
Cobb County School District 
Mathematics (Updated July 2004) 
Mathematics  Analysis 
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Goals and Descriptions 

PS1: PATTERNS, RELATIONS, AND FUNCTIONS
The learner will be able to
use functions to represent and analyze patterns and quantitative relationships.


M.ANALY.1.1 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.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Master 
5.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #6 


M.ANALY.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.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #8 


M.ANALY.1.3 Functions: Discuss/Terms
The learner will be able to
discuss given functions using the terms of symmetry, continuity, asymptotes, basic shape, rate of change, intercepts, maxima, minima, boundedness, end behavior, exclusion from the domain, and intervals in which zero occur.
Bloom's 
Scope 
Hours 
Source 
Analysis 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Analysis, #4 


M.ANALY.1.4 Trigonometric Functions: Evaluate
The learner will be able to
evaluate and graph trigonometric functions using period, phase shift, vertical shift, and amplitude.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #16 


M.ANALY.1.5 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.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
5.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #17 


M.ANALY.1.6 Trigonometric Functions: Graph
The learner will be able to
evaluate and graph inverse trigonometric functions and solves equations using these function.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #20 


M.ANALY.1.7 Conic Sections: Identify/Write
The learner will be able to
recognize, write, and graph equations of conic sections, using properties such as properties, intercepts, asymptotes, and eccentricity when appropriate.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #30 


M.ANALY.1.8 Series: Sigma Notation
The learner will be able to
uses sigma notation to represent series.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
1.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #33 


M.ANALY.1.9 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.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #33 


M.ANALY.1.10 Sequences/Series: Determine
The learner will be able to
describes sequence in terms of recurrence formulas, relates to linear and exponential functions and determines the arithmetic, geometric, and harmonic means.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #34, #36 


M.ANALY.1.11 Series: Limits/Definitions
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.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Introduce 
3.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #35 


M.ANALY.1.12 Binomial Expansion: Simplify
The learner will be able to
use the Binomial Theorem to expand and simplify binomial expressions.
Bloom's 
Scope 
Hours 
Source 
Application 
Introduce 
1.5 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #37 


M.ANALY.1.13 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.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
5.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #3 


M.ANALY.1.14 Graphing: Create/Transform
The learner will be able to
construct an equation or graph that results from transformations, (translation, dilation, reflection) using a parent equation or graph.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
4.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #7 


M.ANALY.1.15 Graphing Functions: Method
The learner will be able to
graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #9 


M.ANALY.1.16 Mapping: Image/Preimage/Inverse
The learner will be able to
determine the image, preimage, or inverse of a given mapping, and the composite of two mappings.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Analysis, #3 


M.ANALY.1.17 Equivalence: Identify/Relations
The learner will be able to
identify equivalence relations.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Master 
1.0 
GA: Quality Core Curriculum, December 2000, Analysis, #5 


M.ANALY.1.18 Graph: Polar
The learner will be able to
solve and graph equations written in polar form.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Analysis, #8 


M.ANALY.1.19 DeMoivre's Theorem: Apply
The learner will be able to
apply DeMoivre's Theorem.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
2.0 
GA: Quality Core Curriculum, December 2000, Analysis, #7 


M.ANALY.1.20 Polar Equations: Graph
The learner will be able to
identify and graph vectors in a plane as directed distances, ordered pairs of numbers, and polar forms.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
1.0 
GA: Quality Core Curriculum, December 2000, Analysis, #6 


M.ANALY.1.21 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.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Master 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #31 


M.ANALY.1.22 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.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Reinforce 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #5 


M.ANALY.1.23 Compositions: Determine/2 Functions
The learner will be able to
determine the composite of two functions and its domain and range.
Bloom's 
Scope 
Hours 
Source 
Application 
Reinforce 
1.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #4 


M.ANALY.1.24 Logarithmic/Exponential: Define
The learner will be able to
define, graph, and show the inverse relationship between logarithmic and exponential functions.
Bloom's 
Scope 
Hours 
Source 
Analysis 
Reinforce 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #10 


M.ANALY.1.25 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.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Master 
1.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #29 

PS2: ALGEBRAIC PROBLEM SOLVING
The learner will be able to
use a variety of functions to model and solve problems.


M.ANALY.2.1 Logarithmic/Exponential: Solve
The learner will be able to
obtain solutions to logarithmic and exponential problems especially applications.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
1.5 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #11 


M.ANALY.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.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
1.5 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #18 


M.ANALY.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.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #27 


M.ANALY.2.4 Conic Sections: Solve/Systems
The learner will be able to
solves systems of equations involving conics and other types of equations.
Bloom's 
Scope 
Hours 
Source 
Application 
Develop 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #32 


M.ANALY.2.5 Logarithmic/Exponential: Solve
The learner will be able to
solve problems involving exponential and logarithmic functions using appropriate methods and tools.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #12 


M.ANALY.2.6 Predictions: Regression Techniques
The learner will be able to
make predictions from collected data using regression techniques.
Bloom's 
Scope 
Hours 
Source 
Analysis 
Master 
1.5 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #12 


M.ANALY.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.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
8.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #1and #2; GA: Quality Core Curriculum, December 2000, Analysis, #1 

PS3: OPERATIONS AND THEIR RELATIONSHIPS
The learner will be able to
apply the operations and properties of real numbers to solve problems.


M.ANALY.3.1 Polar Equations: Solve
The learner will be able to
find sums, differences, multiples, and absolute values of vectors.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
2.0 
GA: Quality Core Curriculum, December 2000, Analysis, #6 and #9 


M.ANALY.3.2 Vectors: Dot Product
The learner will be able to
find the dot product of two vectors and determine whether vectors are parallel or perpendicular.
Bloom's 
Scope 
Hours 
Source 
Application 
Develop 
3.0 
GA: Quality Core Curriculum, December 2000, Analysis, #10 


M.ANALY.3.3 Matrices: Evaluate Results
The learner will be able to
evaluates the results of matrix operations (such as addition, multiplication, and scalar operations) when defined.
Bloom's 
Scope 
Hours 
Source 
Evaluation 
Reinforce 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #24 


M.ANALY.3.4 Complex Numbers: Define/Apply
The learner will be able to
define and apply the basic operations and properties of complex numbers.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Reinforce 
3.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #21 


M.ANALY.3.5 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.
Bloom's 
Scope 
Hours 
Source 
Application 
Reinforce 
1.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #25 


M.ANALY.3.6 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.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
4.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #22 


M.ANALY.3.7 Matrices: Inverse
The learner will be able to
find the inverse of a square matrix, if it exists, for 2x2 and/or 3x3 matrices.
Bloom's 
Scope 
Hours 
Source 
Application 
Reinforce 
1.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #26 

PS4: COMPUTATION AND ESTIMATION
The learner will be able to
develop fluency in all operations with real numbers in real world problem solving situations.


M.ANALY.4.1 Vectors: Problem Solving
The learner will be able to
apply vectors to solve simple problems such as velocity and force problems.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
1.0 
GA: Quality Core Curriculum, December 2000, Analysis, #11 

PS5: NUMBER SENSE Level 14
The learner will be able to
reason and draw conclusions from numerical information.


M.ANALY.5.1 Set Theory: Concepts
The learner will be able to
define, use notation of, and pictorially represent set theory concepts.
Bloom's 
Scope 
Hours 
Source 
Comprehension 
Master 
1.0 
GA: Quality Core Curriculum, December 2000, Analysis, #13 


M.ANALY.5.2 Proofs: Indirect
The learner will be able to
construct direct and indirect proofs.
Bloom's 
Scope 
Hours 
Source 
Application 
Introduce 
2.0 
GA: Quality Core Curriculum, December 2000, Analysis, #14 


M.ANALY.5.3 Set Theory: Represent
The learner will be able to
represent sentences in symbolic form and use the tools of truth tables and symbolic logic in assessing equivalence and validity.
Bloom's 
Scope 
Hours 
Source 
Evaluation 
Master 
2.0 
GA: Quality Core Curriculum, December 2000, Analysis, #17 


M.ANALY.5.4 Set Theory: Equivalence
The learner will be able to
determine equivalence between sentences involving conjunctions, disjunctions, negations, and/or conditionals.
Bloom's 
Scope 
Hours 
Source 
Analysis 
Master 
1.0 
GA: Quality Core Curriculum, December 2000, Analysis, #15 


M.ANALY.5.5 Proofs: Mathematical Induction
The learner will be able to
use mathematical induction to prove statements.
Bloom's 
Scope 
Hours 
Source 
Evaluation 
Develop 
2.0 
GA: Quality Core Curriculum, December 2000, Analysis, #18 


M.ANALY.5.6 Venn Diagrams: Apply
The learner will be able to
determine truth tables for sentences and use Venn diagrams to illustrate the relationships represented by these truth tables.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
1.0 
GA: Quality Core Curriculum, December 2000, Analysis, #16 

PS6: TOOLS, TECHNIQUES, AND FORMULAS
The learner will be able to
estimate and apply tools and formulas for various measures in problem solving.


M.ANALY.6.1 Formulas: Determine/Triangle/Area
The learner will be able to
determine the area of any triangle using an appropriate formula.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
1.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #19 

PS7: ATTRIBUTES AND UNITS
The learner will be able to
select appropriate standard units for measuring.


M.ANALY.7.1 Angle Measures: Degree/Radians
The learner will be able to
convert measures of angles between degrees and radians.
Bloom's 
Scope 
Hours 
Source 
Synthesis 
Master 
1.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #13 

PS8: FIGURES IN SPACE
The learner will be able to
analyze properties of geometric shapes, develop related mathematical arguments, and solve related problems.


M.ANALY.8.1 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.
Bloom's 
Scope 
Hours 
Source 
Comprehension 
Master 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #15 


M.ANALY.8.2 Coordinate Geometry: Represent
The learner will be able to
represent graphically, by coordinates or vectors, the locus of points determined by given conditions.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
3.0 
GA: Quality Core Curriculum, December 2000, Analysis, #12 


M.ANALY.8.3 Angle: Standard Position
The learner will be able to
sketch an angle in standard position and determine the reference and coterminal angles.
Bloom's 
Scope 
Hours 
Source 
Application 
Master 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #14 

Data Analysis and Probability

PS9: DATA ORGANIZATION
The learner will be able to
conduct investigations using statistical tools and display resulting data.


M.ANALY.9.1 Data Display: Graphically
The learner will be able to
organize, display, and interpret data in tables, charts, and graphs.
Bloom's 
Scope 
Hours 
Source 
Synthesis 
Reinforce 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #41 

PS10: DATA ANALYSIS
The learner will be able to
evaluate statistical studies and determine inferences that can be justified.


M.ANALY.10.1 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.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Introduce 
3.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #42 


M.ANALY.10.2 Predictions: Curve Fitting
The learner will be able to
analyze data and predict results by fitting a curve to the data.
Bloom's 
Scope 
Hours 
Source 
Analysis 
Develop 
1.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #44 

PS11: PROBABILITY
The learner will be able to
apply the laws of probability and counting principles in real world contexts.


M.ANALY.11.1 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.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Introduce 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #38 


M.ANALY.11.2 Combinations/Permutations:
The learner will be able to
discriminate between and determine the number of combinations and permutations of n things taken r at a time.
Bloom's 
Scope 
Hours 
Source 
Application 
Introduce 
2.0 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #40 


M.ANALY.11.3 Probability Distribution:
The learner will be able to
identify common statistical distribution such as the normal distribution.
Bloom's 
Scope 
Hours 
Source 
Knowledge 
Master 
1.5 
GA: Quality Core Curriculum, December 2000, Advanced Algebra and Trigonometry, #43 

2003 Cobb County School
District. All Rights Reserved
514 Glover Street  Marietta, Ga. 30060  (770) 4263300
Send your comments to Sue Brown
visitors since July 18, 2004
