Curriculum Map 2012-2013
Pre-Calculus
Pre-Cal Unit Name:
Unit Number: 1
Functions and Their Graphs
Enduring Understanding:
Students will investigate the following parent functions: linear, quadratic, cubic, square root, reciprocal, absolute value, piecewise, greatest integer. These
investigations will include transformations (reflections, horizontal & vertical shifts, stretches & compressions) as well as composite and inverse functions.
Standard
1.01 Transform relations in two dimensions;
describe the results algebraically and
geometrically.
Essential Questions
Can I evaluate the domain, range, intercepts, zeros and
difference quotient of a function?
Pacing Guideline
12 days including
review and test
Key
Academic
Vocabular
Piecewise
function
Can I determine whether a function is increasing or
decreasing?
Greatest
Integer
function
Can I determine whether a function is odd or even?
1.02 Use the quadratic relations (parabola, circle,
ellipse, hyperbola) to model and
Can I determine transformations of a graph from an
equation? Can I write an equation of a function given a
graph?
solve problems; justify results.
Can I evaluate a composite function?
a) Solve using tables, graphs, and algebraic
properties.
Can I determine if a function has an inverse function and if
so find it algebraically and graphically?
b) Interpret the constants and coefficients in the
context of the problem.
Can I use knowledge of functions to solve mathematical
models?
Difference
Quotient
Domain
Range
Can I use direct and inverse variation to model linear and
reciprocal functions?
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Curriculum Map 2012-2013
Pre-Calculus
2.01 Use functions (polynomial, power, rational,
exponential, logarithmic, logistic,
One-to-One
piecewise-defined, and greatest integer) to model
and solve problems; justify
Horizontal
Line Test
results.
a) Solve using graphs and algebraic properties.
Direct and
Inverse
Variation
b) Interpret the constants, coefficients, and bases in
the context of the
problem.
2.04 Use the composition and inverse of functions to
model and solve problems.
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Curriculum Map 2012-2013
Pre-Calculus
Suggested Resources by Unit
Location of these resources
Pre-Cal Unit : Quadratic and Polynomial Functions
Unit Number: 2
Enduring Understanding:
Students will investigate quadratic and rational functions. Students will be able to find all zeros, real and imaginary; determine asymptotes and holes.
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Curriculum Map 2012-2013
Pre-Calculus
Standard
1.01 Transform relations in two dimensions;
describe the results algebraically and
geometrically.
2.01 Use functions (polynomial, power, rational,
exponential, logarithmic, logistic,
piecewise-defined, and greatest integer) to model
and solve problems; justify
Essential Questions
Can I find the zeros of polynomial functions by the following
methods:
Factoring
Using the quadratic equation
Completing the square
Using synthetic division
Pacing Guideline
15 days including
review and test
Remainder
Theorem
Multiplicity
Can I determine were a function is undefined and how that
affects the graph of the function?
Factor
Theorem
Can I determine the end behavior of a polynomial function?
Can I use a quadratic to solve applications problems? Can I
apply knowledge of polynomial and rational functions to
solve application problems?
Descartes
Rule of Signs
results.
a) Solve using graphs and algebraic properties.
Key
Academic
Vocabular
Can I determine the limit of a function by examining the
graph of the function?
Intermediate
Value
Theorem
b) Interpret the constants, coefficients, and bases in
the context of the
problem.
Vertex
2.08 Explore the limit of a function graphically,
numerically, and algebraically.
Axis of
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Curriculum Map 2012-2013
Pre-Calculus
Symmetry
Maximum
Minimum
Suggested Resources by Unit
Location of these resources
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Curriculum Map 2012-2013
Pre-Calculus
Resources:
Http://illuminations.nctm.org/LessonDetail.aspx?id=L606
www.kutasoftware.com
http://illuminations.nctm.org/Lessons/9-12/egglaunch/egglaunchAS-Sheet1.pdf
http://www.ilovemath.org/index.php?option=com_docman&task=c
at_view&gid=50&Itemid=31
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Curriculum Map 2012-2013
Pre-Calculus
Pre-Cal Unit : Exponential/Logarithmic Functions
Unit Number: 3
Enduring Understanding:
Students will investigate exponential and logarithmic functions. Students will be able to use properties of exponents and logarithms to solve and graph equations.
Standard
2.01 Use functions (polynomial, power, rational,
exponential, logarithmic, logistic,
piecewise-defined, and greatest integer) to model
and solve problems; justify
Essential Questions
Understanding the characteristics of exponential and
logarithmic functions can I determine the affects of
transformations on the graph?
Pacing Guideline
20 days including
review and test
Key
Academic
Vocabular
Common
Logarithm
Can I use the properties of exponents and logarithms to
solve equations?
Can I determine the end behavior of a polynomial function?
Natural
Logarithm
a) Solve using graphs and algebraic properties.
Can I use a exponential and/or logarithmic functions to solve
applications problems?
Domain
b) Interpret the constants, coefficients, and bases in
the context of the
Can I determine the limit of a function by examining the
graph of the function?
results.
Range
problem.
Asymptotes
2.03 For sets of data, create and use calculatorgenerated models of linear,
Exponentia
polynomial, exponential, trigonometric, power,
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Curriculum Map 2012-2013
Pre-Calculus
Growth and
Decay
logistic, and logarithmic
functions.
a) Interpret the constants, coefficients, and bases in
the context of the data.
Logistic
Growth
Models
b) Check models for goodness-of-fit; use the most
appropriate model to draw
conclusions or make predictions.
2.08 Explore the limit of a function graphically,
numerically, and algebraically.
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Curriculum Map 2012-2013
Pre-Calculus
Resources:
www.kutasoftware.com
http://www.math.vt.edu/people/hagen/Fall/EDCI4744sp03/sample
unitplan2.pdf
Pre-Cal Unit : Sequences, Series & Binomial Theorem
Unit Number: 4
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Curriculum Map 2012-2013
Pre-Calculus
Enduring Understanding:
Students will investigate arithmetic and geometric sequences and series. Students will be able use the Binomial Theorem to expand binomials..
Standard
2.07 Use recursively-defined functions to model and
solve problems.
a) Find the sum of a finite sequence.
b) Find the sum of an infinite sequence.
c) Determine whether a given series converges or
diverges.
d) Translate between recursive and explicit
representations.
Essential Questions
Can I determine the difference between an arithmetic and
geometric sequence?
Pacing Guideline
10 days including
review and test
Key
Academic
Vocabular
Infinite
Sequence
Can I find the sum of a finite and/or infinite sequence?
Can I determine whether a series is convergent or
divergent?
Finite
Sequence
Using fundamental idea of limits can I find the sum of a
infinite convergent series?
Series
Can I translate between recursive and explicit
representations of arithmetic and/or geometric sequences
Ca n I expand a binomial using the Binomial Theorem and
Pascal’s Triangle?
Recursive
2.08 Explore the limit of a function graphically,
numerically, and algebraically.
Factorial
Summation
Notation
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Curriculum Map 2012-2013
Pre-Calculus
Binomial
Theorem
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Curriculum Map 2012-2013
Pre-Calculus
Pre-Cal Unit : Trigonometric Functions and Equations
Unit Number: 5
Enduring Understanding:
Students will investigate trigonometric functions. Students will be able to verify trigonometric identities and solve trigonometric equations.
Standard
2.02 Use trigonometric and inverse trigonometric
functions to model and solve
problems; justify results.
Essential Questions
Can I use the six trigonometric functions of solve right
triangles? Can I use special right triangles to evaluate the
six trig functions?
Pacing Guideline
15 days including
review and test
Reference
Angle
Can I verify trigonometric identities?
Coterminal
Angles
a) Solve using graphs and algebraic properties.
b) Create and identify transformations with respect
to period, amplitude, and
Can I use trigonometric identities to solve
trigonometric equations?
Quadrantal
Angles
vertical and horizontal shifts.
c) Develop and use the law of sines and the law of
cosines.
Key
Academic
Vocabular
Can I use the Law of Sines and/or Law of Cosines to
Sine
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Curriculum Map 2012-2013
Pre-Calculus
solve a triangle?
2.03 For sets of data, create and use calculatorgenerated models of linear,
polynomial, exponential, trigonometric, power,
logistic, and logarithmic
Cosine
Can I use the Law of Sines and/or Law of Cosines to
solve application problems?
Tangent
functions.
Cosecant
a) Interpret the constants, coefficients, and bases in
the context of the data.
Secant
b) Check models for goodness-of-fit; use the most
appropriate model to draw
Cotangent
conclusions or make predictions.
Radians
Unit Circle
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Curriculum Map 2012-2013
Pre-Calculus
Resources:
http://illuminations.nctm.org/LessonDetail.aspx?id=L383
www.kutasoftware.com
www.regentsprep.org/Regents/math/ALGEBRA/AT2/Ttrig.htm
http://www.ilovemath.org/index.php?option=com_docman&task=c
at_view&gid=26&Itemid=31
http://www.cimt.plymouth.ac.uk/projects/mepres/book9/y9s15act1.
pdf
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Curriculum Map 2012-2013
Pre-Calculus
Pre-Cal Unit : Graphs of Trig Functions & the Inverse
Unit Number: 6
Enduring Understanding:
Students will investigate the graphs of trigonometric functions. Students will be able to find the inverse of trigonometric functions..
Standard
Essential Questions
Can I graph the sine, cosine and tangent functions?
2.02 Use trigonometric and inverse trigonometric
functions to model and solve
problems; justify results.
a) Solve using graphs and algebraic properties.
Pacing Guideline
15 days including
review and test
Key
Academic
Vocabular
Amplitude
Can I identify transformations of the graphs of trigonometric
functions using the amplitude, period, and vertical and
horizontal shifts?
Period
Given a graph can I write the equation of a trigonometric
function?
b) Create and identify transformations with respect
Phase Shift
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Curriculum Map 2012-2013
Pre-Calculus
to period, amplitude, and
Can I find the inverse of a trigonometric function?
Sinusoids
vertical and horizontal shifts.
c) Develop and use the law of sines and the law of
cosines.
Can I use the graphs of trigonometric functions to
model real world problems and make predictions?
2.03 For sets of data, create and use calculatorgenerated models of linear,
polynomial, exponential, trigonometric, power,
logistic, and logarithmic
functions.
a) Interpret the constants, coefficients, and bases in
the context of the data.
b) Check models for goodness-of-fit; use the most
appropriate model to draw
conclusions or make predictions.
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Curriculum Map 2012-2013
Pre-Calculus
Resources:
www.kutasoftware.com
http://www.emathinstruction.com/sitebuildercontent/sitebuilderfiles/
U7L8TheFrequencyAndPeriodOfSinusoidalGraphs.pdf
http://www.emathinstruction.com/sitebuildercontent/sitebuilderfiles/
http://www.emathinstruction.com/sitebuildercontent/sitebuilderfiles/ U7L9SinusoidalModeling.pdf
U7L6BasicGraphsOfSineAndCosine.pdf
http://pchs.pcschools.us/woadhttp://www.emathinstruction.com/sitebuildercontent/sitebuilderfiles/ local/users/dhall/spaghetti_sine_graph.pdf
U7L7VerticalShiftingOfSinusoidalGraphs.pdf
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Curriculum Map 2012-2013
Pre-Calculus
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