometric, exponential, logarithmic).
2.8.A2.E: Use combinations of symbols and numbers to create expressions, equations and
inequalities in two or more variables, systems of equations and inequalities, and
functional relationships that model problem situations.
2.8.A2.F: Interpret the results of solving equations, inequalities, systems of equations and
inequalities in the context of the situation that motivated the model.
2.8.11.C Recognize, describe and generalize patterns using sequences and sries to predict
long term outcomes
2.5.11.A: Develop a plan to analyze a problem, identify the information needed to solve the
problem, carry out the plan, check whether an answer makes sense, and explain how
the problem was solved in grade appropriate contexts.
2.5.11.B: Use symbols, mathematical terminology, standard notation, mathematical rules,
graphing and other types of mathematical representations to communicate
observations, predictions, concepts, procedures, generalizations, ideas and results.
Modified: 06/28/2011
Student Objectives
At the end of the third marking period, students should be able to successfully manage the
following skills:
 How to find the length and midpoint of a segment
 How to find the equation of a conic section (circle, ellipse, hyperbola, parabola) given
certain characteristics
 How to graph a conic section
 How to identify conic sections from their equations or graphs
 How to find the six trigonometric function values for an angle
 How to find the reference angle of a rotation and use it to find trigonometric function
values
 How to convert from degrees to radian measures and back again
 How to graph trigonometric functions (sin, cos, tan and cot) with transformations
Activities, Assignments, & Assessments
ACTIVITIES
 Use the distance formula to find the distance between any two points in the plane
 Use the midpoint formula to find the midpoint between any two points in the plane
 Find the equations of a circle (given appropriate information)
 Work backwards to find the radius and center of a circle
 Given the equation of an ellipse, determine its vertices and foci, and graph the shape
 Given the equation of a hyperbola, determine its vertices, foci and asymptotes, and
graph it
 Given the equation of a parabola, find its vertex, focus and directrix, then graph
 Determine the type of conic from the equation
 Find the six trigonometric ratios for an angle of a right triangle
 Find the lengths of sides in special triangles
 Use the Pythagorean theorem to solve non-special right triangles
 Using angle relationships, determine various coterminal angles, reference angles, and
the like
 Use the definitions of trigonometric functions to find function values
 Use inverse trigonometric functions to determine angle values
 Define radian measure, and convert between radians and degrees
 Use radian measure to find applications of radian measure (arc measure,
latitude/longitude, etc.)
 Determine circular functions
 Apply radian measure to solve linear and angular velocity problems
 Graph sine and cosine using vertical and horizontal stretches and a vertical shift
Modified: 06/28/2011
ASSIGNMENTS
Chapter 10
HW #
Section
Topic
Assignment
54
10.1
Distance, Midpoint
Page 431 #1-15 odds, 28, 29
55
10.2
Conic Sections: Circles
Page 436 #1-11 odds, 17-22 all,
24, 39
56
10.2
Conic Sections: Circles
Worksheet
57
10.3
Conic Sections: Ellipses
Page 442 #1-11 odds, 21, 23,
25
58
10.3
Conic Sections: Ellipses
Worksheet
59
10.4
Conic Sections: Hyperbola
Page 450 #1-6 all, 7-13 odds,
17-22 all
60
10.4
Conic Sections: Hyperbola
Worksheet
61
10.5
Conic Sections: Parabolas
Page 456 #1 -8 all, 19-27 odds
62
10.5
Conic Sections: Parabolas
Worksheet
63
Ch 10
Chapter 10 Review
Worksheet
Chapter 17A
HW #
Section
Topic
Assignment
64
17.5
Right Triangle Trigonometry
Page 732 #1-21 odds
65
17.1
Right Triangle Trigonometry
Page 732 #2-18 evens, 22
66
Supp
Solving Non-Special Right Δs
Worksheet
67
17.4, 18.6
Solving Non-Special Right Δs with
Degrees, Minutes, Seconds
Page 753 #23-26 all,31-34 all,
Applications, Solving Non-Special
Right Δs
Page 808 #17-29 odds, include
labeled drawing of triangle
68
18.6
Modified: 06/28/2011
Page 807 #1-13 odds, include
labeled drawing of triangle
69
17.2
More on Trigonometric
Functions:Coterminaland
Reference angles (SUPP)
Page 739 #1 -17 odds, 21, 22
70
Supp
More on Trigonometric Functions:
Function values of special angles
Worksheet
71
Supp
More on Trigonometric Functions:
Reciprocal Functions, Inverse
Functions and Calculator Values
Page 753 #1-21 odd, #39-49
odd, #63-68 all
72
17.3
Radian Measure Conversions,
Reference of Special Angles
Worksheet
73
17.3
Radian Measure Conversions,
Reference of Special Angles
Worksheet
74
17.3
Arc Length, Angular Velocity,
Linear Speed
Page 746 #19, 21, 33-41 odds
75
17.3
Arc Length, Angular Velocity,
Linear Speed
Page 746 #20, 22, 32-42 evens
76
Ch 17
Chapter 17 Review
Page 779 #1*-13 all
Chapter 17B
HW #
Section
Topic
Assignment
77
Supp
Graphing Sine and Cosine (No
Trans)
Worksheet
78
Supp
Amplitude Transformations and
Vertical Shifts
Worksheet
79
Supp
Amplitude Transformations and
Vertical Shifts
Worksheet
80
Supp
Period Transformations
Worksheet
81
Supp
Period Transformations
Worksheet
82
Supp
Graphing Sine and Cosine with all
transformations and working
backwards
Worksheet
Modified: 06/28/2011
83
Supp
Graphing Sine and Cosine with all
transformations and working
backwards
Worksheet
84
Supp
Graphing Tangent and Cotangent
(No trans)
Worksheet
85
Supp
Graphing Review
Worksheet
ASSESSMENTS
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.
Grades will be based on quizzes, tests, homework, group activities and projects. The Radnor
High School grading system and scale will be used to determine letter grades.
Terminology
Asymptotes of a hyperbola, branches of a hyperbola, center of a circle, center of a hyperbola,
center of an ellipse, circle, cone, conic section, conjugate axis, directrix, distance formula,
ellipse, foci, focus, major/minor axes of an ellipse, parabola, radius of a circle, transverse axis,
vertex, vertices of a hyperbola/of an ellipse. (Chapter 10).
Sine, cosine, tangent, cosecant, secant, cotangent, adjacent angles, linear pair, vertical
angles, opposite, adjacent, initial side, terminal side, vertex, positive angle, negative angle,
degree, complementary angles, supplementary angles, minute ('), secont ("), standard
position, quadrantal angle, coterminal angle, identify, quadrants, reference angle, angle of
elevation, angle of depression, radian measure, sector of a circle, unit circle, linear velocity,
angular velocity. (Chapter17A).
Periodic function, period, sinusoid, odd function, even function, amplitude, argument,
 2 
vertical asymptote, period 
 . (Chapter 17B).
 b 
Materials & Texts
Smith, Stanley A., Randall, Charles I., Dossey, John A., Bittinger, Marvin L. (2001). Algebra 2
with Trigonometry. Upper Saddle River, NJ: Prentice-Hall, Inc.
ISBN 0-13-051968-5
Modified: 06/28/2011
Media, Technology, Web Resources



Prentice Hall Algebra 2 With Trigonometry Home Page
Teacher-developed smart-board documents
Calculator based documents
Modified: 06/28/2011
MARKING PERIOD FOUR



TRIGONOMETRIC FUNCTIONS AND APPLICATIONS
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
SEQUENCES AND SERIES
Common Core Standards
F-TF.1. Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle.
F-TF.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.
F-TF.3. (+) Use special triangles to determine geometrically the values of sine, cosine,
tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine,
cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is
any real number.
F-TF.4. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of
trigonometric functions.
F-TF.5. Choose trigonometric functions to model periodic phenomena with specified
amplitude, period, and sinusoidal axis.
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.
Modified: 06/28/2011
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.
Keystone Connections
2.8.A2.B: Evaluate and simplify algebraic expressions, for example: products/quotients of
polynomials, logarithmic expressions and complex fractions; and solve and graph
linear, quadratic, exponential and logarithmic equations and inequalities, and solve
and graph systems of equations and inequalities.
2.8.11.B: Evaluate and simplify algebraic expressions and solve and graph linear, quadratic,
exponential and logarithmic equations and inequalities, and solve and graphic
systems of equations and inequalities.
2.8.A2.D: Demonstrate an understanding and apply properties of functions (domain, range,
inverses) and characteristics of families of functions (linear, polynomial, rational,
trigonometric, exponential, logarithmic).
Modified: 06/28/2011
2.8.A2.E: Use combinations of symbols and numbers to create expressions, equations and
inequalities in two or more variables, systems of equations and inequalities, and
functional relationships that model problem situations.
2.8.A2.F: Interpret the results of solving equations, inequalities, systems of equations and
inequalities in the context of the situation that motivated the model.
2.5.11.A: Develop a plan to analyze a problem, identify the information needed to solve the
problem, carry out the plan, check whether an answer makes sense, and explain how
the problem was solved in grade appropriate contexts.
2.5.11.B: Use symbols, mathematical terminology, standard notation, mathematical rules,
graphing and other types of mathematical representations to communicate
observations, predictions, concepts, procedures, generalizations, ideas and results.
Student Objectives
At the end of the fourth marking period, students should be able to successfully manage the
following skills:
 Recognize and solve problems that require the Law of Sines and/or the Law of Cosines
 Solve basic trigonometric equations that require a minimum of algebraic manipulation
with some reference to Pythagorean identities
 Take inverses of linear functions
 Recognize that the exponential and logarithmic functions are inverses of each other
 Take the inverse of an exponential function, and conversely take the inverse of a
logarithmic function
 Graph an exponential and/or a logarithmic function with various transformations
 Solve exponential and logarithmic problems using the properties of exponents and the
properties of logarithms
 Solve specific applications of exponents and logarithms
 Recognize and articulate the difference between a sequence and a series
 Given a reasonable sequence, be able to write the next three terms in that sequence
 Recognize sigma notation, and given specific directions, be able to write out and sum
the required terms
 Recognize an arithmetic sequence; be able to collect all required terms for its algorithm
and be able to construct a particular term from that information.
 Recognize an arithmetic series; be able to collect all required terms for its algorithm and
be able to construct a particular sum from that information.
 Recognize a geometric sequence; be able to collect all required terms for its algorithm
and be able to construct a particular term from that information.
 Recognize a geometric series; be able to collect all required terms for its partial sum
algorithm and be able to construct a particular sum from that information.
 Recognize an infinite convergent geometric series; be able to collect all required terms
for its algorithm and be able to construct a particular sum from that information.
Modified: 06/28/2011
Activities, Assignments, & Assessments
ACTIVITIES
 Find the inverse of a function
 Use trigonometric identities
 Use cosine, sine, and tangent identities to simplify trigonometric expressions
 Use trigonometry to solve problems involving triangles
 Solve problems by applying trigonometric equations
 Solve equations involving trigonometric expressions
 Solve triangle perimeter problems using Law of Sines/Law of Cosines methods
 Graph exponential and logarithmic functions
 Determine whether the graph of a relation is symmetric with respect to the line y = x
 Simplify exponential and logarithmic expressions
 find natural and common logarithms and antilogarithms using a calculator, a table, or
linear interpolation
 Solve exponential and logarithmic equations
 Define sequences, define specific terms and general terms of a sequence, and find partial
sums
 Use sigma notation
 Find the first and nth terms and the common difference of an arithmetic sequence
 Find specific terms and find partial and infinite sums of a geometric series
 Determine whether a geometric series has an infinite sum
 Find the common ratio of a series
ASSIGNMENTS
Chapter 18
HW #
Section
Topic
Assignment
86
17.6, 17.8
Algebra Manipulations of
Trigonometric Functions
(Quotient and Pythagorean
Identities)
Page 773 #1-41 odds
87
17.6, 17.8
Algebra Manipulations of
Trigonometric Functions
(Quotient and Pythagorean
Identities)
Worksheet
Modified: 06/28/2011
88
18.5
Solving Trigonometric Equations
Page 802 #1-10 all, 15,25
89
18.5
Solving Trigonometric Equations
Worksheet
90
18.7
Law of Sines
Page 815 #1-19 odds
91
18.7
Law of Sines
Page 815 #21-33 odds
92
18.8
Law of Cosines
Page 815 #1-17 odds
93
18.8
Law of Cosines
Page 815 #8-24 all
94
Ch 18
Chapter 18 Review
Worksheet
HW #
Section
Topic
Assignment
95
12.1
Inverse Relation and Functions
Page 519 #1-11 odds, 25-39
odds, 48-50 all
96
12.2
Exponential and Logarithmic
Functions (Incl Natural Log)
Page 525 #1,5,11, 13, 18, 19, 21,
22, 30, 31
97
12.3
Exponential and Logarithmic
Relationships (Incl Natural Log)
Page 528 #1-37 odds
98
12.4
Properties of Logarithmic
Functions (Incl Change of Base)
Page 532 #1-23 odds 33-43 odds
99
12.4
Properties of Logarithmic
Functions (Incl Change of Base)
Page 532 #2-24 evens 34-44
evens
100
12.7
Exponential and Logarithmic
Equations
Page 547 #1-23 odds, 38, 39
101
12.7
Exponential and Logarithmic
Equations
Worksheet
102
12.7, 12.8
Applications Exponential and
Logarithmic Functions
Page 547 #26-29 all
Page 555 #23-29 odds, 39
103
Ch 12
Chapter 12 Review
Worksheet
HW #
Section
Topic
Assignment
104
14.1
Sequences and Series
Page 615 #1-7 odds, 13-24 all
Chapter 12
Chapter 14
Modified: 06/28/2011
105
14.1
Sigma Notation
Page 616 #25-36 all
106
14.2
Arithmetic Sequences
Page 622 #1-18 all
107
14.2
Arithmetic Series
Page 622 #19- 35 all
108
14.3
Geometric Sequences
Page 628 #1-14 all
109
14.3
Geometric Series
Page 628 #15-28 all, 31
110
14.4
Infinite Geometric Series
Page 632 #1-13 all
111
Ch 14
Chapter 14 Review
Page 641 #1-19 all
ASSESSMENTS
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.
Grades will be based on quizzes, tests, homework, group activities and projects. The Radnor
High School grading system and scale will be used to determine letter grades.
Terminology
Trigonometric identities (Pythagorean), trigonometric equations, basic identities, reciprocal
identities, quotient identities, law of sines, law of cosines. (Chapter 18).
Common logarithm, compound interest, base e, exponential decay, exponential equation,
exponential function, exponential growth, inverse equation, half life, log, log ax, natural
logarithm, properties of exponents, properties of logs. (Chapter12).
Arithmetic means, arithmetic sequence, arithmetic series, common difference, common ratio,
converge, convergent, general term, geometric means, geometric sequence, geometric series,
infinite sequence, infinite series, nth term, partial sums, sequence, series, sigma    , term.
(Chapter 14).
Materials & Texts
Smith, Stanley A., Randall, Charles I., Dossey, John A., Bittinger, Marvin L. (2001). Algebra 2
with Trigonometry. Upper Saddle River, NJ: Prentice-Hall, Inc.
ISBN 0-13-051968-5
Media, Technology, Web Resources
Modified: 06/28/2011



Prentice Hall Algebra 2 With Trigonometry Home Page
Teacher-developed smart-board documents
Calculator based documents
Modified: 06/28/2011