SCHOLARS ONLINE
Course Syllabus
PRECALCULUS
20182019
PRECALCULUS
Instructor 

ARTHUR MABBOTT MATHGUY SCHOLARS ONLINE ART@MABBOTT.ORG (206) 6057393 

Course Description
This course is part of the
sequence of courses that make up the SCHOLARS ONLINE Mathematics Department.
General Course Goals
This course will focus on
how to do mathematics including functions and trigonometry. This course will focus on how to do
mathematics including functions and trigonometry. The Fall and Spring Semester Guides at
the end are the goal for this course.
Chapter by Chapter Calendars will be distributed just in time and will
reflect adjustments to meet the needs of the students each year.
Course Location
WIZIQ
SYNCHRONIS SESSIONS 
Start Time 
End Time 
MONDAY 
11:00AM 
12:00PM 
WEDNESDAY 
11:00AM 
12:00PM 
FRIDAY 
11:00AM 
12:00PM 
UNIT
I  FUNCTIONS
A.
CHAPTER 1 –
FUNCTIONS AND
B.
CHAPTER 7 –
PROPERIES OF ELEMENTARY FUNCTIONS
C.
CHAPTER 15
– POLY AND RATIONAL FUNCTIONS
UNIT
II  TRIGONOMETRY
A.
CHAPTER 2 –
PERIODIC FUNCTIONS
B.
CHAPTER 3 –
CIRC FUNCTIONS
C.
CHAPTER 4 –
TRIG IDENTITIES
D.CHAPTER 5 – COMBINED SINUSOID
E.
CHAPTER 6 –
TRIANGLE TRIG
UNIT
III – ADVANCED TOPICS
A.
CHAPTER 11
– MATRICES
B.
CHAPTER 12
– CONICS & QUAD SURFACES
Chapter 1 – 18 Days
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
September


Day
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
Chapter 7 – 22 Days
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Day
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 



Chapter 15 – 16 Days
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 


Day
41 
42 
42 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 


Chapter 2 – 15 Days
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Day
57 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 
59 
70 
71 
Christmas Break
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
December
24 
25 
26 
27 
28 
31 
January
1 
2 
3 
4 
Chapter 3 – 19 Days
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Day
72 
73 
74 
75 
76 
77 
78 
79 
80 
81 
82 
83 
84 
85 
86 
87 
88 
89 
90 
91 
Chapter 4 – 25 Days
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Day
92 
93 
94 
95 
96 
97 
98 
99 
100 
101 
102 
103 
104 
105 
106 
107 
108 
109 
110 
111 
112 
113 
114 
115 
116 
Chapter 5 – 20 Days
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Day
117 
118 
119 
120 
121 
122 
123 
124 
125 
126 
127 
128 
129 
130 
131 
EASTER BREAK 

132 
133 
134 
135 
136 
Chapter 6 – 14 Days
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
137 
138 
139 
140 
141 
142 
143 
144 
145 
146 
147 
148 
149 
150 
151 
Chapter 11 – 10 days
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
152 
153 
154 
155 
156 
157 
158 
159 
160 
161 
Chapter 12 – 15 days
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
162 
163 
164 
165 
166 
167 
168 
169 
170 
171 
172 
173 
174 
175 
176 
Course Agenda
Unit I
(Functions): Chapter 1  Functions and Mathematical Models 

Suggested Timeframe: 21 Days (approximate unit
completion date: October 5) 

Unit Rationale: Reviewing
functions studied in algebra and generalizing the concepts of transformations
and compositions of these functions will allow us to apply them to more
complicated function families. 
Essential
Questions: How do families of functions relate to the types of transformations
that are used and how does each transformation affect an equation, graph,
table, or data set? How can a function composition and/or an inverse function
be used in applications? 

STANDARDS 
Vocabulary 
Reasoning, Problem Solving, &
Communication 
Planning 

Chapter Sequence 
Explorations 

Focus Standards: PC.F.3 Identify
parent functions of polynomials, power, exponential, inverse variation and
rational from a table, graph, equation or situation. (1.1, 1.2) 
á
Domain/range á
Argument of
the function á
Asymptote á
Discontinuity á
Boolean
variable á
Restricted
domain á
Dilation,
reflection, translations, á
Displacement
vs. distance á
Even and odd
functions á
Domain and
range of composite functions á
Invertible,
onetoone function á
Strictly
increasing and strictly decreasing á
f^{1}(f(x))
= f(f^{1}(x)) = x 
PC.8.E Read and interpret diagrams, graphs, and
text containing the symbols, language, and conventions of mathematics PC.8.B Select and apply strategies to solve
problems. 
11 12 13 Quiz 11 to 13 14 15 Quiz 14 to 15 16 17 Optional 18 Review Unit Assessment 
13a,
13c 14a 15a 16a 

PC.F.4 Perform
algebraic operations on functions (polynomial, power, exponential, rational,
absolute value, etc.) and apply transformations. (1.3, 1.6) 

PC.F.5 Write an
expression for the composition of one function with another and find the
domain, range and graph the composite function. (1.4) 

PC.F.6 Determine
whether a function (equation or graph) has an inverse. Express the inverse as
an equation or graph if it exists. Use function notation for inverses. (1.5) 

Supporting
Standards: 

As a result of this unit,
students will be able to: á
Use multiple
representations of polynomial, quadratic, linear, direct variation, power,
exponential, inverse variation, and rational functions. á
Use transformations
to identify functions from the parent in a function family. á
Compose
functions. á
Understand and
apply inverse and absolute value functions. 

Unit I
(Functions): Chapter 7  Properties of Elementary Functions 

Suggested Timeframe: 18 Days (approximate unit
completion date: November 1) 

Unit Rationale: In
order to apply mathematics, students must understand the differences between
different types of functions in order to be able to model realworld
situations. 
Essential
Questions: How can determine different types of functions be determined from
data? How can I find a missing exponent? 

STANDARDS 
Vocabulary 
Reasoning, Problem Solving, &
Communication 
Planning 

Chapter Sequence 
Explorations 

Focus Standards: PC.F.3 Identify
parent functions of polynomials, power, exponential, inverse variation and
rational from a table, graph, equation or situation. (7.1, 7.2) 
á
Proportionality
constant á
Second and
third difference á
Common
logarithm á
Natural
logarithm á
Base, exponent 
PC.8.E Read and interpret diagrams, graphs, and
text containing the symbols, language, and conventions of mathematics. PC.8.B Select and apply strategies to solve
problems. PC.8.A Analyze a problem situation and represent
it mathematically. PC.8.D Generalize a solution strategy for a
single problem to a class of related problems and apply a strategy for a
class of related problems to solve specific problems. PC.8.C Evaluate a solution for reasonableness,
verify its accuracy, and interpret the solution in the context of the
original problem. 
71 72 73 Quiz 71 to 73 74 75 76 Quiz 74 to 76 *77 (Optional) 78 (Review) Unit
Assessment 
72a 73a,
73b 74a 78a 
PC.F.4 Perform
algebraic operations on functions (polynomial, power, exponential, rational,
absolute value, etc.) and apply transformations. 

PC.F.12 Compare
the rates of change of functions in different families (linear, quadratic,
exponential, and power). (7.3) 

PC.E.1 Use the
inverse relationship between exponential and logarithmic functions to solve
equations and problems. (7.4, 7.5) 

PC.E.2 Solve
exponential and logarithmic equations algebraically and graphically. (7.4,
7.5, 7.6) 

PC.E.3 Find an
exponential and logarithmic function to model a given data set or
situation. Solve problems
involving exponential growth or decay. (7.6, 7.7) 
Notes: 1.
Avoid
Qproblems from chapters 2 – 6. 2.
Review
properties of exponents. 

Supporting
Standards: 

As a result of this unit,
students will be able to: á
Recognize
various functions from patterns, graphs, equations, and/or tables of values. á
Use the
properties of exponents and logarithms to simplify expressions and solve
equations. á
Use
exponential and logarithmic functions to solve realworld problems involving
growth and decay. 
Unit I
(Functions): Chapter 15  Polynomial and Rational Functions 

Suggested Timeframe: 15 Days (approximate unit
completion date: November 23) 

Unit
Rationale: Analyzing polynomial functions will facilitate graphing
and will allow us to also work with rational functions that are the quotient
of two polynomials. This study will lead to the concept of limits and rates
of change at any point on a graph. 
Essential
Questions: How
does knowledge and analysis of the characteristics of polynomial and rational
functions help us easily graph and apply them? 

STANDARDS 
Vocabulary 
Reasoning, Problem Solving, &
Communication 
Planning 

Chapter Sequence 
Explorations 

Focus Standards: PC.F.13 Know and apply the Remainder Theorem: For a polynomial p(x) and
a number a, the remainder on division by x – a is p(a), so p(a) = 0 if
and only if (x – a) is a factor of p(x). (15.2) 
á
Critical point á
End behavior á
Remainder
Theorem á
Discontinuous á
Removable
discontinuity á
Indeterminate
form á
Infinite form á
Limit á
Synthetic
division 
PC.8.A Analyze a problem situation and represent
it mathematically. PC.8.B Select and apply strategies to solve
problems. PC.8.C Evaluate a solution for reasonableness,
verify its accuracy, and interpret the solution in the context of the
original problem. PC.8.E Read and interpret diagrams, graphs, and
text containing the symbols, language, and conventions of mathematics. 
151 152 Quiz *153 (optional) 154 *155 (optional) 156 Review Unit AssessmenT 
151a 152a,
2b 
PC.F.14 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. (15.1) 

PC.F.15 Graph linear, quadratic, polynomial, rational, exponential, and logarithmic functions expressed
symbolically and show key features of the graph, including zeros, intercepts,
critical points, and asymptotic and end behavior. (15.1, 15.2) 

PC.F.8 Identify and describe
discontinuities (removable, step, asymptotes) of a function and how these
relate to the graph. (15.4) 
Notes: *Omit concepts typically taught in a
calculus course, including limits and derivatives. 

Supporting Standards: PC.F.2 Find the domains and ranges of functions. 

As a result of
this unit, students will be able to: á
Determine the
degree of a polynomial from its graph. á
Find the zeros
of a polynomial from graph or equation. á
Use the
Remainder Theorem to find the zeros of a polynomial function. á
Determine
whether and how many zeros a polynomial function may have. á
Know how
complex solutions to a polynomial equation translate to the graphic
representation of that equation. á
Determine if a
polynomial model fits a set of data. á
Simplify
rational expressions, solve rational equations, and analyze the graphs of
rational functions. á
Use partial
fractions to solve or graph rational equations or functions. 
Unit II (Trigonometry): Chapter 2  Periodic Functions and
Right Triangle Problems 

Suggested Timeframe: 15 days (approximate unit
completion date: December 16) 

Unit Rationale: Understanding
the trigonometric ratios and their relationship to right triangles will allow
us to solve many realworld applications involving measures of triangles and
will lead to an understanding of trigonometric functions. 
Essential Questions: What situations
can be modeled with periodic equations? Why are there six trigonometric
functions? Where do they come from? How do you find an unknown angle in a
right triangle? 

STANDARDS 
Vocabulary 
Reasoning,
Problem Solving, & Communication 
Planning 

Chapter
Sequence 
Explorations 

Focus Standards: PC.T.1 Define (using the unit
circle), graph, and use all six trigonometric functions of any angle. Convert between radians and degrees.
(2.2, 2.3, 2.4) 
á
Periodic,
sinusoid, á
Standard
position á
Coterminal á
Reference
angle á
Cycle á
Period á
Sine, cosine,
tangent, cotangent, secant, and cosecant á
Inverse
trigonometric function á
Principal
branch 
PC.8.E Read and interpret diagrams, graphs, and
text containing the symbols, language, and conventions of mathematics PC.8.B Select and apply strategies to solve
problems. PC.8.A Analyze a problem situation and represent
it mathematically. PC.8.D Generalize a solution strategy for a
single problem to a class of related problems and apply a strategy for a
class of related problems to solve specific problems. PC.8.C Evaluate a solution for reasonableness,
verify its accuracy, and interpret the solution in the context of the
original problem. 
21 22 23 24 Quiz
21 to 2.4 25 Quiz
25 26 Unit
Assessment 
21a 22a 23a,b,c 24a,
b 25a,
b 

PC.T.2 Students
know the definition of sine and cosine as y and xcoordinates of points on
the unit circle. (2.4) 

PC.T.3 Students
can compute (by hand) the values of six trigonometric functions at any
standard point on the unit circle. (2.4) 

PC.T.4 Know the
definitions of the sine and cosine functions (amplitude, period, sinusoidal
axis, frequency and phase shift), and explain the relationship between
constants in the formula, and transformed graph. (2.3, 

PC.T.8 Solve
trigonometric equations using basic identities and inverse trigonometric
functions. (2.5) 
NOTE: Radian measures will be primarily used in calculus. Students
should be fluent with graphs of all six trig functions using radian measures
as well as degrees. 

PC.T.9 Use
trigonometry to determine unknown sides or angles in right triangles. (2.5) 

Supporting Standards: 

As a result of this unit,
students will be able to: á
Use the unit
circle values to define trigonometric functions. á
Extend
definitions for sine and cosine to tangent, cotangent, secant, and cosecant. á
Use inverse
trigonometric functions to solve equations and problems. á
Graph sine and
cosine functions. á
Solve for
missing parts of right triangles. 

Unit
II (Trigonometry): Chapter 3  Applications of Trigonometric and Circular
Functions 

Suggested Timeframe: 17 Days (approximate unit
completion date: January 26) 

Unit Rationale: Extending
our understanding of periodic functions by using our knowledge of
transformations learned (Unit 1  Chapter 1) will allow us to model
realworld sinusoidal relationships. 
Essential
Questions: How can you write periodic equation from a situation or graph? What
is a radian? Why do we need to use radians? 

STANDARDS 
Vocabulary 
Reasoning, Problem Solving, &
Communication 
Planning 

Chapter Sequence 
Explorations 

Focus Standards: PC.T.5 Find and use a sinusoidal function to model a given data set or
situation. (3.1,3.7) 
á
Amplitude á
Phase
displacement á
Sinusoidal
Axis á
Cycle á
Frequency á
Convex/Concave á
Point of
inflection á
Upper
bound/Lower bound á
Asymptotes á
Radian á
Arc length á
Circular
functions á
Arc functions á
Inverse
functions 
PC.8.A Analyze a problem situation and represent
it mathematically. PC.8.B Select and apply strategies to solve
problems. PC.8.D Generalize a solution strategy for a
single problem to a class of related problems and apply a strategy for a
class of related problems to solve specific problems. PC.8.E Read and interpret diagrams, graphs, and
text containing the symbols, language, and conventions of mathematics. 
31 32 *33
(optional) 34 35 36 37 *38
(optional) 39
Review Unit
Assessment 
31b 32a,
b 33a 34a,b 35a 36

PC.T.1 Define (using the unit circle), graph, and use all six
trigonometric functions of any angle.
Convert between radians and degrees. (3.1, 3.4  radians, 3.5 –
unit circle) 

PC.T.4 Graph transformations of the
sine and cosine functions (amplitude, period, sinusoidal axis, frequency and
phase shift), and explain the relationship between constants in the formula
and transformed graph. (3.2) 

Supporting
Standards: PC.T.6 Know
the definitions of the inverse trigonometric functions, including their
domains and ranges; recognize their graphs. (3.6) 
NOTE: 

As a result of
this unit, students will be able to: á
Write a
particular equation for a sinusoid that fits any given conditions. á
Graph any
trigonometric function from its equation or given amplitude, period or frequency, phase displacement,
and sinusoidal axis. á
Find a
trigonometric equation from its graph or given amplitude, period, phase
displacement, and sinusoidal axis. á
Find the
amplitude, period, phase displacement, and sinusoidal axis from an equation
or graph. 
Unit II (Trigonometry): Chapter 4  Trigonometric
Function Properties: Identities 

Suggested Timeframe: 20 Days (approximate unit
completion date: March 2) 

Unit Rationale: Learning
the Pythagorean properties will allow us to transform one trigonometric
expression into an equivalent form, prove identities, and derive other
properties, such as the double and halfangle properties. 
Essential
Questions: When we solve a trigonometric equation, how can we know that we have
found all possible solutions? How can we use what we know about proof to show that two
trigonometric expressions are equivalent? 

STANDARDS 
Vocabulary 
Reasoning, Problem Solving, & Communication 
Planning 

Chapter Sequence 
Explorations 

Focus Standards: PC.T.7 Use the basic trigonometric identities for sine, cosine and
tangent to prove additional trigonometric identities and derive some of the
basic ones (e.g. Use cos^{2}x
+ sin^{2}x = 1 to prove
that sec^{2}x = tan^{2}x + 1). (4.1 – 4.3) 
á
Pythagorean
property á
Reciprocal
property á
Quotient
property á
Identity á
Conjugate á
Closed
interval á
Open interval
(Notation) á
Principal
branch 
PC.8.B Select and apply strategies to solve problems. PC.8.C Evaluate a solution for reasonableness, verify its accuracy,
and interpret the solution in the context of the original problem 
41 42 43 Quiz 1 44 46 Quiz 2 47 Test Ch 4/5 
42a 43a 44a 46a,
b 
PC.T.8 Solve trigonometric equations using basic identities and inverse trigonometric functions. (4.4) 

PC.T.6 Know the definitions of the inverse trigonometric
functions, including their domains and ranges; recognize their graphs. (4.6) 

Supporting
Standards: PC.5 Write an expression for the composition of one function with
another and find the domain, range and graph of the composite function. Recognize components when a function
is composed of two or more elementary functions. 
NOTE: Check the recommended explorations
for more practice problems. 

As a result of
this unit, students will be able to: á
Transform a
trigonometric expression to an equivalent expression. á
Use inverse
trigonometric functions to solve equations. á
Find the
graphs and characteristics of inverse trigonometric functions. á
Recognize that
some triangles have two possible solutions (ambiguous case). 
Unit II
(Trigonometry): Chapter 5  Properties of Combined Sinusoids 

Suggested Timeframe: 6 days (approximate unit
completion date: March 12) 

Unit
Rationale: Learning how to work with trigonometric arguments that
are sums, differences, composites, double, and halfangles allows us to
simplify and solve more complicated trigonometric expressions and equations. 
Essential
Questions: How
can we use identities to simplify and solve more quickly trigonometric
expressions and equations involving double and half angles? 

STANDARDS 
Vocabulary 
Reasoning, Problem Solving, &
Communication 
Planning 

Chapter Sequence 
Explorations 

Focus Standards: PC.T.7 Use the basic trigonometric identities for sine, cosine and
tangent to prove trigonometric identities and derive some of the basic ones (e.g., doubleangle formula from
sum and difference formula, halfangle formula from double angle formula) (5.2, 5.3, 5.6) 
á
Cofunctions á
Odd and even
functions á
Double and
half angle argument 
PC.8.D Generalize a solution strategy for a
single problem to a class of related problems and apply a strategy for a
class of related problems to solve specific problems. 
*5.1 (optional) 52 53 *54
(optional) *55
(optional) 56 57
Review Quiz 
52b,
c 56a 
PC.T.8 Solve trigonometric equations using basic identities and
inverse trigonometric functions. (5.2, 5.3, 5.6) 

Supporting
Standards: 
NOTE: Review problems from 5.7 should
include only those sections covered in this unit. 

As a result of
this unit, students will be able to: á
Derive and use
properties for trigonometric functions of sums and differences of angles. á
Derive and use
properties of products of arguments, including double and halfarguments. á
Use algebraic
techniques to solve trigonometric equations. 
Unit II (Trigonometry): Chapter 6  Triangle Trigonometry 

Suggested Timeframe: 14 Days (approximate unit
completion date: March 30 

Unit Rationale: Learning
how to find unknown measurements in oblique triangles (sides, angles, and
areas) will allow us to solve any triangle given enough information. 
Essential Questions: How
can the formulas and techniques that we have learned to solve a right
triangle help us solve any oblique triangle? 

STANDARDS 
Vocabulary 
Reasoning,
Problem Solving, & Communication 
Planning 

Chapter
Sequence 
Explorations 

Focus Standards: PC.T.10 Use law of sines and law of cosines to solve problems. (62,
64, 65, 67) 
á
Oblique
triangle á
Law of Sines á
Law of Cosines á
Semiperimeter á
HeroÕs Formula á
Ambiguous 
PC.8.B Select and apply strategies to solve problems. PC.8.C Evaluate a solution for reasonableness, verify its accuracy,
and interpret the solution in the context of the original problem. 
61 62 63 Quiz
1 64 65 Quiz
2 *66
(optional) 67 68
Review Unit
Assessment 
62a,b 63a 65a,b 
Supporting Standards: 


As a result of
this unit, students will be able to: á
Solve an
oblique triangle, given enough information. á
Apply the Laws
of Sines and Cosines to solve triangles. á
Find the area
of triangles using trigonometry, including HeroÕs formula. 
Unit III
(Advanced Topics): Chapter 11  Matrices – Operations 

Suggested Timeframe: 10 days (approximate unit
completion date: April 13) 

Unit Rationale: Learning
to work with matrices can simplify work with transformations, data display,
and system solutions. 
Essential
Questions: How can we use matrices to transform geometric figures, display data,
and/or solve a system? 

STANDARDS 
Vocabulary 
Reasoning, Problem Solving, &
Communication 
Planning 

Chapter Sequence 
Explorations 

Focus Standards: PC.M.1 Add, subtract, and multiply matrices of appropriate dimensions.
(112) 
á
Matrix á
Scalar á
Determinant á
Adjoint á
Transformation matrix á
Image matrix á
Iterate 
PC.8.A Analyze a problem situation and represent
it mathematically. PC.8.D Generalize a solution strategy for a
single problem to a class of related problems and apply a strategy for a
class of related problems to solve specific problems. 
112 *113
(optional) *114
(optional) *115
(optional) *116
(optional) 117
Review Unit
Assessment 

PC.M.2 Multiply matrices by scalars to produce new matrices, e.g., as
when all of the payoffs in a game are doubled. (112) 

PC.M.4 Work with 2 × 2 matrices as transformations of the plane,
and interpret the absolute value of the determinant in terms of area. (in skipped chapter 10) 

Supporting Standards: PC.M.3 Understand that, unlike multiplication of numbers, matrix
multiplication for square matrices is not a commutative operation, but still
satisfies the associative and distributive properties. 

PC.M.5 Understand that the zero and identity matrices play a role in
matrix addition and multiplication similar to the role of 0 and 1 in the real
numbers. The determinant of a square matrix is nonzero if and only if the
matrix has a multiplicative inverse. 

As a result of
this unit, students will be able to: á
Perform
operations with matrices. á
Use matrices
to rotate and dilate figures on the coordinate plane. 
Unit III
(Advanced Topics): Chapter 12  Analytic Geometry of Conic Sections and Quadric
Surfaces 

Suggested Timeframe: 15 Days (approximate unit
completion date: May 11) 

Unit Rationale: Defining and
understanding conic sections, algebraically and geometrically, will allow us
to apply them to realworld problems, including design, orbital paths, marketing,
and threedimensional rotations of conic sections. 
Essential
Questions: How are the equations and graphs of different conic sections related
to each other and how are they applied? 

STANDARDS 
Vocabulary 
Reasoning, Problem Solving, &
Communication 
Planning 

Chapter Sequence 
Explorations 

Focus Standards: PC.C.1 Derive the equations of ellipses and hyperbolas given the foci,
using the fact that the sum or difference of distances from the foci is
constant. (124) 
á
Conic sections á
Ellipse,
hyperbola á
xradius,
yradius á
Major axis,
minor axis á
Asymptotes á
Quadric á
Paraboloid á
Transverse axis á
Conjugate axis á
Focus 
foci á
Directrix á
Eccentricity 
PC.8.A Analyze a problem situation and represent
it mathematically. PC.8.B Select and apply strategies to solve problems. PC.8.E Read and interpret diagrams, graphs, and
text containing the symbols, language, and conventions of mathematics. 
121 122 Quiz *123
(optional) 124 Review Unit
Assessment 
122a,b 124a,
b, c 
PC.C.2 Given a Cartesian or parametric equation of
a conic section, sketch or plot the graph, and given the graph, find an
equation. (121, 122) 

Supporting Standards: 
Set
aside an Exploration day for 124, using the explorations listed above. 

As a result of
this unit, students will be able to: á
Graph a conic
section from an equation. á
Given a graph
of a conic section find the equation. á
Recognize
conic sections from equations. á
Translate
between Cartesian and parametric forms of equations for conic sections. á
Analyze conic
sections to find foci, directrix, and eccentricity. 
Unit III
(Advanced Topics): Chapter 14  Sequences and Series 

Suggested Timeframe: 14 days (approximate unit
completion date: June 1) 

Unit
Rationale: Geometric and arithmetic
sequences and series are logical mathematical models for functions, including
those involving compound interest, general growth and decay, and movement. 
Essential
Questions: How can sequences of numbers and their sums be applied
to reallife problems? 

STANDARDS 
Vocabulary 
Reasoning, Problem Solving, & Communication 
Planning 

Chapter Sequence 
Explorations 

Focus Standards: PC.S.1 Recognize that sequences are
functions, sometimes defined recursively, whose domain is a subset of the
integers. (141) 
á
Sequence,
series á
Common
difference á
Common ratios á
Arithmetic
sequence á
Geometric
sequence á
Partial sum á
Convergent,
divergent á
Binomial series 
PC.8.A Analyze a problem situation and represent
it mathematically. PC.8.B Select and apply strategies to solve problems. PC.8.C Evaluate a solution for reasonableness, verify its accuracy,
and interpret the solution in the context of the original problem. 
141 142 143 144 Review Unit Assessment 
141a 142a 143b,c 
PC.S.2 Write arithmetic and geometric
sequences both recursively and with an explicit formula, use them to model
situations, and translate between the two forms. (142) 

PC.S.3 Construct linear and
exponential functions, including arithmetic and geometric sequences, given a
graph, a description of a relationship, or two inputoutput pairs (include
reading these from a table). (142) 

PC.S. 4 Understand, explain and use
formulas for the sums of finite arithmetic and geometric sequences. (143) 

PC.S.5 Know and apply the Binomial Theorem
for the expansion of (x + y)^{n}
in powers of x and y for a positive integer n, where x and y are any numbers,
with coefficients determined for example by PascalÕs Triangle. (143) 

PC. S. 6 Compute the sums of infinite
geometric series; understand and apply the convergence criteria for geometric
series. (143) 

Supporting Standards: 




As a result of
this unit, students will be able to: á
Expand a
sequence. á
Find a partial
sum of a series. á
Express a
sequence or series recursively and explicitly. á
Find a
specific term or specific partial sum of a sequence or series. á
Find the sum
of an infinite geometric series, and recognize when an infinite sum is
possible. á
Use sigma
notation to express sums. á
Expand a power
of a binomial as a binomial series, using the Binomial Formula. á
Recognize and
understand what it means to be a converging or diverging series. 
PRECALCULUS WITH
TRIGONOMETRY: Concepts and Applications, Paul A. Foerster, 2^{nd}
Edition, 2007
TI Graphing Calculator
– TI nSpire or TI84
Students are expected to
reach mastery level of all concepts explored in this class. Our goal is to work at a speed so that
the students meet that goal. We get
to where we get in preparation for Calculus.
Participants must attend all
course sessions. If a participant
must miss any portion of a session, the instructor should be notified prior to
the absence in order to make appropriate arrangements. All sessions are
archived on WIZIQ and students can rewatch any sessions – use the same
url as the class session.
This course is for letter
grade only: A or Inc. Successful
completion includes mastering (100%) all quizzes & exams. Students will have ample opportunity to
retake every exam t reach mastery level.