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Cobb County School District
Mathematics (Updated July 2004)
Mathematics - Analysis
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 Algebraic Concepts
 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
 Math Tool, http://rtt.pbs.org/rtt/interactives.cfm Click on RTT Quadratic Grapher Online Resource:  Grapher Online Resource:  Slope of a Line Online Resource:  Construct a Parabola Online Resource:  General Equation of a Line: ax + by = c Online Resource:  Slope Intercept Form of the Equation of a Line Online Resource:  Find Equation of a Line Online Resource:  Graphs of Basic Functions Online Resource: Quadratic Functions (general form) Online Resource: Quadratic Functions (standard form) Online Resource: Horizontal Shifting Online Resource: Vertical Shifting Online Resource: Horizontal Stretching and compression Online Resource: Vertical Stretching and Compression Online Resource:  Absolute Value Functions Online Resource: Explore graphs of functions
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
 Online Resource:  Graphs of Basic Trigonometric Functions Online Resource:  Sine Function Online Resource:  Cosine Function Online Resource:  Tangent Function Online Resource:  Secant Function
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
 Online Resource: Inverse Trigonometric Functions
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
 Online Resource: Construct a Parabola Online Resource: Equation of Parabola Online Resource: Find Equation of Parabola Online Resource: Equation of a Circle Online Resource: Find Equation of a Circle Online Resource: Equation of an Ellipse Online Resource: Equation of Hyperbola Online Resource: Graphs of Hyperbolic Functions
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
 Online Resource: Building Connections among Classes of Polynomial Functions Online Resource: Horizontal Shifting Online Resource: Vertical Shifting Online Resource: Horizontal Stretching and compression Online Resource: Vertical Stretching and Compression

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
 Online Resource:  Grapher Online Resource:  Graphs of Basic Functions Online Resource: Explore graphs of functions Online Resource:  Polynomial Functions in Factored Form Online Resource:  Polynomial Functions Online Resource:  Rational Functions

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
 Online Resource: Polar Coordinates and Equations

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
 Online Resource: Equation of Parabola Online Resource: Find Equation of Parabola Online Resource: Equation of a Circle Online Resource: Find Equation of a Circle Online Resource: Equation of an Ellipse Online Resource: Equation of Hyperbola Online Resource: Graphs of Hyperbolic Functions

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
 Online Resource: Inverse Function Definition Online Resource: Inverse Functions

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
 Online Resource: Exponential Functions Online Resource: Logarithmic Functions

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
 Online Resource: Shedding Light on the Subject: Function Models of Light Decay
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
 Online Resource: Sine Law - Ambiguous Case
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

 Number and Operations
 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
 Online Resource: The Process of Matrix Multiplication

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

 Measurement
 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

 Geometry
 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

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