Download Precalculus

Precalculus Correlated to 2000 Standards
Standard ID
PC.1.1
PC.1.1
PC.1.1
PC.1.1
PC.1.1
PC.1.1
PC.1.1
PC.1.1
Standard Text
Recognize and graph various types
of functions, including polynomial,
rational, algebraic, and absolute
value functions. Use paper and
pencil methods and graphing
calculators.
Recognize and graph various types
of functions, including polynomial,
rational, algebraic, and absolute
value functions. Use paper and
pencil methods and graphing
calculators.
Recognize and graph various types
of functions, including polynomial,
rational, algebraic, and absolute
value functions. Use paper and
pencil methods and graphing
calculators.
Recognize and graph various types
of functions, including polynomial,
rational, algebraic, and absolute
value functions. Use paper and
pencil methods and graphing
calculators.
Recognize and graph various types
of functions, including polynomial,
rational, algebraic, and absolute
value functions. Use paper and
pencil methods and graphing
calculators.
Recognize and graph various types
of functions, including polynomial,
rational, algebraic, and absolute
value functions. Use paper and
pencil methods and graphing
calculators.
Recognize and graph various types
of functions, including polynomial,
rational, algebraic, and absolute
value functions. Use paper and
pencil methods and graphing
calculators.
Recognize and graph various types
of functions, including polynomial,
rational, algebraic, and absolute
value functions. Use paper and
pencil methods and graphing
calculators.
Lesson
Lesson Title
1-1
Functions
1-2
Analyzing Graphs of
Functions and
Relations
1-4
Extrema and Average
Rates of Change
1-5
Parent Functions and
Transformations
2-2
Polynomial Functions
2-3
The Remainder and
Factor Theorems
2-5
Rational Functions
2-6
Nonlinear Inequalities
PC.1.1
PC.1.1
PC.1.10
PC.1.10
PC.1.10
PC.1.10
PC.1.2
PC.1.2
Recognize and graph various types
of functions, including polynomial,
rational, algebraic, and absolute
value functions. Use paper and
pencil methods and graphing
calculators.
Recognize and graph various types
of functions, including polynomial,
rational, algebraic, and absolute
value functions. Use paper and
pencil methods and graphing
calculators.
Write the equations of conic sections
in standard form (completing the
square and using translations as
necessary), in order to find the type
of conic section and to find its
geometric properties (foci,
asymptotes, eccentricity, etc.).
Write the equations of conic sections
in standard form (completing the
square and using translations as
necessary), in order to find the type
of conic section and to find its
geometric properties (foci,
asymptotes, eccentricity, etc.).
Write the equations of conic sections
in standard form (completing the
square and using translations as
necessary), in order to find the type
of conic section and to find its
geometric properties (foci,
asymptotes, eccentricity, etc.).
Write the equations of conic sections
in standard form (completing the
square and using translations as
necessary), in order to find the type
of conic section and to find its
geometric properties (foci,
asymptotes, eccentricity, etc.).
Find domain, range, intercepts,
zeros, asymptotes, and points of
discontinuity of functions. Use paper
and pencil methods and graphing
calculators.
Find domain, range, intercepts,
zeros, asymptotes, and points of
discontinuity of functions. Use paper
and pencil methods and graphing
calculators.
3-1
Exponential Functions
3-2
Logarithmic Functions
7-1
Parabolas
7-2
Ellipses and Circles
7-3
Hyperbolas
7-4
Rotations of Conic
Sections
1-1
Functions
1-2
Analyzing Graphs of
Functions and
Relations
PC.1.2
Find domain, range, intercepts,
zeros, asymptotes, and points of
discontinuity of functions. Use paper
and pencil methods and graphing
calculators.
Find domain, range, intercepts,
zeros, asymptotes, and points of
discontinuity of functions. Use paper
and pencil methods and graphing
calculators.
PC.1.3
Model and solve word problems
using functions and equations.
10-6
Functions as Infinite
Series
PC.1.3
Model and solve word problems
using functions and equations.
1-4
Extrema and Average
Rates of Change
PC.1.3
Model and solve word problems
using functions and equations.
2-4
Zeros of Polynomial
Functions
PC.1.3
Model and solve word problems
using functions and equations.
3-5
Modeling with
Nonlinear Regression
PC.1.3
Model and solve word problems
using functions and equations.
4-5
Graphing Other
Trigonometric
Functions
PC.1.4
Define, find, and check inverse
functions.
1-7
PC.1.2
PC.1.5
Define, find, and check inverse
functions.
Describe the symmetry of the graph
of a function.
PC.1.5
Describe the symmetry of the graph
of a function.
PC.1.4
PC.1.5
Describe the symmetry of the graph
of a function.
Describe the symmetry of the graph
of a function.
PC.1.5
PC.1.5
PC.1.5
1-3
Continuity, End
Behavior, and Limits
1-5
Parent Functions and
Transformations
0-3
Inverse Relations and
Functions
Graphing Technology
Lab: Graphing Inverses
Using Parametric
Equations
Quadratic Functions
and Equations
1-2
Analyzing Graphs of
Functions and
Relations
Extend 1-7
2-1
Parent Functions and
Transformations
Power and Radical
Functions
Describe the symmetry of the graph
of a function.
2-5
Rational Functions
Describe the symmetry of the graph
of a function.
7-1
Parabolas
1-5
PC.1.6
Decide if functions are even or odd.
1-2
Analyzing Graphs of
Functions and
Relations
PC.1.6
Decide if functions are even or odd.
2-1
Power and Radical
Functions
PC.1.6
Decide if functions are even or odd.
2-2
PC.1.7
1-5
PC.1.8
Apply transformations to functions.
Understand curves defined
parametrically and draw their
graphs.
Polynomial Functions
Parent Functions and
Transformations
7-5
Parametric Equations
PC.1.9
Compare relative magnitudes of
functions and their rates of change.
PC.1.9
Compare relative magnitudes of
functions and their rates of change.
Connect to
AP 1
PC.1.9
Compare relative magnitudes of
functions and their rates of change.
Connect to
AP 3
Extrema and Average
Rates of Change
Connect to AP
Calculus: Rate of
Change at a Point
Connect to AP
Calculus:
Approximating Rates of
Change
PC.1.9
Compare relative magnitudes of
functions and their rates of change.
Connect to
AP 4
Connect to AP
Calculus: Related Rates
Connect to
AP 5
Connect to AP
Calculus: Rates of
Change for Sine and
Cosine
PC.1.9
PC.2.1
PC.2.1
PC.2.1
PC.2.1
PC.2.1
PC.2.1
PC.2.2
Compare relative magnitudes of
functions and their rates of change.
Solve word problems involving
applications of logarithmic and
exponential functions.
Solve word problems involving
applications of logarithmic and
exponential functions.
Solve word problems involving
applications of logarithmic and
exponential functions.
Solve word problems involving
applications of logarithmic and
exponential functions.
Solve word problems involving
applications of logarithmic and
exponential functions.
Solve word problems involving
applications of logarithmic and
exponential functions.
Find the domain, range, intercepts,
and asymptotes of logarithmic and
exponential functions.
1-4
3-1
Exponential Functions
3-2
Logarithmic Functions
3-3
Properties of
Logarithms
3-4
Exponential and
Logarithmic Equations
Extend 3-1
Modeling with
Nonlinear Regression
Graphing Technology
Lab: Financial Literacy:
Exponential Functions
3-1
Exponential Functions
3-5
PC.2.2
Find the domain, range, intercepts,
and asymptotes of logarithmic and
exponential functions.
3-2
Logarithmic Functions
PC.2.3
Draw and analyze graphs of
logarithmic and exponential
functions.
3-1
Exponential Functions
PC.2.3
Draw and analyze graphs of
logarithmic and exponential
functions.
3-2
Logarithmic Functions
PC.2.4
Define, find, and check inverse
functions of logarithmic and
exponential functions.
3-2
Logarithmic Functions
PC.3.1
Solve word problems involving right
and oblique triangles.
4-1
Right Triangle
Trigonometry
PC.3.3
Apply the laws of sines and cosines
to solving problems.
Find the area of a triangle given two
sides and the angle between them.
PC.4.1
Define sine and cosine using the unit
circle.
4-3
The Law of Sines and
the Law of Cosines
The Law of Sines and
the Law of Cosines
Trigonometric
Functions on the Unit
Circle
PC.4.10
Know that the tangent of the angle
that a line makes with the x-axis is
equal to the slope of the line.
5-4
Sum and Difference
Identities
PC.4.11
Make connections between right
triangle ratios, trigonometric
functions, and circular functions.
4-3
Trigonometric
Functions on the Unit
Circle
4-2
Degrees and Radians
4-2
Degrees and Radians
4-4
Graphing Sine and
Cosine Functions
PC.3.2
4-7
4-7
PC.4.3
Convert between degree and radian
measures.
Learn exact sine, cosine, and
tangent values for 0, ?2, ?3, ?4, ?6,
and multiples of ?. Use those values
to find other trigonometric values.
PC.4.4
Solve word problems involving
applications of trigonometric
functions.
PC.4.4
Solve word problems involving
applications of trigonometric
functions.
4-5
Graphing Other
Trigonometric
Functions
PC.4.4
Solve word problems involving
applications of trigonometric
functions.
4-6
Inverse Trigonometric
Functions
PC.4.2
PC.4.5
Define and graph trigonometric
functions (i.e., sine, cosine, tangent,
cotangent, secant, cosecant).
PC.4.5
Define and graph trigonometric
functions (i.e., sine, cosine, tangent,
cotangent, secant, cosecant).
PC.4.5
Define and graph trigonometric
functions (i.e., sine, cosine, tangent,
cotangent, secant, cosecant).
PC.4.6
Find domain, range, intercepts,
periods, amplitudes, and asymptotes
of trigonometric functions.
PC.4.6
Find domain, range, intercepts,
periods, amplitudes, and asymptotes
of trigonometric functions.
PC.4.6
Find domain, range, intercepts,
periods, amplitudes, and asymptotes
of trigonometric functions.
PC.4.7
Draw and analyze graphs of
translations of trigonometric
functions, including period,
amplitude, and phase shift.
PC.4.7
Draw and analyze graphs of
translations of trigonometric
functions, including period,
amplitude, and phase shift.
PC.4.7
Draw and analyze graphs of
translations of trigonometric
functions, including period,
amplitude, and phase shift.
PC.4.8
Define and graph inverse
trigonometric functions.
4-6
PC.4.9
Find values of trigonometric and
inverse trigonometric functions.
4-1
PC.4.9
Find values of trigonometric and
inverse trigonometric functions.
4-3
PC.4.9
Find values of trigonometric and
inverse trigonometric functions.
4-4
PC.4.9
Find values of trigonometric and
inverse trigonometric functions.
4-5
4-4
Graphing Sine and
Cosine Functions
4-5
Graphing Other
Trigonometric
Functions
Explore 44
Graphing Technology
Lab: Graphing the Sine
Function Parametrically
4-4
Graphing Sine and
Cosine Functions
4-5
Graphing Other
Trigonometric
Functions
Explore 4-4
Graphing Technology
Lab: Graphing the Sine
Function Parametrically
4-4
Graphing Sine and
Cosine Functions
4-5
Graphing Other
Trigonometric
Functions
Explore 4-4
Graphing Technology
Lab: Graphing the Sine
Function Parametrically
Inverse Trigonometric
Functions
Right Triangle
Trigonometry
Trigonometric
Functions on the Unit
Circle
Graphing Sine and
Cosine Functions
Graphing Other
Trigonometric
Functions
PC.4.9
Find values of trigonometric and
inverse trigonometric functions.
4-6
Inverse Trigonometric
Functions
4-7
The Law of Sines and
the Law of Cosines
5-1
Trigonometric
Identities
5-1
Trigonometric
Identities
PC.5.2
Find values of trigonometric and
inverse trigonometric functions.
Know the basic trigonometric
identity cos2x + sin2x = 1 and prove
that it is equivalent to the
Pythagorean Theorem.
Use basic trigonometric identities to
verify other identities and simplify
expressions.
PC.5.2
Use basic trigonometric identities to
verify other identities and simplify
expressions.
5-2
Verifying Trigonometric
Identities
PC.5.2
Use basic trigonometric identities to
verify other identities and simplify
expressions.
5-4
Sum and Difference
Identities
PC.5.2
Use basic trigonometric identities to
verify other identities and simplify
expressions.
5-5
Multiple-Angle and
Product-to-Sum
Identities
PC.5.2
Use basic trigonometric identities to
verify other identities and simplify
expressions.
PC.5.3
Understand and use the addition
formulas for sines, cosines, and
tangents.
PC.4.9
PC.5.1
Extend 5-4
Graphing Technology
Lab: Reduction
Identities
5-4
Sum and Difference
Identities
PC.5.4
Understand and use the half-angle
and double-angle formulas for sines,
cosines, and tangents.
5-5
Multiple-Angle and
Product-to-Sum
Identities
PC.5.5
Solve trigonometric equations.
5-3
Solving Trigonometric
Equations
PC.5.6
Solve word problems involving
applications of trigonometric
equations.
5-3
Solving Trigonometric
Equations
PC.5.6
PC.5.6
Solve word problems involving
applications of trigonometric
equations.
Solve word problems involving
applications of trigonometric
equations.
5-4
5-5
Sum and Difference
Identities
Multiple-Angle and
Product-to-Sum
Identities
PC.6.1
PC.6.2
PC.6.2
PC.6.2
PC.6.3
Define polar coordinates and relate
polar coordinates to Cartesian
coordinates.
Represent equations given in
rectangular coordinates in terms of
polar coordinates.
Represent equations given in
rectangular coordinates in terms of
polar coordinates.
Represent equations given in
rectangular coordinates in terms of
polar coordinates.
Graph equations in the polar
coordinate plane.
PC.6.4
Graph equations in the polar
coordinate plane.
Define complex numbers, convert
complex numbers to trigonometric
form, and multiply complex numbers
in trigonometric form.
PC.6.5
PC.7.1
PC.6.3
PC.7.3
PC.7.4
9-3
Polar and Rectangular
Forms of Equations
9-4
9-2
Explore 9-2
Polar Forms of Conic
Sections
Graphs of Polar
Equations
Graphing Technology
Lab: Investigate
Graphs of Polar
Equations
9-5
Complex Numbers and
De Moivre's Theorem
Understand and use summation
notation.
10-1
Sequences, Series, and
Sigma Notation
Find sums of infinite geometric
series.
PC.7.3
Polar Coordinates
State, prove, and use De Moivre's
Theorem.
PC.7.2
PC.7.3
9-1
Complex Numbers and
De Moivre's Theorem
PC.7.1
PC.7.2
Polar Coordinates
9-5
Understand and use summation
notation.
Understand and use summation
notation.
PC.7.1
9-1
Find sums of infinite geometric
series.
Prove and use the sum formulas for
arithmetic series and for finite and
infinite geometric series.
Prove and use the sum formulas for
arithmetic series and for finite and
infinite geometric series.
Prove and use the sum formulas for
arithmetic series and for finite and
infinite geometric series.
Use recursion to describe a
sequence.
10-3
Arithmetic Sequences
and Series
Geometric Sequences
and Series
10-1
Sequences, Series, and
Sigma Notation
10-6
Functions as Infinite
Series
10-2
Arithmetic Sequences
and Series
10-3
Geometric Sequences
and Series
10-2
10-6
10-1
Functions as Infinite
Series
Sequences, Series, and
Sigma Notation
PC.7.5
Use recursion to describe a
sequence.
Use recursion to describe a
sequence.
Understand and use the concept of
limit of a sequence or function as
the independent variable approaches
infinity or a number. Decide whether
simple sequences converge or
diverge.
Understand and use the concept of
limit of a sequence or function as
the independent variable approaches
infinity or a number. Decide whether
simple sequences converge or
diverge.
Understand and use the concept of
limit of a sequence or function as
the independent variable approaches
infinity or a number. Decide whether
simple sequences converge or
diverge.
Understand and use the concept of
limit of a sequence or function as
the independent variable approaches
infinity or a number. Decide whether
simple sequences converge or
diverge.
Understand and use the concept of
limit of a sequence or function as
the independent variable approaches
infinity or a number. Decide whether
simple sequences converge or
diverge.
PC.7.6
Solve word problems involving
applications of sequences and series.
10-1
Sequences, Series, and
Sigma Notation
PC.7.6
Solve word problems involving
applications of sequences and series.
10-2
Arithmetic Sequences
and Series
PC.7.6
Solve word problems involving
applications of sequences and series.
10-3
Geometric Sequences
and Series
10-6
Functions as Infinite
Series
11-7
Correlation and Linear
Regression
PC.7.4
PC.7.4
PC.7.5
PC.7.5
PC.7.5
PC.7.5
PC.7.6
PC.8.1
Solve word problems involving
applications of sequences and series.
Find linear models using the median
fit and least squares regression
methods. Decide which model gives
a better fit.
10-3
Arithmetic Sequences
and Series
Geometric Sequences
and Series
10-1
Sequences, Series, and
Sigma Notation
10-3
Geometric Sequences
and Series
10-6
Functions as Infinite
Series
1-3
Continuity, End
Behavior, and Limits
10-2
Extend 103
Graphing Technology
Lab: Continued
Fractions
PC.8.2
PC.8.2
PC.8.3
PC.8.3
Calculate and interpret the
correlation coefficient. Use the
correlation coefficient and residuals
to evaluate a "best-fit" line.
Calculate and interpret the
correlation coefficient. Use the
correlation coefficient and residuals
to evaluate a "best-fit" line.
Find a quadratic, exponential,
logarithmic, power, or sinusoidal
function to model a data set and
explain the parameters of the
model.
Find a quadratic, exponential,
logarithmic, power, or sinusoidal
function to model a data set and
explain the parameters of the
model.
11-7
Extend 117
Correlation and Linear
Regression
Graphing Technology
Lab: Median-Fit Lines
3-5
Modeling with
Nonlinear Regression
4-4
Graphing Sine and
Cosine Functions