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© 2003 by
Cobb County School District
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All Rights Reserved.
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Scantron Corporation
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Cobb County School District |
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Mathematics (Updated July 2003) |
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Mathematics - Advanced Algebra/Trig |
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Goals and Descriptions |
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PS1: PATTERNS, RELATIONS, AND FUNCTIONS
The learner will be able to
use functions to represent and analyze patterns and quantitative relationships.
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M.AAT.1.1 Graphing Functions: Concepts
The learner will be able to
graph relations and functions using concepts including domain, range, rule of a function, symmetry, asymptotes, and periodicity and end behavior.
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M.AAT.1.2 Polynomials: Solve
The learner will be able to
solve polynomial equations over the field of complex numbers, using the following theorems: Remainder, Factor, Rational Root, and Fundamental Theorem of Algebra.
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M.AAT.1.3 Trigonometric Functions: Evaluate
The learner will be able to
evaluate and graph trigonometric functions using period, phase shift, vertical shift, and amplitude.
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M.AAT.1.4 Trig. Expressions: Simplify
The learner will be able to
simplify trigonometric expressions and solve trigonometric equations using trigonometric identities and inverse functions including Pythagorean, double angle, sum and difference and half angle identities for sine and cosine.
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M.AAT.1.5 Trigonometric Functions: Graph
The learner will be able to
evaluate and graph inverse trigonometric functions and solves equations using these function.
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M.AAT.1.6 Conic Sections: Identify/Write
The learner will be able to
recognize, write, and graph equations of conic sections, using properties such as symmetry, intercepts, asymptotes, and eccentricity when appropriate.
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M.AAT.1.7 Series: Arithmetic/Geometric
The learner will be able to
define and discriminate between arithmetic and geometric series. Determines the sum of the first n terms of arithmetic and geometric series.
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M.AAT.1.8 Sequences/Series: Determine
The learner will be able to
describe sequence in terms of recurrence formulas, relate to linear and exponential functions and determine the arithmetic, geometric, and harmonic means.
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M.AAT.1.9 Series: Limits/Definitions/Sums
The learner will be able to
evaluate the limit of an infinite series, define converging and diverging series, and find the sum of an infinite series if it exists.
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M.AAT.1.10 Functions: Define/Graph
The learner will be able to
define and graph by hand and calculate the following functions: identity, constant, absolute value, step, greatest integer, polynomial (including linear and quadratic), square root, and piecewise.
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M.AAT.1.11 Graphing: Create/Transformations
The learner will be able to
construct an equation or graph that results from transformations, (translation, dilation, reflection) using a parent equation or graph.
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M.AAT.1.12 Graphing Functions: Methods
The learner will be able to
graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
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M.AAT.1.13 Logarithmic/Exponential: Define
The learner will be able to
define, graph, and show the inverse relationship between logarithmic and exponential functions.
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M.AAT.1.14 Series: Sigma Notation
The learner will be able to
uses sigma notation to represent series.
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M.AAT.1.15 Binomial Expansion: Simplify
The learner will be able to
use the Binomial Theorem to expand and simplify binomial expressions.
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M.AAT.1.16 Inverses
The learner will be able to
determine the inverse of a function, it's domain and range, and states whether the inverse is a function.
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M.AAT.1.17 Compositions: Determine/2 Functions
The learner will be able to
determine the composite of two functions and its domain and range.
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M.AAT.1.18 Conic Sections: Recognize
The learner will be able to
identify each conic section, including degenerates, as the intersection of a plane and a conical surface.
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PS2: ALGEBRAIC PROBLEM SOLVING
The learner will be able to
use a variety of functions to model and solve problems.
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M.AAT.2.1 Logarithmic/Exponential: Solve
The learner will be able to
obtain solutions to logarithmic and exponential problems especially applications.
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M.AAT.2.2 Trig. Ratios: Law of Sines/Cosines
The learner will be able to
use the Law of Sines and Cosines and right triangles ratios to solve problems.
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M.AAT.2.3 System of Equations: Solve
The learner will be able to
solves systems of equations with two and three unknowns using a variety of methods, including technology. Applies matrices to practical situations.
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M.AAT.2.4 Conic Sections: Solve/Systems
The learner will be able to
solves systems of equations involving conics and other types of equations.
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M.AAT.2.5 Predictions: Regression Techniques
The learner will be able to
make predictions from collected data using regression techniques.
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M.AAT.2.6 Conic Sections: Identify/Graph
The learner will be able to
identify and sketch the graphs for the parabola, circle, ellipse and hyperbola, with and without center at the origin.
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M.AAT.2.7 Problem Solving: Relate
The learner will be able to
solve problems throughout this course that involve selecting appropriate approaches and tools using estimating strategies to predict computational results, and judging reasonableness of results. Solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
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M.AAT.2.8 Logarithmic/Exponential: Solve
The learner will be able to
solve problems involving exponential and logarithmic functions using appropriate methods and tools.
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PS3: OPERATIONS AND THEIR RELATIONSHIPS
The learner will be able to
apply the operations and properties of real numbers to solve problems.
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M.AAT.3.1 Complex Numbers: Define/Apply
The learner will be able to
define and apply the basic operations and properties of complex numbers.
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M.AAT.3.2 Matrices: Evaluate Results
The learner will be able to
evaluates the results of matrix operations (such as addition, multiplication, and scalar operations) when defined.
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M.AAT.3.3 Complex Numbers: Theorem/Define
The learner will be able to
apply appropriate theorems and definitions to find powers, roots, and absolute values of complex numbers, graph and express complex numbers in rectangular and polar form.
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M.AAT.3.4 Matrices: Determinant/2x2/3x3
The learner will be able to
evaluate the determinant for 2 by 2 and 3 by 3 matrices using appropriate methods.
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M.AAT.3.5 Matrices: Inverse
The learner will be able to
find the inverse of a square matrix, if it exists, for 2x2 and/or 3x3 matrices.
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PS4: TOOLS, TECHNIQUES, AND FORMULAS
The learner will be able to
estimate and apply tools and formulas for various measures in problem solving.
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M.AAT.4.1 Formulas: Determine/Triangle/Area
The learner will be able to
determine the area of any triangle using an appropriate formula.
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PS5: ATTRIBUTES AND UNITS
The learner will be able to
select appropriate standard units for measuring.
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M.AAT.5.1 Angle Measures: Degree/Radian
The learner will be able to
convert measures of angles between degrees and radians.
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PS6: FIGURES IN SPACE
The learner will be able to
analyze properties of geometric shapes, develop related mathematical arguments, and solve related problems.
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M.AAT.6.1 Trigonometric Functions: Define
The learner will be able to
define the six trigonometric functions as both circular functions and as ratios of sides of right triangles, and show the relationships between these functions.
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M.AAT.6.2 Angle: Standard Position
The learner will be able to
sketch an angle in standard position and determine the reference and coterminal angles.
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Data Analysis and Probability
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PS7: DATA ORGANIZATION
The learner will be able to
conduct investigations using statistical tools and display resulting data.
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M.AAT.7.1 Data Display: Graphically
The learner will be able to
organize, display, and interpret data in tables, charts, and graphs.
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PS8: DATA ANALYSIS
The learner will be able to
evaluate statistical studies and determine inferences that can be justified.
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M.AAT.8.1 Data Analysis
The learner will be able to
analyze data by using correctly the mean, median, mode, variance, and standard deviation, and identify common misuses of statistics.
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M.AAT.8.2 Predictions: Curve Fitting
The learner will be able to
analyze data and predict results by fitting a curve to the data.
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PS9: PROBABILITY
The learner will be able to
apply the laws of probability and counting principles in real world contexts.
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M.AAT.9.1 Probability: Define
The learner will be able to
define probability in terms of sample spaces, outcomes and events. Determine probability of independent, dependent, and conditional events.
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M.AAT.9.2 Combinations/Permutations: Discriminate
The learner will be able to
discriminate between and determine the number of combinations and permutations of n things taken r at a time.
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M.AAT.9.3 Probability Distribution: Recognize
The learner will be able to
identify common statistical distribution such as the normal distribution.
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й 2003 Cobb County School
District. All Rights Reserved
514 Glover Street | Marietta, Ga. 30060 | (770) 426-3300
Send your comments to Sue Brown
visitors since July 18, 2003
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