
Teach=
er: CORE
HONORS PRE CALCULUS 
Updat=
ed 2014 
=
; 
=
; 
<=
/td>
 =
; 
=
; 

Cours=
e: HONORS
PRE CALCULUS 
Month=
:
All Months 













S 
Revie=
w of
Algebra 






e 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 
p 
Can I
use a variety of algebraic techniques to solve various types of algebraic
equations and inequalities using appropriate notation? 
Facto=
rable
polynomial equations. 
Ident=
ify and
use appropriate factoring techniques to solve polynomial equations. 
Homew=
ork 

Students
will know and be able to solve equations and inequalities using a variety=
of
techniques and write solutions using correct notation. 
M.11=
12.N.02Number
Sense and Operations ~ Simplify numerical expressions with powers and roo=
ts,
including fractional and negative exponents. 
t 
=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
M.11=
12.P.07Patterns,
Relations and Algebra ~ Find solutions to quadratic equations (with real
coefficients and real or complex roots) and apply to the solutions of
problems. 
e 
Inequ=
alities
(Conjuction vs. Disjunction) 
Solve
polynomial inqualites. 
=
; 
M.11=
12.P.08Patterns,
Relations and Algebra ~ Solve a variety of equations and inequalities usi=
ng
algebraic, graphical, and numerical methods, including the quadratic form=
ula;
use technology where appropriate. Include polynomial, exponential, logari=
thmic,
and trigonometric functions; expressions involving absolute values;
trigonometric relations; and simple rational expressions. 
m 
=
; 
=
; 
=
; 
=
; 
b 
Inter=
val
Notation 
Inter=
pret and
use correct notation  set notation and interval notation. 
=
; 
=
; 
e 
=
; 
=
; 
=
; 
=
; 
r 
Ratio=
nal
Exponents 
Demon=
strate an
understanding of rational exponents and properties of exponents. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Funct=
ions 







Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 

Can I
interpret various types of functions in regards to notation, graphs, and
various operations on these functions? 
Relat=
ions,
functions, and onetoonefunctions. 
Use f=
unction
notation in identifying and evaluating functions. 
Homew=
ork 

Students
will know and be able to use function notation and terminology in the
graphical, numerical, and algebraic interpretation of various function ba=
sed
problems. 
M.11=
12.P.05Patterns,
Relations and Algebra ~ Perform operations on functions, including
composition. Find inverses of functions. 

=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
M.11=
12.P.06Patterns,
Relations and Algebra ~ Given algebraic, numeric and/or graphical
representations, recognize functions as polynomial, rational, logarithmic,
exponential, or trigonometric. 

Domai=
n and
Range 
Demon=
strate an
understanding of the concepts of domain and range by interpretting functi=
ons
graphically, numerically, and algebraically. 
=
; 
M.11=
12.P.11Patterns,
Relations and Algebra ~ Solve everyday problems that can be modeled using
polynomial, rational, exponential, logarithmic, trigonometric, and step
functions, absolute values, and square roots. Apply appropriate graphical,
tabular, or symbolic methods to the solution. Include growth and decay; j=
oint
(e.g., I =3D Prt, y =3D k(w1 + w2)) and combined (F =3D G(m1m2)/d2) varia=
tion, and
periodic processes. 

=
; 
=
; 
=
; 
M.11=
12.P.13Patterns,
Relations and Algebra ~ Describe the translations and scale changes of a
given function Ć’(x) resulting from substitutions for the various paramet=
ers
a, b, c, and d in y =3D aĆ’(b(x + c/b)) + d. In particular, describe the =
effect
of such changes on polynomial, rational, exponential, logarithmic, and
trigonometric functions. 

Evalu=
ating
functions. 
Demon=
strate an
understanding of ten essential functions by analyzing their graphs, making
tables of values, plotting intercepts, and interpretting graph behavior u=
sing
appropriate vocabulary and notation. (constant, linear, quadratic, absolu=
te
value, round down or greatest integer, piecewise, square root, reciproca=
l,
and reciprocal squared functions) 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Compo=
sition and
Arithmetic of Functions 
Ident=
ify odd,
even, and neither functions. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Graph=
ing
Functions 
Write=
the
inverse of a function and interpret its characteristics vs. the parent
function (domain, range, intercepts, behavior) 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

=
; 
Refle=
cting and
translating graphs and identifying the change in the function rule that
indicates such a reflection or translation. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

=
; 
Inter=
preting
word problems and use function notation in the solution of these problems=
. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
O 
Polyn=
omial
functions 






c 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 
t 
Am I =
able to
use various algebraic principles to solve and interpret higher order
equations? 
Synth=
etic
Division 
Solve=
higher
order polynomial equations using synthetic division, remainder and factor
theorems, conjugate root theorem, and rational root theorem. 
Homew=
ork 

Students
will know and be able to solve and interpret higher order equations using
appropratiate algebraic, numeric, and graphical approaches. 
M.11=
12.P.05Patterns,
Relations and Algebra ~ Perform operations on functions, including
composition. Find inverses of functions. 
o 
=
; 
=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
M.11=
12.P.07Patterns,
Relations and Algebra ~ Find solutions to quadratic equations (with real
coefficients and real or complex roots) and apply to the solutions of
problems. 
b 
Can I=
use
technology to enhance my understanding of polynomial functions and their
characteristics? 
Remai=
nder and
Factor Theorems 
Solve,
identify, and interpret points of intersections graphically, algerbaicall=
y,
and with the aid of a graphing calculator. 
=
; 
M.11=
12.P.08Patterns,
Relations and Algebra ~ Solve a variety of equations and inequalities usi=
ng
algebraic, graphical, and numerical methods, including the quadratic form=
ula;
use technology where appropriate. Include polynomial, exponential, logari=
thmic,
and trigonometric functions; expressions involving absolute values;
trigonometric relations; and simple rational expressions. 
e 
=
; 
=
; 
=
; 
=
; 
M.11=
12.P.11Patterns,
Relations and Algebra ~ Solve everyday problems that can be modeled using
polynomial, rational, exponential, logarithmic, trigonometric, and step
functions, absolute values, and square roots. Apply appropriate graphical,
tabular, or symbolic methods to the solution. Include growth and decay; j=
oint
(e.g., I =3D Prt, y =3D k(w1 + w2)) and combined (F =3D G(m1m2)/d2) varia=
tion, and
periodic processes. 
r 
=
; 
Ratio=
nal Root
Theorem 
Inter=
pret
polynomial functions and inequalities through the use of a sign chart to
determine graph behavior. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Conju=
gate Root
Theorem 
Solve=
applied
problems including maximum profit, minimum requirements, and optimal size
probems. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Point=
s of
Intersection 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Calcu=
lator use
and approximation of roots. 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Polyn=
omial
Inequalites and Sign Charts 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Appli=
ed
problems 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Calcu=
lator Use
 zeroes, max and min, intersections 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

Expon=
ential and
Logarithmic Functions 







Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 

Do I
understand the inverse relationship between exponential and logarithmic
functions and be able to use the properties of each to solve various type=
s of
problems. 
Expon=
ential and
Logarthmic Graphs 
Graph
exponential and logarithmic functions. 
Homew=
ork 

Students
will know and be able to identify exponential and logarithmic functions as
inverses and use this property to solve various types of problems. 
M.11=
12.P.04Patterns,
Relations and Algebra ~ Demonstrate an understanding of the trigonometric,
exponential, and logarithmic functions. 

=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
M.11=
12.P.05Patterns,
Relations and Algebra ~ Perform operations on functions, including
composition. Find inverses of functions. 

Domai=
n and
Range 
Ident=
ify and
interpret domain and range for exponential and logarithmic functions. 
=
; 
M.11=
12.P.06Patterns,
Relations and Algebra ~ Given algebraic, numeric and/or graphical
representations, recognize functions as polynomial, rational, logarithmic,
exponential, or trigonometric. 

=
; 
=
; 
=
; 
M.11=
12.P.08Patterns,
Relations and Algebra ~ Solve a variety of equations and inequalities usi=
ng
algebraic, graphical, and numerical methods, including the quadratic form=
ula;
use technology where appropriate. Include polynomial, exponential, logari=
thmic,
and trigonometric functions; expressions involving absolute values;
trigonometric relations; and simple rational expressions. 

Expon=
ential and
Logarthmic Equations 
Solve
exponential and logarithmic equations using properties of logarithms and
exponents. 
=
; 
M.11=
12.P.10Patterns,
Relations and Algebra ~ Use symbolic, numeric, and graphical methods to s=
olve
systems of equations and/or inequalities involving algebraic, exponential,
and logarithmic expressions. Also use technology where appropriate. Descr=
ibe
the relationships among the methods. 

=
; 
=
; 
=
; 
M.11=
12.P.11Patterns,
Relations and Algebra ~ Solve everyday problems that can be modeled using
polynomial, rational, exponential, logarithmic, trigonometric, and step
functions, absolute values, and square roots. Apply appropriate graphical,
tabular, or symbolic methods to the solution. Include growth and decay; j=
oint
(e.g., I =3D Prt, y =3D k(w1 + w2)) and combined (F =3D G(m1m2)/d2) varia=
tion, and
periodic processes. 

Simpl=
ifying and
Evaluating Logarithms 
Defin=
e and use
irrational number e and natural log in problem solving. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

e and=
ln 
Solve=
applied
problems including exponential growth and decay, half life and doubling t=
ime,
banking, and appreciation or depreciation problems. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Appli=
ed
problems 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
N 
Trigo=
nometry I 






o 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 
v 
Can I
evaluate trigonmetric functions in all four quadrants and understand the
relationship between a triangle and the unit circle? 
Angle=
s 
initial side, terminal side, vertex, positive/negative measures, standard
position 
Ident=
ify and
use appropriate technology in relations to angles and the unit circle.
 Homew=
ork 

Stude=
nts will
know and be able to evaluate the six trigonometric functions in all four
quadrants by creating appropriate reference angles and using SOH CAH TOA =
in
both degrees and radian measure. 
M.11=
12.G.01Geometry
~ Define the sine, cosine, and tangent of an acute angle. Apply to the
solution of problems. 
e 
=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
=
; 
M.11=
12.M.01Measurement
~ Describe the relationship between degree and radian measures, and use
radian measure in the solution of problems, in particular, problems invol=
ving
angular velocity and acceleration. 
m 
Coter=
minal
angles 
List =
coterminal
angles. 
=
; 
Stude=
nts will
know and be able to apply their understanding of trigonometry to solve re=
al
world problems using right triangle trigonometry and angles of
elevation/depression. 
M.11=
12.P.04Patterns,
Relations and Algebra ~ Demonstrate an understanding of the trigonometric,
exponential, and logarithmic functions. 
b 
=
; 
=
; 
=
; 
=
; 
M.11=
12.P.06Patterns,
Relations and Algebra ~ Given algebraic, numeric and/or graphical
representations, recognize functions as polynomial, rational, logarithmic,
exponential, or trigonometric. 
e 
Degre=
es 
Conve=
rt between
radian and degree measure. 
=
; 
=
; 
=
; 
r 
=
; 
=
; 
=
; 
=
; 
=
; 

Radia=
ns 
define and convert. 
Find =
the length
of an arc using appropriate formulas and equations. 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

Arc L=
ength 
Evalu=
ate the
six trigonometry functions all four quadrants when the reference angle is=
30,
45, or 60. 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

Six
Trigonometry Functions 
Evalu=
ate and
draw the reference angle for each quadrant. 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

Speci=
al Right
Triangles  Important Angles 
Evalu=
ate
quadrantal angles. 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

Refer=
ence
Angles 
Solve=
real
world problems relating to angles of elevation and depression. 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

Simple
Trigonometric Equations 
=
; 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

Right=
Triangle
Trigonometry  SOHCAHTOA 
=
; 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

Trigo=
nometry
Applications 
=
; 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 

Quadr=
antal
Angles 
=
; 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 
D 
Trigo=
nometry II
 Trig Graphing 






e 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 
c 
Can I
create the graph of sin x and cos x and understand the relationship betwe=
en
the function rule and properties of the graph? 
Ampli=
tude 
Defin=
e and
calculate the amplitude, period, and frequency for a sine or cosine funct=
ion. 
Homew=
ork 

Students
will know and be able to use their understanding of sine and cosine funct=
ions
to create accurate graphs of these functions including the use of appropr=
iate
terminolgy and calculation of important points. 
M.11=
12.G.01Geometry
~ Define the sine, cosine, and tangent of an acute angle. Apply to the
solution of problems. 
e 
=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
M.11=
12.M.01Measurement
~ Describe the relationship between degree and radian measures, and use
radian measure in the solution of problems, in particular, problems invol=
ving
angular velocity and acceleration. 
m 
Perio=
d 
Creat=
e complete
and accurate graphs of sine and cosine functions. 
=
; 
M.11=
12.P.04Patterns,
Relations and Algebra ~ Demonstrate an understanding of the trigonometric,
exponential, and logarithmic functions. 
b 
=
; 
=
; 
=
; 
M.11=
12.P.06Patterns,
Relations and Algebra ~ Given algebraic, numeric and/or graphical
representations, recognize functions as polynomial, rational, logarithmic,
exponential, or trigonometric. 
e 
Frequ=
ency 
Demon=
strate an
understanding of vertical shifts and the changes in the function rule that
indicate such changes. 
=
; 
M.11=
12.P.13Patterns,
Relations and Algebra ~ Describe the translations and scale changes of a
given function Ć’(x) resulting from substitutions for the various paramet=
ers
a, b, c, and d in y =3D aĆ’(b(x + c/b)) + d. In particular, describe the =
effect
of such changes on polynomial, rational, exponential, logarithmic, and
trigonometric functions. 
r 
=
; 
=
; 
=
; 
=
; 

Verti=
cal Shift 
Demon=
strate an
understanding of phase shifts and the changes in the function rule that
indicate such changes. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Phase=
/Horizontal
Shift 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Sine =
function 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Cosin=
e Function 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Trigo=
nometry
III  Identities 







Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 

Can I
use trigonometric identities and formulas to simply expressions and verify
trigonometric statements? 
Ratio
Identities 
Simpl=
ify
trigonometric expressions using ratio and reciprocal identities. 
Homew=
ork 

Students
will know and be able to use a variety of identities and formulas for the
simplificaiton and verification of trigonometric expressions. 
M.11=
12.G.01Geometry
~ Define the sine, cosine, and tangent of an acute angle. Apply to the
solution of problems. 

=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
M.11=
12.G.02Geometry
~ Derive and apply basic trigonometric identities (e.g., sin2q + cos2q =
=3D 1,
tan2q + 1 =3D sec2q) and the laws of sines and cosines. 

Recip=
rocal
Identities 
Apply=
the
pythagorean identities and factoring skills to simplify trigonometry
expressions. 
=
; 
M.11=
12.P.04Patterns,
Relations and Algebra ~ Demonstrate an understanding of the trigonometric,
exponential, and logarithmic functions. 

=
; 
=
; 
=
; 
=
; 

Pytha=
gorean
Identities 
Verif=
y a
trigonometric expression by factoring, multiplying by the conjugate, crea=
ting
fractions and applying trigonmetric identities. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Sum/D=
ifference
Identities 
Evalu=
ate unique
angles (15 degrees, 75 degrees, etc.) through the use of sum and differen=
ce
identities. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Doubl=
e Angle
Identities 
Creat=
e the
double angle formulas by using prior knowlege and use them to simplify
expressions and verify trigonometric statements. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

=
; 
Apply=
all
trigonometric identities and formulas to the simplification and verificat=
ion
of complex trig statements. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
J 
Midte=
rm 






a 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 
n 
=
; 
=
; 
=
; 
=
; 
<=
/td>
 =
; 
=
; 
u 
Trigo=
nometry IV
 Equations 






a 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 
r 
Can I=
solve a
trigonometric equation and interpret its solution for all four quadrants?=

Domai=
n 
Solve
trigonometric equations under certain domain restrictions. 
Homew=
ork 

Stude=
nts will
know and be able to solve trigonometric equations using a variety of skil=
ls,
identities, and techniques and apply their solution to all four quadrants=
. 
M.11=
12.G.01Geometry
~ Define the sine, cosine, and tangent of an acute angle. Apply to the
solution of problems. 
y 
=
; 
=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
=
; 
M.11=
12.G.02Geometry
~ Derive and apply basic trigonometric identities (e.g., sin2q + cos2q =
=3D 1,
tan2q + 1 =3D sec2q) and the laws of sines and cosines. 

Can I=
use my
knowledge of trigometry to solve nonright triangles and calculate the ar=
ea
of triangles using appropriate formulas? 
Range=

Solve
trigonometric equations using a variety of techniques including the use of
identites, factoring, multipliying by the conjuage, squaring both sides, =
and
evaluating the relevance of solutions in the unit circle. 
=
; 
Stude=
nts will
know and be able to solve nonright triangles using law of sines and cosi=
nes
and find the area of these triangles using a variety of approaches. 
M.11=
12.M.01Measurement
~ Describe the relationship between degree and radian measures, and use
radian measure in the solution of problems, in particular, problems invol=
ving
angular velocity and acceleration. 

=
; 
=
; 
=
; 
=
; 
=
; 
M.11=
12.P.04Patterns,
Relations and Algebra ~ Demonstrate an understanding of the trigonometric,
exponential, and logarithmic functions. 

=
; 
Trigo=
nometric
Identities 
Solve=
triangles
using the law of sines and cosines. 
=
; 
=
; 
M.11=
12.P.08Patterns,
Relations and Algebra ~ Solve a variety of equations and inequalities usi=
ng
algebraic, graphical, and numerical methods, including the quadratic form=
ula;
use technology where appropriate. Include polynomial, exponential, logari=
thmic,
and trigonometric functions; expressions involving absolute values;
trigonometric relations; and simple rational expressions. 

=
; 
=
; 
=
; 
=
; 
=
; 
M.11=
12.P.11Patterns,
Relations and Algebra ~ Solve everyday problems that can be modeled using
polynomial, rational, exponential, logarithmic, trigonometric, and step
functions, absolute values, and square roots. Apply appropriate graphical,
tabular, or symbolic methods to the solution. Include growth and decay; j=
oint
(e.g., I =3D Prt, y =3D k(w1 + w2)) and combined (F =3D G(m1m2)/d2) varia=
tion, and
periodic processes. 

=
; 
Trigo=
nometric
Equations 
Calcu=
late the
area of triangles using trigonometry and Heron's Formula. 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Law o=
f Sines 
=
; 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Law o=
f Cosines 
=
; 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Area =
of
triangles 
=
; 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Heron=
's Formula 
=
; 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 
=
; 

=
; 
Radia=
n and
Degree Measure 
=
; 
=
; 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
=
; 
=
; 
F 
Conic=
Sections 






e 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 
b 
Can I
recognize, interpret, graph, and find key points of circles, hyperbolas,
ellipses, and parabolas? 
Dista=
nce
Formula 
Calcu=
late the
length of segments on the coordinate plane. 
Homew=
ork 

Students
will know and be able to recognize equations, analyze and graph conic
sections and apply this knowlege to solve systems of second degree equati=
ons
and inequalities. 
M.11=
12.G.04Geometry
~ Relate geometric and algebraic representations of lines, simple curves,=
and
conic sections. 
r 
=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
M.11=
12.P.08Patterns,
Relations and Algebra ~ Solve a variety of equations and inequalities usi=
ng
algebraic, graphical, and numerical methods, including the quadratic form=
ula;
use technology where appropriate. Include polynomial, exponential, logari=
thmic,
and trigonometric functions; expressions involving absolute values;
trigonometric relations; and simple rational expressions. 
u 
Midpo=
int
Formula 
Find =
the
midpoint between two points on the coordinate plane. 
=
; 
M.11=
12.P.13Patterns,
Relations and Algebra ~ Describe the translations and scale changes of a
given function Ć’(x) resulting from substitutions for the various paramet=
ers
a, b, c, and d in y =3D aĆ’(b(x + c/b)) + d. In particular, describe the =
effect
of such changes on polynomial, rational, exponential, logarithmic, and
trigonometric functions. 
a 
=
; 
=
; 
=
; 
=
; 
r 
Circl=
es 
Creat=
e the
equation of a circle in standard form and graph by finding the center,
radius, all intercepts. 
=
; 
=
; 
y 
=
; 
=
; 
=
; 
=
; 

Parab=
olas 
Creat=
e the
equation of a parabola in vertex and standard form and graph by finding t=
he
vertex, axis of symmetry, general behavior (up or down), and all intercep=
ts. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Ellip=
ses 
Creat=
e the
equation of an ellipse with a horizontal and vertical major axis in stand=
ard
from. Graph an ellipse by finding the center, vertices, endpoints of minor
axes, focal points, and all intercepts. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Hyper=
bolas 
Creat=
e the
equation of a hyperbola in standard form with horizontal and vertical
transverse axes. Graph a hyperbola by finding the center, vertices, focal
points, equations of asymptotes, and all intercepts. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Syste=
ms of
second degree equations in two variables 
Solve=
systems
of second degree equations algebraically and graphically and evaluate the
reasonableness of solutions through the use of prior knowlege and graphing
calculators. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Inequ=
alities of
second degree equations in two variables. 
Solve=
systems
of second degree inequalites graphically and interpret solutions. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
A 
Seque=
nces and
Series 






p 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 
r 
Can I
use appropriate notation, terminology, and formulas to evaluate a variety=
of
sequences and series problems? 
Arith=
metic and
Geometric Sequences 
Write=
the
formula for and find specific terms of a finite arithmetic and geometric
sequence. 
Homew=
ork 

Students
will know and be able to recongnize sequences and series as arithmetic,
geometric, or neither and use their understanding of these sequences/seri=
es
to find spefic terms or sums. 
M.11=
12.P.01Patterns,
Relations and Algebra ~ Describe, complete, extend, analyze, generalize, =
and
create a wide variety of patterns, including iterative and recursive patt=
erns
such as Pascal's Triangle. 
i 
=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
M.11=
12.P.02Patterns,
Relations and Algebra ~ Identify arithmetic and geometric sequences and
finite arithmetic and geometric series. Use the properties of such sequen=
ces
and series to solve problems, including finding the general term and sum
recursively and explicitly. 
l 
Finite
Arithmetic and Geometric Series 
Write=
the
formula and calculate the sum of finite arithmetic or geometric series.
 =
; 
M.11=
12.P.11Patterns,
Relations and Algebra ~ Solve everyday problems that can be modeled using
polynomial, rational, exponential, logarithmic, trigonometric, and step
functions, absolute values, and square roots. Apply appropriate graphical,
tabular, or symbolic methods to the solution. Include growth and decay; j=
oint
(e.g., I =3D Prt, y =3D k(w1 + w2)) and combined (F =3D G(m1m2)/d2) varia=
tion, and
periodic processes. 

=
; 
=
; 
=
; 
=
; 

Infin=
ite
Geometric Series 
Write=
the
formula and calculate the sum of an infinte geometry series. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Appli=
ed
problems 
Apply
understanding of sequence and series to the solution of various applied
problems. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

=
; 
Use a=
ppropriate
notation and terminology of various types of sequence and serires. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
M 
Limit=
s 






a 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 
y 
Can I
define and evaluate limits using a variety of techniques and interpret th=
ese
solutions to create accurate sketches of a variety of functions? 
Defin=
ition of a
Limit 
Defin=
e and
interpret limits graphically and numerically. 
Homew=
ork 

Students
will know and be able to evaluate limits at a point and infinity using a
variety of approaches and interpret results to gain a better understandin=
g of
the behavior of a graph. 
M.11=
12.G.04Geometry
~ Relate geometric and algebraic representations of lines, simple curves,=
and
conic sections. 

=
; 
=
; 
Quiz<=
span
style=3D'msospacerun:yes'> 
M.11=
12.P.06Patterns,
Relations and Algebra ~ Given algebraic, numeric and/or graphical
representations, recognize functions as polynomial, rational, logarithmic,
exponential, or trigonometric. 

Left =
and right
handed limits 
Demon=
strate and
understanding of left handed and right handed limits by evaluating limits
from the left and right algebraically, numerically, and graphically. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Limit=
s at a
point. 
Evalu=
ating
limits using a variety of techniques including: numerically, graphically,
direct substitutiong, factoring, and rationalizing. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Limit=
s at
infinity. 
Evalu=
ate limits
at set point and interpret result as an point of continuity, vertical
asymptote, or excluded point. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Ratio=
nal
Functions 
Evalu=
ate limits
at infinity and intepret results as end behavior of a graph including
horizontal asymptotes. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Verti=
cal
asymptotes, excluded points, horizontal asymptotes, and cross points. 
Deter=
mine
points of continuity/discontinuity by using limits. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 

Conti=
nuity 
Creat=
e accurate
sketches of rational functions by finding domain, excluded points, vertic=
al
asymptotes, horizontal asymptotes, cross points, and all intercepts. Then
interpreting these results to create an accurate graph. 
=
; 
=
; 

=
; 
=
; 
=
; 
=
; 
J 
Revie=
w 






u 
Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 
n 
=
; 
=
; 
=
; 
=
; 
<=
/td>
 =
; 
=
; 
e 
Final=
Exam 







Essen=
tial
Questions 
Conte=
nt 
Skill=
s 
Asses=
sments 
Lessons=

Learn=
ing
Benchmarks 
Stand=
ards 

=
; 
=
; 
=
; 
=
; 
<=
/td>
 =
; 
=
; 







