Download Pre-Calculus Pre-AP – Scope and Sequence - Year at a...

Pre-Calculus Pre-AP – Scope and Sequence - Year at a Glance
Three Weeks
Topics/
Concepts
Pre-Calculus Pre-AP - First Semester – Merrill – Advanced Mathematical Concepts
1st 3 weeks
2nd 3 weeks
3rd 3 weeks
4th 3 weeks
Polynomials and
Rational Functions
Quadratic Equations
and Inequalities
Remainder and Factor
Theorems
Circle
Exponential and
Logarithmic
Functions
Parabola
Rational Exponents
Ellipse
Number e
Conics
Hyperbola
Rational Root Theorem
Common
Logarithms
Transformations
Locating Zeros of a
Function
Rational Equations and
Partial Fractions
Radical Equations and
Inequalities
Natural Logarithms
Systems of Second
Degree Equations and
Inequalities
Sequences and Series
Arithmetic
Geometric
Infinite
5th 3 weeks
6th 3 weeks
Combinatorics and
Probability
Statistics and Data
Analysis
Permutations
Frequency
Distribution
Repetitions and
Circular
Convergent and
Divergent
Combinations
Sigma Notation and
the nth Term
Probability and
Odds
Binomial Theorem
Mathematical
Induction
Tangents and Normals
to Conic Sections
Measures of Central
Tendency,
Variability
Normal Distribution
Sample Sets of Data
Independent and
Dependent Events
Scatter Plots and
Regression Lines
Mutually Exclusive
or Inclusive Events
Conditional
Probability
Resource:
Merrill
Advanced
Mathematical
Concepts
Foerster (f)
Chapter 4
Chapter 16(f)
Teks - c1C, c1D, c1E,
c3A
Chapter 10
Chapter 12 & 13 (f)
Teks - c1D, c2A, c5A,
c5B, c5C
Chapter 11
Teks - c1A, c1B,
c1D, c1E, c2C, c3A
Chapter 12
Teks - c4A, c4B,
c4C, c4D
Binomial Theorem
and Probability
Chapter 14
Teks –
111.35, c1B, c3A,
c3B, c3C
111.36c
4A, 4B
111.24b
8.11A, 8.11B, 8.11C
Chapter 15
Teks –
111.36c, 2A, 2B,
2C, 2D, 3A, 3B, 3C
Three Weeks
Topics/
Concepts
Pre-Calculus Pre-AP - Second Semester – Merrill – Advanced Mathematical Concepts
1st 3 weeks
2nd 3 weeks
3rd 3 weeks
4th 3 weeks
Trigonometric
Functions
Angles and Their
Measure
Central Angles and
Arcs
Graphs and Inverses of
Trigonometric
Functions
Amplitude, Period and
Phase Shift
Principal Values of
Inverses
Circular Functions
Special Angles
Simple Harmonic
Motion
Trigonometric
Identities and
Equations
Sum and
Difference
Identities
Double Angle and
Half-Angle
Identities
Solving
Trigonometric
Equations
Right Triangles
Vectors and
Parametric Equations
Geometric and
Algebraic Vectors
Perpendicular
Vectors
Applications with
Vectors
Resource:
Merrill
Advanced
Mathematical
Concepts
Foerster (f)
Chapter 5
Teks - c1C, c2B, c3A,
c3C, c3D
Chapter 7
Teks - c2C, c3A,
c3C, c3D
Applied Problems
Connections to
Calculus
Polar Graphs
Polar-Rectangular
Coordinates
Derivatives
Polar Form of
Linear Function
Polar Form of
Complex Numbers
Products and
Quotients of
Complex Numbers
Distance form a
Point to a Line
Chapter 6
Teks - c1A, c1B , c1C,
c1D, c2A, c2B, c2C,
c3A, c3B, c3C
Polar Coordinates
and Complex
Numbers
Motion Modeling
Normal Form of a
Linear Equation
Area of Triangles
6th 3 weeks
Limits
3D Space
Law of Sines
Law of Cosines
5th 3 weeks
Chapter 8
Teks - c5A, c5C,
c5D, c6A, c6B
Powers and Roots
of Complex
Numbers
Chapter 9
Teks - c1A, c1B,
c2A, c3D
Chapter 17
Various Chapters
Foerster and Larson
Books
Polynomials and Rational Functions
Objectives/concepts
TEKS
111.35
Describe symmetry of
c1C
graphs of even and odd
functions.
(1st 3 weeks)
Topics (not in sequential order)
Suggested Resources
Polynomials and Rational Functions
4.1-4.7
Recognize and use
connections among
significant points of a
function (roots, maximum
points, and minimum
points), the graph of a
function, and the symbolic
representation of a
function.
Remainder and Factor Theorems
Investigate continuity, end
behavior, vertical and
horizontal asymptotes, and
limits and connect these
characteristics to the graph
of a function.
Use functions such as
logarithmic, exponential,
trigonometric, polynomial,
etc., to model real life data.
Quadratic Equations and Inequalities
c1D
Rational Root Theorem
Locating Zeros of a Function
Rational Equations and Partial Fractions
Radical Equations and Inequalities
c1E
c3A
Assessments
TAKS
Objectives
1,2,3,4
Conics (2nd 3 weeks)
Objectives/concepts
Recognize and use connections among
significant points of a function (roots,
maximum points, and minimum points),
the graph of a function, and the symbolic
representation of a function.
Apply basic transformations, including
a • f(x), f(x) + d, f(x - c), f(b • x), |f(x)|,
f(|x|), to the parent functions.
TEKS
111.35
c1D
Suggested Resources
Circle
10.1-10.8
Parabola
Ellipse
c2A
Hyperbola
Transformations
Systems of Second Degree Equations and
Inequalities
Use conic sections to model motion, such
as the graph of velocity vs. position of a
pendulum and motions of planets.
c5A
Use properties of conic sections to
describe physical phenomena such as the
reflective properties of light and sound.
c5B
Convert between parametric and
rectangular forms of functions and
equations to graph them.
Topics (not in sequential order)
Tangents and Normals to Conic Sections
c5C
Assessments
TAKS
Objectives
1,2,3,4,5,6,7
Exponential and Logarithmic Functions (3rd 3 weeks)
Objectives/concepts
TEKS Topics (not in sequential order)
111.35
Exponential and Logarithmic Functions
Describe parent functions symbolically c1A
and graphically, including y = xn , y =
Rational Exponents
ln x, y = loga x, y = 1/x, y =ex, y = ax,
y = sin x, etc.
Number e
c1B
Determine the domain and range of
Common Logarithms
functions using graphs, tables, and
symbols.
Natural Logarithms
Recognize and use connections among
significant points of a function (roots,
c1D
maximum points, and minimum
points), the graph of a function, and the
symbolic representation of a function.
Investigate continuity, end behavior,
vertical and horizontal asymptotes, and
limits and connect these characteristics
to the graph of a function.
Investigate identities graphically and
verify them symbolically, including
logarithmic properties, trigonometric
identities, and exponential properties.
Use functions such as logarithmic,
exponential, trigonometric, polynomial,
etc. to model real-life data.
c1E
c2C
c3A
Suggested Resources
11.1-11.7
Assessments
TAKS
Objectives
1,2,3,4,5
Sequences and Series (4th 3 weeks)
Objectives/concepts
Represent patterns using
arithmetic and geometric
sequences and series.
Use arithmetic, geometric,
and other sequences and
series to solve real-life
problems.
Describe limits of
sequences and apply their
properties to investigate
convergent and divergent
series.
Apply sequences and series
to solve problems
including sums and
binomial expansion.
TEKS
111.35
c4A
Topics (not in sequential order)
Suggested Resources
Sequences and Series
12.1-12.8
Arithmetic
Geometric
c4B
Infinite
Convergent and Divergent
Sigma Notation and the nth Term
c4C
Binomial Theorem
Mathematical Induction
c4D
Assessments
TAKS
Objectives
1,2,3,4,5,6,10
Combinatorics and Probability (5th 3 weeks)
Objectives/concepts
TEKS
Compare theoretical and empirical
probability.
111.36c
4A
Use experiments to determine the
reasonableness of a theoretical
model such as binomial, geometric.
4B
Find the probabilities of compound
events (dependent and
independent).
111.24b
8.11A
Use theoretical probabilities and
experimental results to make
predictions and decisions.
8.11B
Select and use different models to
simulate an event.
8.11C
Topics (not in sequential order)
Suggested Resources
Combinatorics and Probability
14.1-14.8
Permutations
Repetitions and Circular
Combinations
Probability and Odds
Independent and Dependent Events
Mutually Exclusive or Inclusive Events
Conditional Probability
Determine the domain and range
of functions using graphs, tables,
and symbols.
Use functions such as logarithmic,
exponential, trigonometric,
polynomial, etc., to model real life
data.
Use regression to determine a
function to model real life data.
Use properties of functions to
analyze and solve problems and
make predictions
Binomial Theorem and Probability
111.35
c1B
c3A
c3B
c3C
Assessments
TAKS
Objectives
1,2,3,4,5,8
Statistics and Data Analysis (6th 3 weeks)
Objectives/concepts
TEKS
111.36c
2A
Interpret information from various
graphs, including line graphs, bar
graphs, circle graphs, histograms,
and scatterplots to draw
conclusions from the data.
Analyze numerical data using
measures of central tendency,
variability, and correlation in order
to make inferences.
Topics (not in sequential order)
Suggested Resources
Statistics and Data Analysis
15.1-15.6
Frequency Distribution
Measures of Central Tendency, Variability
Normal Distribution
2B
Sample Sets of Data
Scatter Plots and Regression Lines
Analyze graphs from journals,
newspapers, and other sources to
determine the validity of stated
arguments.
Use regression methods available
through technology to describe
various models for data such as
linear, quadratic, exponential, etc.,
select the most appropriate model,
and use the model to interpret
information.
Formulate a meaningful question,
determine the data needed to
answer the question, gather the
appropriate data, analyze the data,
and draw reasonable conclusions.
Communicate methods used,
analysis conducted, and
conclusions drawn for a dataanalysis project by written report,
visual display, oral report, or multimedia presentation.
Determine the appropriateness of a
model for making predictions from
a given set of data
2C
2D
3A
3B
3C
Assessments
TAKS
Objectives
1,2,3,4,5,8
Trigonometric Functions (7th 3 weeks)
Objectives/concepts
TEKS Topics (not in sequential order)
111.35
Trigonometric Functions
Describe symmetry of
c1C
graphs of even and odd
Angles and Their Measure
functions.
Perform operations
including composition on
functions, find inverses,
and describe these
procedures and results
verbally, numerically,
symbolically, and
graphically.
Central Angles and Arcs
c2B
Circular Functions
Special Angles
Right Triangles
Law of Sines
Use functions such as
logarithmic, exponential,
trigonometric, polynomial,
etc., to model real life data.
c3A
Use properties of functions
to analyze and solve
problems and make
predictions.
c3C
Solve problems from
physical situations using
trigonometry, including the
use of Law of Sines, Law
of Cosines, and area
formulas.
c3D
Law of Cosines
Area of Triangles
Suggested Resources
5.1-5.8
Assessments
TAKS
Objectives
1,2,3,4
Graphs and Inverses of Trigonometric Functions (8th 3 weeks)
Objectives/concepts
TEKS Topics (not in sequential
111.35 order)
Graphs and Inverses of
c1A
Describe parent functions symbolically and
Trigonometric Functions
graphically, including y = xn , y = ln x, y = loga
x, y = 1/x, y =ex, y = ax, y = sin x, etc.
Amplitude, Period and Phase
Shift
c1B
Determine the domain and range of functions
using graphs, tables, and symbols.
Principal Values of Inverses
c1C
Describe symmetry of graphs of even and odd
Simple Harmonic Motion
functions.
Recognize and use connections among
significant points of a function (roots, maximum
points, and minimum points), the graph of a
function, and the symbolic representation of a
function.
c1D
Apply basic transformations, including a • f(x),
f(x) + d, f(x - c), f(b • x), |f(x)|, f(|x|), to the parent
functions.
c2A
Perform operations including composition on
functions, find inverses, and describe these
procedures and results verbally, numerically,
symbolically, and graphically.
c2B
Investigate identities graphically and verify
them symbolically, including logarithmic
properties, trigonometric identities, and
exponential properties.
c2C
Use functions such as logarithmic, exponential,
trigonometric, polynomial, etc. to model real-life
data.
c3A
Use regression to determine a function to model
real-life data.
c3B
Use properties of functions to analyze and solve
problems and make predictions.
c3C
Suggested Resources
6.1 – 6.7
Assessments
TAKS
Objectives
1,2,3,4,5
Trigonometric Identities and Equations (9th 3 weeks)
Objectives/concepts
TEKS Topics (not in sequential order)
111.35
Trigonometric Identities and Equations
c2C
Investigate identities
graphically and verify them
Sum and Difference Identities
symbolically, including
logarithmic properties,
Double Angle and Half-Angle Identities
trigonometric identities,
and exponential properties.
Solving Trigonometric Equations
Use functions such as
Normal Form of a Linear Equation
c3A
logarithmic, exponential,
trigonometric, polynomial,
Distance form a Point to a Line
etc. to model real-life data.
Use properties of functions
to analyze and solve
problems and make
predictions.
Solve problems from
physical situations using
trigonometry, including the
use of Law of Sines, Law
of Cosines, and area
formulas.
c3C
c3D
Suggested Resources
7.1-7.7
Assessments
TAKS
Objectives
1,2,3,4,5,6
Vectors and Parametric Equations (10th 3 weeks)
Objectives/concepts
TEKS Topics (not in sequential order)
111.35
Vectors and Parametric Equations
c5A
Use conic sections to
model motion, such as the
Geometric and Algebraic Vectors
graph of velocity vs.
position of a pendulum and
3D Space
motions of planets.
Convert between
parametric and rectangular
forms of functions and
equations to graph them.
Perpendicular Vectors
c5C
Applications with Vectors
Motion Modeling
Use parametric functions to
simulate problems
involving motion.
Use the concept of vectors
to model situations defined
by magnitude and
direction.
Analyze and solve vector
problems generated by
real-life situations.
c5D
c6A
c6B
Suggested Resources
8.1-8.7
Assessments
TAKS
Objectives
1,2,3,4,5,6
Polar Coordinates and Complex Numbers (11th 3 weeks)
Objectives/concepts
TEKS Topics (not in sequential order)
111.35
Polar Coordinates and Complex Numbers
c1A
Describe parent functions
symbolically and
Polar Graphs
graphically, including y =
xn , y = ln x, y = loga x, y
Polar-Rectangular Coordinates
= 1/x, y =ex, y = ax, y = sin
x, etc.
Polar Form of Linear Function
Determine the domain
Polar Form of Complex Numbers
c1B
and range of functions
using graphs, tables, and
Products and Quotients of Complex Numbers
symbols.
Apply basic
transformations, including
a • f(x), f(x) + d, f(x - c),
f(b • x), |f(x)|, f(|x|), to the
parent functions.
Solve problems from
physical situations using
trigonometry, including the
use of Law of Sines, Law
of Cosines, and area
formulas.
Powers and Roots of Complex Numbers
c2A
c3D
Suggested Resources
9.1-9.8
Assessments
TAKS
Objectives
2, 5
Connections to Calculus, Applied Problems (12th 3 weeks)
Objectives/concepts
TEKS
Topics (not in sequential order)
Limits of Functions
All 111.35
Applied Problems
Asymptotic Behavior
111.54b
Calculus AB
Connections to Calculus
Continuity
Limits
Concept of a Derivative
Derivatives
Suggested Resources
Chapter 17 Merrill
Various Chapters
Foerster and Larson Books
Assessments
TAKS
Objectives
N/A