Download Algebra 3

Radnor High School
Course Syllabus
Algebra 3 and Trigonometry
0446
General Information
Credits: 1.0 Credits
Weighted: Unweighted
Prerequisite: Algebra 2
Length: Full Year
Format: Meets Daily
Grade: 11, 12
Course Description
Algebra 3 is intended to complete the topics of Algebra not developed in Algebra 2. In addition,
the course will review, reinforce and strengthen the concepts and skills studied in Algebra 2
with emphasis on equation and inequality solving. The new topics will include but not be
limited to complex numbers, exponential and logarithmic functions, and sequences and series.
Trigonometry will be introduced through right triangles and extended to include the circular
functions.
MARKING PERIOD ONE



LINEAR EQUATIONS AND INEQUALITIES IN 1 AND 2
VARIABLES, WITH GRAPHING
EXPONENTS, POLYNOMIALS AND POLYNOMIAL FUNCTIONS
FACTORING
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
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).
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 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
 Define and use the rules of exponents for products & quotients and the power rule
 Define and use negative exponents and the zero power
 Simplify exponential expression
 Define polynomials
 Find the degree of a polynomial







Add, subtract and multiply polynomials
Divide polynomials, through both long division and synthetic division
Evaluate polynomial functions through function notation
Define and use composite functions
Factor using GCF; by grouping; factoring trinomials; factoring differences of squares;
factoring perfect square trinomials
Using the zero product property
Quadratic Formula
Materials & Texts
Lial, Margaret L., Hornsby, John, (2011). Algebra and trigonometry for college readiness.
Boston, MA: Pearson Education, Inc.
ISBN 0-13-136626-2
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








Use the product rule, the quotient rule and the power rule for exponents
Use the negative exponent rule and the zero exponent rule
Add and subtract polynomials; use descending powers rule and combine like terms
Define and use function compositions; define new domain and range
Use synthetic division and or long division to divide polynomials
Factoring techniques
o GCF; Binomial factor; Negative common factor; Grouping; Rearrange Terms, then
Factor; Factor Trinomials; Difference of Squares; Perfect Square Trinomials;
Difference of Cubes; Sum of Cubes
Solve Quadratic Equations by Factoriong and Using the ZPP
Review the Quadratic Equation
ASSIGNMENTS
CHAPTERS 2, 3, 4
HW #
Section
Topic
Assignment
1
2.1`
Solving Equations
Pg 50-51: 11, 13, 17, 21, 23,
33, 35
2
2.4
Solving Inequalities (graphs
required
Pg. 80-81: 11, 15, 17, 21, 27,
31, 33
3
2.6
Absolute value equations
Pg 96-98: 5-13odd, 59, 63, 65,
85
4
2.6
Absolute value inequalities
Pg 96-98: 21-25odd, 29, 31,
35-45 odd
5
Ch. 2
Review
Pg. 102-105: 1, 5, 7, 27, 28,
51, 53, 55, 59, 61, 62
6
3.5
Functions
Pg. 157-158: 1, 2, 5, 7, 1121odd
7
3.5
F(x) notation
Pg. 158-159: 41, 43, 49, 51,
53, 61, 63, 65
8
Ch. 3
Review
Worksheet
9
4.1
2 variable systems
Pg. 179: 1, 7-13
10
4.1
Solve systems by graphing (on calc)
Worksheet
11
4.1
Solve systems by substitution
179-180: 17-25 odd, 29, 33
12
4.1
Solve systems by elimination
180: 35-47odd
13
Ch. 4
Chapter 4 reveiw
Pg 180: 58-62
Pg 230-231 2, 3, 5, 14
CHAPTER 5
HW #
Section
Topic
Assignment
14
5.1
Exponents
Pg246: 19-39odd
15
5.1
Rules of exponents
Pg 246-248: 7-15odd, 6377odd, 89, 105
16
5.1
Rules of exponents
247-248: 79-87odd, 93, 95,
99, 101
17
5.2
Standard form and degree
Pg 253: 1-25odd
18
5.2
Add/subtract polynomials
Pg. 253-254: 29, 31, 39, 43,
51, 57, 63-69odd
19
5.3
Add/subtract polynomial functions
Pg 262-263: 1, 3, 7, 13, 15,
17, 18, 25, 27
20
5.3
Composition of functions
Pg. 263: 35-47odd
21
5.3
Add/subtract/compositions
Worksheet
22
5.4
Multiply polynomials
Pg. 270-271: 1, 3, 5, 11, 3339o, 47, 59, 15(do last)
23
5.4
Multiply polynomials
Pg 270-271: 7, 9, 16, 19, 49,
51, 55, 61, 63, 85
24
5.4
Multiply polynomial functions
Pg 271: 93-105odd
25
5.5
Polynomial division
Pg 277: 5-19odd
26
5.5
Polynomial division
277: 21-31 odd
27
Ch.5
Review
281-283: 3, 9, 11, 13, 23, 39,
40, 47, 53, 59, 71
CHAPTER 6
HW #
Section
Topic
Assignment
28
6.1
Factoring (GCF only)
Pg. 290: 1-19odd
29
6.1
GCF’s
290: 2-20even
30
6.2
Factoring trinomials
297: 5-19odd
31
6.2
Factoring trinomials
297: 33-39odd, 45, 46, 47
32
6.2
Factoring trinomials
Worksheet
33
6.3
Special cases (factoring)
302: 7-23odd
34
6.3
Special cases
Worksheet
35
6.5
Factoring to solve equations (ZPP)
312: 3-15odd
36
6.5
Factoring, including GCF
312: 19, 23, 29, 31, 39, 41
37
9.2
Quadratic formula
pg 450: 5-13 odd
38
Ch. 6
Review
Pg 315: 1, 3, 11, 13, 15, 25,
28, 37, 41, 45
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
Linear equations, solution, solution set, equivalent equations, identity, inequality, linear
inequality, absolute value, absolute value inequality, independent and dependent variables,
relation, function, domain, range, function notation, linear function, constant function, systems
of equations, system of linear equations, solution set of a linear system, consistent system,
independent equations, inconsistent system, dependent equations, elimination method,
substitution method (Chapters 2, 3, 4)
Term, coefficient, algebraic expression, polynomial, descending powers, trinomial, binomial,
monomial, degree of a term, degree of a polynomial, negative of a polynomial, polynomial
function, composition of functions, identity function, squaring function, cubing function (Chapter
5).
Factoring, greatest common factor (GCF), prime polynomial, difference of squares, perfect
square trinomial, difference of cubes, sum of cubes, quadratic equation, standard form of a
quadratic equation (Chapter 6).
Media, Technology, Web Resources



Teacher-developed documents
Calculator based documents
MathXLforSchool.com
MARKING PERIOD TWO


RATIONAL EXPRESSIONS AND FUNCTIONS
ROOTS, RADICALS AND ROOT FUNCTIONS
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
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.
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:
 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”
Materials & Texts
Lial, Margaret L., Hornsby, John, (2011). Algebra and trigonometry for college readiness.
Boston, MA: Pearson Education, Inc.
ISBN 0-13-136626-2
Activities, Assignments, & Assessments
ACTIVITIES
 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
Chapter 7
HW #
Section
Topic
Assignment
39
7.1
Simplify rational expressions
pg 328: 9, 11, 17, 25, 27, 35,
37, 39
40
7.1
Multiply/divide rational expressions
329: 61-64, 67-71
41
7.1
Multiply/divide rational expressions
(w/factoring
329: 71-75, 79-83
42
7.2
Add/subtract rational expressions
336: 1-12
43
7.2
Add/subtract rational expressions
(unlike denoms)
336-337: 21-29odd, 39, 49,
53, 55
44
7.4
Solving rational equations
348-349: 1, 3, 9, 11, 15-23odd
45
7.4
Solving rational equations
348-349: 25-33odd
46
7.4
Solving rational equations
348-349: 2, 4, 6, 16, 18, 22,
26, 28
47
Ch. 7
Review
Pg 375-377: 3, 5, 9, 17, 18,
25, 27
HW #
Section
Topic
Assignment
48
8.1
Simplify square roots
Worksheet
49
8.1
Other roots
Pg 384: 13-27odd
50
8.6
Radical equations
418-419: 1, 7-17odd, 37,38
Chapter 8
51
8.6
Radical equations
418-419: 23-31odd, 43,45
52
8.7
Square roots of negative numbers
425: 1-12
53
8.7
Square roots of negative numbers
425: 15, 17, 23, 39, 41, 43, 45
54
Ch. 8
Review
Pg430-433: 3, 5, 103, 105,
107, 110, 120, 121, 126, plus
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
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
MathXLforSchool.com
MARKING PERIOD THREE



EXPONENTIAL AND LOGARITHMIC FUNCTIONS
SEQUENCES AND SERIES
RIGHT TRIANGLE TRIGONOMETRY
Common Core Standards
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.
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.
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).
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 third marking period, students should be able to successfully manage the
following skills:
 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
 Understand the basic terminology of angles
 Find measures of complementary and supplementary angles
 Calculate with degrees, minutes, and seconds
 Find the measures of coterminal angles
 Classify triangles
 Find the unknown angles and side lengths in similar triangles
 Find the values of the six trigonometric functions of a triangle
 Solve right triangles with Pythagorean theorem
Materials & Texts
Lial, Margaret L., Hornsby, John, (2011). Algebra and trigonometry for college readiness.
Boston, MA: Pearson Education, Inc.
ISBN 0-13-136626-2
Activities, Assignments, & Assessments
ACTIVITIES
 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
 Find the complement and supplement of an angle
 Calculate with degrees minutes and seconds
 Find measures of coterminal angles
 Find angle measures based on relationships
 Apple the angle sum of a triangle property
 Find angle measures in similar triangles
 Find side lengths in similar triangles
 Find the six trigonometric values given a right triangle
 Solve right triangles both with Pythagorean theorem and trigonometry
 Solve right triangles given an angle and a side
 Solve right triangles given two sides
 Find angles of elevation and depression
ASSIGNMENTS
Chapter 11 and sequence/series assignments
HW #
Section
Topic
Assignment
55
11.2
Exponential function graphs (by
hand)
Pg 545: 1,3, 5-9
56
11.2
Exponential function graphs (by
hand)
Worksheet
57
11.2
Exponential equations
Pg 546: 15-31odd, 37
58
11.3
Logarithmic function graphs (by
hand)
Worksheet
59
11.3
Logarithmic function graphs (by
hand)
Worksheet
60
11.3
Explore log/exponential relationship
Pg 552-553: 1-19odd
61
11.3
Evaluate logs
Worksheet
62
11.3
Solve exponential equations
Worksheet
63
11.3
Solve log equations
Worksheet
64
Add
Evaluate sequences
Worksheet
65
Add
Arithmetic sequences
Worksheet
66
Add
Sigma notation
Worksheet
67
Add
Arithmetic series
Worksheet
68
Add
Geometric sequences
Worksheet
69
Add
Geometric series
Worksheet
70
Add
Infinite geometric series
worksheet
.Chapter 14 (part one) assignments
HW #
Section
Topic
Assignment
71
14.1
Comp/Supp. Angles
pg 665: 1-21odd
72
14.1
Degree subunits (calc only)
666: 33, 35, 39, 41, 45, 47,
53, 57, 59, 63
73
14.1
Angles in standard position
(coterminal values)
666-667: 69, 73, 75, 77, 83,
103, 105, 109
74
14.1
Angles in standard position
(coterminal values)
Worksheet
75
14.2
Angle relationships from geometry
673: 3-15odd
76
14.2
Triangle similarity
674-675: 25-39odd, 43, 49,
51, 53
77
14.3
Right triangles/Pythagorean thm.
Worksheet
78
14.3
Right triangle trigonometry (6
definitions)
Worksheet
79
14.3
Right triangle trig
Worksheet
80
15.4
Solving right triangles
724-725: 9-15odd, 21, 23, 27,
33
81
15.4
Solving right triangles
724-725: 10-16even,25, 31, 35
82
15.4
Solving right triangles (word
problems)
725-727: 39,41,42,45
83
15.4
Solving right triangles
(elevation/depression)
726-727: 49-53
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
Exponential function, asymptote, exponential equation, logarithm, logarithmic equation,
sequence, series, arithmetic sequence, arithmetic series, geometric sequence, geometric series,
infinite geometric series, sigma notation, angle, side of an angle, vertex of an angle, initial side of
an angle, terminal side of an angle, right angle, acute angle, obtuse angle, complements,
supplements, degrees, minutes, seconds, vertical angles, similar triangles, sine, cosine, tangent,
cotangent, secant, cosecant, coterminal
Media, Technology, Web Resources



Teacher-developed documents
Calculator based documents
MathXLforSchool.com
MARKING PERIOD FOUR



RIGHT TRIANGLE TRIGONOMETRY
TRIGONOMETRIC FUNCTIONS
TRIGONOMETRIC APPLICATIONS
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-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
2.10.11.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.
Student Objectives
At the end of the fourth marking period, students should be able to successfully manage the
following skills:
 Define and find the six trigonometric function values for an angle, including quadrantal
angles
 Ability to use the definitions of the trigonometric functions to find both special angles
and points on the unit circle.
 Use the Pythagorean and quotient identities to find function values
 Identify and use reciprocal identities to find function values
 Define and use cofunction identities
 Use special right triangles to identify points on the unit circle for 300, 450, 600 angles
 Identify reference angles and positive/negative angles
 Identify coterminal angles
 Use trigonometric applications
 Convert from degrees to radians and from radians to degrees
 Use the Law of Sines/Law of Cosines to solve triangle perimeter problems
Materials & Texts
Lial, Margaret L., Hornsby, John, (2011). Algebra and trigonometry for college readiness.
Boston, MA: Pearson Education, Inc.
ISBN 0-13-136626-2
Activities, Assignments, & Assessments
ACTIVITIES
 Find the function values of an acute angle using trigonometric ratios
 Find the function values of an angle using quadrantal angles given specific values
 Use reciprocal identities to find function values
 Determine the signs of the trigonometric functions of nonquadrantal angles
 Find all function values given one value and the quadrant











Define quotient and reciprocal identities
Use the Pythagorean and quotient identities to find function values
Find trigonometric function values of an acute angle
Writing functions in terms of cofunctions
Solving equations using the cofunction identities
Comparing function values fo acute angles
Finding function values for special right triangles
Finding reference angles in all quadrants
Use reference angles, quotient and reciprocal identities plus trigonometric functions to solve
application problems
Convert from radians to degrees and from degrees to radians
Solve triangle perimeter problems using Law of Sines/Law of Cosines methods
ASSIGNMENTS
CHAPTER 14
HW #
Section
Topic
Assignment
84
14.3
Right triangles in standard position
Worksheet
85
14.3
Intro to the unit circle
Pg 681: 1-8, 25-33odd
86
14.3
Intro to the unit circle
681: 26-34even, 37-43odd
87
14.4
Unit circle definitions (quadrantal
values)
681: 55-63odd, 73-79odd
88
14.4
Reciprocal functions
689: 1-11odd, 19, 21, 25, 29
89
14.4
Locations
690: 23, 26, 30, 31-41odd
90
14.4
Using “p of theta”
690-691: 61-65odd, 69-77odd
91
14.4
Using “p of theta”
690-691: 45,62-66even, 7278even
92
Ch.14
Review
694-697: 1, 5, 9, 12, 13, 17,
19, 21, 23, 25, 29, 37, 41, 43
CHAPTERS 15, 16 AND 20
HW #
Section
Topic
Assignment
93
15.1
Reference angles and families
Worksheet
94
15.1
Reference angles and families
Worksheet
95
15.2
Intro to special angles on the unit
circle
Worksheet
96
15.2
Intro to special angles on the unit
circle
Worksheet
97
15.2
Intro to special angles on the unit
circle
Pg 713-714: 1, 3, 5, 11, 13,
15, 19, 21, 30
98
15.3
Evaluating trig functions (on calc)
718: 5-21odd
99
15.3
Evaluating trig functions (on calc)
718-719: 37-51odd
100
15.3
Determine the value of theta (on
calc)
718: 23-31
101
Ch.15
Review
730-732: 1, 7, 12, 14, 23, 2937odd, 47, 53, 54
102
16.1
Radians/degrees
740-741: 7-15odd, 25-37odd
103
16.1
Radians/degrees
740-741: 8-16even, 2638even
104
20.1
Law of sines
886-887: 1-11odd
105
20.1
Law of sines
887: 13-19odd, 25
106
20.2
Law of cosines
899: 1-17odd
107
20.2
Law of cosines
900-901: 19, 21, 23, 27, 37, 39
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
Sine, cosine, tangent, cotangent, secant, cosecant, reciprocal, adjacent angles, linear pair,
vertical angles, opposite, adjacent, initial side, terminal side, vertex, positive angle, negative
angle, degree, complementary angles, supplementary angles, minute ('), second ("), 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, Trigonometric identities (Pythagorean), trigonometric equations, basic
identities, reciprocal identities, quotient identities, law of sines, law of cosines.
Media, Technology, Web Resources



Teacher-developed documents
Calculator based documents
MathXLforSchool.com