TAG PreAP/IB Pre-Calculus (second semester)
Curriculum-Map
Focus: -
Broad-based
Concept: Generalizations:
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Unit One Sequences
and Series |
Unit Two Parent functions and their Characteristics
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Unit Three Algebra of
Functions |
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Concepts: Definition of Sequences
and Series
The formulas of Sequences and Series Applications Convergence and Divergence Binomial Expansion |
Concepts: Parent
Functions: Parabolic, absolute value,
cubic, reciprocal, square root, cube root, greatest integer Piecewise
defined functions Graphs and Transformations of these functions |
Concepts: Addition,
Subtraction, Multiplication, Division of functions Inverse of a
function Composition
of a function Limit Rational
Functions Intermediate
Value Theorem |
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Enduring
Understandings: The student
uses sequences and series to represent, analyze, and solve real-life
problems. 04 . |
Enduring
Understandings: The student
defines functions, describes characteristics of functions, and translates
among verbal, numerical, graphical, and symbolic representations of
functions, including polynomial, rational, radical, exponential, logarithmic,
trigonometric, and piecewise-defined functions. 01 . The student
interprets the meaning of the symbolic representations of functions and
operations on functions within a context. 02 |
Enduring
Understandings: The student
defines functions, describes characteristics of functions, and translates
among verbal, numerical, graphical, and symbolic representations of
functions, including polynomial, rational, radical, exponential, logarithmic,
trigonometric, and piecewise-defined functions. 01 . The student
interprets the meaning of the symbolic representations of functions and
operations on functions within a context. 02 |
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Guiding
Questions: ·
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Guiding
Questions: ·
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Guiding
Questions: ·
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Essential
TEKS Questions: 1.
Can you represent patterns using arithmetic and geometric sequences
and series? 04A 2.
Can you use arithmetic, geometric, and other sequences and series to
solve real-life problems? 04B 3.
Can you describe limits of sequences and apply their properties to
investigate convergent and divergent series?
O4C 4.
Can you apply sequences and series to solve problems including sums
and binomial expansion? 04D |
Essential
TEKS Questions: 1. Can you describe parent functions
symbolically and graphically, including
01A 2. Can you
determine the domain and range of functions using graphs, tables, and
symbols? 01B 3. Can you describe symmetry of graphs of even
and odd functions? 01C 4.
Can you recognize and use connections among significant points of a functions (roots, maximum points, and minimum
points), the graph of a function, and the symbolic representation of a
function? 01D 5.
Can you investigate continuity, end behavior, vertical and horizontal
asymptotes, and limits and connect these characteristics to the graph of a
function? 01E 6. Can you apply basic transformations,
including to the parent functions?
02A |
Essential
TEKS Questions: 1. Can you determine the domain and range of
functions using graphs, tables, and symbols?
01B 2.
Can you investigate continuity, end behavior, vertical and horizontal
asymptotes, and limits and connect these characteristics to the graph of the
function. 01E 3.
Can you perform operations including composition on functions, find
inverses, and describe these procedures and results verbally, numerically,
symbolically, and graphically? 02B |
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Unit Four Polynomial
Functions |
Unit Five Exponential
and Logarithmic Functions |
Unit Six Introduction
to Calculus |
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Concepts: Remainder
Theorem
Factor
Theorem
Rational
Zeros Theorem Fundamental
Theorem of Algebra Intermediate
Value Theorem |
Concepts: Rational
Exponents Exponential
Functions Logarithmic
Functions Graphs and
Transformations of the Exponential and Logarithmic Functions Properties
of Exponential and Logarithmic Functions Applications
of Exponential and Logarithmic Functions |
Concepts: Definition
of Derivative Properties
of Derivatives First and
Second Derivative Test Applications:
Maximum and Minimum Problems Related Rate
Problems |
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Enduring
Understandings: The student
defines functions, describes characteristics of functions, and translates
among verbal, numerical, graphical, and symbolic representations of
functions, including polynomial, rational, radical, exponential, logarithmic,
trigonometric, and piecewise-defined functions. 01 The student
interprets the meaning of the symbolic representations of functions and
operations on functions within a context. 02 . |
Enduring
Understandings: The student
defines functions, describes characteristics of functions, and translates
among verbal, numerical, graphical, and symbolic representations of
functions, including polynomial, rational, radical, exponential, logarithmic,
trigonometric, and piecewise-defined functions. 01 . The student
interprets the meaning of the symbolic representations of functions and
operations on functions within a context. 02 |
Enduring
Understanding: The student
uses a limit to define a derivative and explores the properties of
derivatives. |
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Guiding
Questions: ·
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·
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Guiding
Questions: ·
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Guiding
Questions: ·
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Essential
TEKS Questions: 1. Can you describe parent functions
symbolically and graphically, including 01A 2. Can you
determine the domain and range of functions using graphs, tables, and
symbols? 01B 3. Can you describe symmetry of graphs of even
and odd functions? 01C 4.
Can you recognize and use connections among significant points of a functions (roots, maximum points, and minimum
points), the graph of a function, and the symbolic representation of a
function? 01D 5.
Can you investigate continuity, end behavior, vertical and horizontal
asymptotes, and limits and connect these characteristics to the graph of a
function? 01E 6. Can you apply basic transformations,
including
to the parent functions? 02A |
Essential
TEKS Questions: 1. Can you describe parent functions
symbolically and graphically, including
01A 2. Can you
determine the domain and range of functions using graphs, tables, and
symbols? 01B 3. Can you describe symmetry of graphs of even
and odd functions? 01C 4.
Can you recognize and use connections among significant points of a functions (roots, maximum points, and minimum
points), the graph of a function, and the symbolic representation of a
function? 01D 5.
Can you investigate continuity, end behavior, vertical and horizontal
asymptotes, and limits and connect these characteristics to the graph of a
function? 01E 6. Can you apply basic transformations,
including to the parent functions? 02A 7.
Can you investigate identities graphically and verify them
symbolically, including logarithmic properties, trigonometric identities, and
exponential properties? 02C 8.
Can you use functions such as logarithmic, exponential, trigonometric,
polynomial, etc. to model real-life data?
03A |
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Unit
Seven More Vectors |
Unit Eight Conics,
Parametric Equations, Partial Fractions, and Regression |
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Concepts: Three
Dimensional Vectors Dot ProductCross
Product |
Concepts: Conic Sections
Applications
Definition
of Parametric Equations Graphs of
Parametric Equations Conversion
between Rectangular Equations and Parametric Equations Applications
of Parametric Equations Partial
Fractions Regression |
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Enduring
Understandings: The
student uses vectors to model physical situations. 06 |
Enduring
Understandings: The student
uses conic sections, their properties, and parametric representations to
model physical situations. 05 The student
uses functions and their properties to model and solve real-life
problems. 03 |
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Guiding
Questions: ·
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Guiding
Questions: ·
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Essential
TEKS Questions: 1. Can you use the
concept of vectors to model situations defined by magnitude and direction. 06A 2. Can you
analyze and solve vector problems generated by real-life situations. 06B |
Essential
TEKS Questions: 1. Can you use conic sections to model motion,
such as the graph of velocity vs. position of a pendulum and motions of
planets? 05A 2. Can you use properties of conic sections to
describe physical phenomena such as the reflective properties of light and
sound? 05B 3. Can you convert between parametric and
rectangular forms of functions and equations to graph them? 05C 4. Can you use parametric functions to simulate problems involving motion? 05D 5. Can you use regression to determine a function to model real-life data? 03B |
Essential
TEKS Questions: |