PreCalculus – Curriculum Map 12 - 13
(Demana/Waits 7th edition)
Marking
Period
September
Connection to text
Where in the Pearson
Demana/Waits PreCalculus text can
you find the resources.
Ch. P Prerequisites
Skills
What do students have to be
able to do connected to the
CCSS?
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Linear Equations,
Inequalities
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Quadratics
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Distances
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Midpoints
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Circles
CCSS
What are the State Standards students
will be learning?
NQ.RN.1-3 Use properties of Rational and
Irrational Numbers
NQ.CN.1-3 Perform arithmetic operations
with complex numbers
NQ.CN.7-9 Use complex numbers in
polynomial identities and equations
NQ.Q.1 Reason Quantitatively and use
units to solve problems
A.SSE.1-2 Interpret the structure of
expressions
Vocabulary/Key concepts
Reso
What vocabulary will support the
students’ learning?
What materials will su
learning?
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Properties of algebra
Properties of Equality
Properties of
Inequalities
Distance Formula
Midpoint Formula
Quadratic Formula
Equations of a Circle
Completing the Square
Solving Quadratics
Algebraically
Approximating
Solutions Graphically
Text Book – Pre-Calc
Demana, Waits, Fole
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http://interactmath.co
A.SSE.3-4 Write Expressions in
Equivalent forms to solve problems
1st Marking
Period
A.APR.1 Perform arithmetic operations on
polynomials
A.APR.2-3 Understand the relationship
between zeros and factors of polynomials
A.CED.1-4 Create equations to describe
numbers and relationships
A.REI.1-2 Understand solving equations
as a process of reasoning and explain the
reasoning
A.REI.3-4 Solve equations and
inequalities in one variable
A.REI.10-12 Represent and solve
equations and inequalities graphically
This first section of th
Algebra 2. Spend NO
including testing time
chapter. The teacher
picking out the proble
review.
In the first section, for
sections on Algebraic
teacher can review th
section on scientific n
in the rest of the cour
By the time the stude
however, they should
equations, graph linea
functions, and operat
October
Ch. 1 Functions and Graphs
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Modeling and
Equation solving
Functions and their
Properties
Twelve Basic
Functions
Building Functions
from Functions
Parametric Relations
and Inverses
Graphical
Transformations
Modeling with
Functions
A.SSE.1-2 Interpret the structure of
expressions
A.SSE.3-4 Write Expressions in
Equivalent forms to solve problems
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A.APR.2-3 Understand the relationship
between zeros and factors of polynomials
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A.CED.1-4 Create equations to describe
numbers and relationships
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F.IF.1-3 Understand the concept of a
function and use function notation
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Zero Product Property
Vertical Line Test
Odd/Even Functions
Horizontal Line Test
Inverses/Composite
functions
Translations of Graphs
Reflections over Axes
Stretches/Shrinks of
Graphs
Roots/Zeros/Xintercept
Problem Solving
Domain
Inverse Notation
Text Book – Pre-Calc
Demana, Waits, Fole
www.khanacademy.o
http://media.pearsonc
na_precalc_7/cw/inde
www.geogebra.com
Investigating function
calculators
Motion Detector Activ
F.IF.4-6 Interpret functions that arise in
applications in terms of the context
F.IF.7-9 Analyze functions using different
representations
F.BF.1-2 Build a function that models a
relationship between 2 quantities
F.BF.3-5 Build a function from existing
functions
F.LE.1-4 Construct and compare linear,
quadratic, and exponential functions and
solve problems
F.LE.5 Interpret expressions for functions
in terms of the situation they model
Skip section 1 of this
taught as you go alon
students may still hav
functions. These sect
important for what fol
talking about continui
explain it in a more fo
However, for the purp
the informal understa
probably of more valu
In section 3, students
functions before, and
done in MA is built up
They may need to be
graph curves, as well
the students write dow
label them clearly.
Demonstrate how to g
calculator, and have t
to help them identify d
zeros and y-intercept
November
Ch. 2 Modeling, Complex
Numbers
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2nd Marking
Period
Linear and Quadratic
Functions and
Modeling
Power Functions with
Modeling
Polynomial Functions
of Higher Degree with
Modeling
Real Zeros of
Polynomial Functions
Complex Zeros
Graphs of Rational
Functions
Solving Equations in
One Variable
Solving Inequ in One
Variable
NQ.Q.1 Reason Quantitatively and use
units to solve problems
A.SSE.1-2 Interpret the structure of
expressions
A.APR.2-3 Understand the relationship
between zeros and factors of polynomials
A.APR.6 -7 Rewrite rational expressions
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Vertex Form of a
Quadratic
Vertical Free Fall
Motion
Local Extrema and
Zeros of a Polynomial
Leading Term Test for
End Behavior
Intermediate Value
Theorem
Division Algorithm for
Polynomials
Remainder Theorem
Factor Theorem
Fundamental Theorem
of Algebra
Linear Factorization
Complex Conjugate
Zeros Theorem
Graph of Rational
Function
Regression Analysis
Polynomial Long
Division
Synthetic Division
Text Book – Pre-Calc
Demana, Waits, Fole
Scatterplots and regre
Graphing Calculator t
roots and max/min va
In Chapter 2, the stud
study of functions and
beginning with linear
The important parts o
the definition of polyn
on modeling vertical f
no more than a day o
Students do not gene
of what is meant by v
idea to take some tim
ideas to the students.
Spend some time talk
Connected to continu
aspect of what we me
a continuous function
In order to analyze gr
be given a variety of f
hand, identifying all p
max, min, y-intercepts
December
January
Ch. 3 Exponential Functions
Logarithmic Functions
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Exponential and
Logistic Functions
Exponential and
Logistic Modeling
Logarithmic Functions
and their graphs
Properties of
Logarithmic Functions
Equation Solving and
Modeling
Mathematics of
finance
NQ.Q.1 Reason Quantitatively and use
units to solve problems
A.SSE.1-2 Interpret the structure of
expressions
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A.SSE.3-4 Write Expressions in
Equivalent forms to solve problems
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A.APR.2-3 Understand the relationship
between zeros and factors of polynomials
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Exponential
Growth/Decay
Exponential Functions
f(x)=b2
Exponential Functions
and Base e
Population Model
Convert
log/exponential form
Basic Logarithm
Properties
Basic Natural Log
Properties
Change of Base
Formula
Compound Interest
Present/Future Value of
Annuities
Text Book – Pre-Calc
Demana, Waits, Fole
Chapter 3 is another
have seen before, an
little quicker. Students
natural base e, as tha
will have seen the nu
derived, and talk abou
exponential function.
logistic function.
As the students go th
teacher may want to p
logarithms, pointing o
identities, and could b
example, the change
be written as
The last section in the
interest to all students
begin with some of th
introduction to expone
and come back to the
chapter.
3rd Marking
Period
February
Ch. 4 Trigonometric Functions
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Angles and their
Measures
Trigonometric
Functions of Acute
Angles
Circular Functions
Graphs of
Sines/Cosines
Graphs of
Tangent/Cotangent
and Secant/Cosecant
Inverse Trig
Functions
Solving Problems
with Trigonometry
NQ.Q.1 Reason Quantitatively and use
units to solve problems
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A.SSE.1-2 Interpret the structure of
expressions
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A.APR.2-3 Understand the relationship
between zeros and factors of polynomials
F.TF.1-4 Expand the domain of Trig
functions using the unit circle
F.TF.5-7 Model periodic phenomena with
trigonometric functions
G.SRT.6-8 Define Trig Ratios and solve
problems involving right triangles
G.SRT.9 Apply Trig to general triangles
March
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Arc Length
Right Triangle Trig
Ratios
Trigonometric
Functions
Inverse Sine
Inverse Cosine
Inverse Tangent
Special Angles
Sinusoids
Angle Measure
Conversion
Text Book – Pre-Calc
Demana, Waits, Fole
http://www.sonom.gr
html (interactive view
graphed)
Activity finding height
objects using trig met
This chapter should ta
period to finish.
The exploration on p.
try with your students
mean when we talk o
done as an introductio
second day when tea
radians.
Having students cons
talking about the circu
and then moving on t
the lengths of the arc
when doing the 16-po
It should be done larg
should keep a copy o
for easy reference. Be
these particular value
the 2nd part of section
As the students move
the functions, remind
translations that were
marking period. For th
point out that each of
translation of the curv
4th Marking
Period
The last part of the in
(section 7) is not a se
sure that students can
sine of the arctan of a
them do problems fro
exercises.
Show Students the M
http://www.pballew.ne
April
Ch. 5 Analytic Trigonometry
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Fundamental
Identities
Law of Sines
Law of Cosines
NQ.Q.1 Reason Quantitatively and use
units to solve problems
A.SSE.1-2 Interpret the structure of
expressions
May
A.SSE.3-4 Write Expressions in
Equivalent forms to solve problems
June
F.TF.8-9 Prove and apply trigonometric
identities
Ch. 6 Applications of Trig.
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Vectors in the Plane
Parametric Equations
and Motion
Polar Equations
NQ.VM.1-3 Represent and model with
vector quantities
NQ.VM.4-5 Perform operations on vectors
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Reciprocal Identities
Quotient Identities
Pythagorean Identities
Cofunction Identities
Law of Sines
Law of Cosines
Heron’s Formula
Strategies for Proving
Identities
Text Book – Pre-Calc
Demana, Waits, Fole
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Component Form of a
Vector
Magnitude or Length of
a Vector
Vector Addition and
Scalar Multiplication
Polar Equations
Text Book – Pre-Calc
Demana, Waits, Fole
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Students should be re
the basic identities re
and the Pythagorean
hexagon is an excelle
the identities.
Mickey Mouse activity
Vectors are also new
Carefully walk studen
presented in this chap
sections 1 and 2. It w
do the explorations se
for sections 1 and 2 w
The teacher should b
explanation of what a
is. There is an earlier
section 1.5, which ma
what a parametric eq
be done both by hand
Parametric equations
for students, so the te
more than a day or tw
The important section
one on Polar equation
new to students, it sh
Ch. 7 Systems and Matrices
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Ch. 10 Introduction to Calculus
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Solving Systems of
Two Equations
Matrix Algebra
Multivariate Linear
Systems and Row
Operations
Partial Fractions
Systems of
Inequalities in Two
Variables
NQ.VM.6-12 Perform operations on
matrices and use matrices in applications
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A.REI.5-9 Solve systems of equations
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Limits and Motion
numeric Derivatives
and Integrals
While there may be correlations to the
CCSS’s, the preview of Calculus unit is
intended to give a look at what the
College Board
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Matrix Operations
Inverses of n x n
matrices
Properties of Matrices
Solving Systems of
Equations
Algebraically
Partial Fraction
Decomposition
Limits
Average Rate of
Change
Derivative at a Point
Derivative
Limit at Infinity
Definite Integral
Properties of Limits
Difference Quotient
Numerical Derivative
Numerical Integral
Text Book – Pre-Calc
Demana, Waits, Fole
Depending on how fa
students have gotten
teacher, the teacher m
sections to teach and
Calculus (the last cha
Students shouldn’t, h
the class being comp
matrix operations and
using matrices.
Text Book – Pre-Calc
Demana, Waits, Fole
As much time as perm
explore limits, rates o
concept of derivative
Also introduce the ide
why it is useful. This
prepped for calculus a