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© 2003 by
Cobb County School District
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All Rights Reserved.
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Cobb County School District |
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Mathematics (Updated July 2003) |
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Mathematics - Algebra III |
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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.ALGIII.1.1 Sequences: Arithmetic/Geometric
The learner will be able to
identifies arithmetic and geometric sequences, finds specified terms of such sequences, and determines the sequence given the first term and either the common difference or the common ratio.
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M.ALGIII.1.2 Series: Sum/Converge
The learner will be able to
determine the sum of an infinite series that converge.
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M.ALGIII.1.3 Series: Find Mean
The learner will be able to
determine the arithmetic and geometric mean.
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M.ALGIII.1.4 Quadratic Equations: Solve
The learner will be able to
solve quadratic equations which have real and imaginary roots by using methods such as completing the square, factoring, and the quadratic formula; uses calculators or computers to approximate and check solutions.
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M.ALGIII.1.5 Functions: Define/Graph
The learner will be able to
define and graph the following types of functions: identity, constant, absolute value, step, greatest integer, polynomial, (including linear and quadratic), square root, and piecewise.
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M.ALGIII.1.6 Function/Relation: Apply Concept
The learner will be able to
apply the concepts of relation, function, domain, and range both graphically and algebraically.
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M.ALGIII.1.7 Compositions: Determine/2 Functions
The learner will be able to
evaluate and determine the composite of two functions.
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M.ALGIII.1.8 Inverses: Domain/Range
The learner will be able to
find the inverse of a function, its domain and range, and state whether the inverse is a function.
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M.ALGIII.1.9 Graphing Functions: Intercepts
The learner will be able to
use symmetry, intercepts, and asymptotes to graph and interpret graphs of quadratic functions, higher degree polynomial functions, and rational functions using appropriate techniques and tools.
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M.ALGIII.1.10 Conic Sections: Identify/Sketch
The learner will be able to
identify and sketch the graphs for the parabola, circle, ellipse, and/or hyperbola with and without center at the origin.
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M.ALGIII.1.11 Series: Partial Sum
The learner will be able to
find the sums of the first n terms of an arithmetic or geometric series.
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M.ALGIII.1.12 Binomial Theorem: Expanding
The learner will be able to
use Binomial Theorem to expand and simplify binomial expressions.
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M.ALGIII.1.13 Simplify Expressions: Rational Exponents
The learner will be able to
simplify algebraic expressions involving rational exponents using appropriate tools.
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M.ALGIII.1.14 Trig. Ratios: Determine
The learner will be able to
finds a trigonometric ratios for angles defined by a point (x,y).
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M.ALGIII.1.15 Trigonometric Functions
The learner will be able to
evaluate and graph trigonometric functions using period, phase shift, vertical shift, and amplitude.
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M.ALGIII.1.16 Graphing: Create/Transformations
The learner will be able to
constructs an equation or graph that results from transformations (translation, dilation, reflection) using a parent equation or graph.
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M.ALGIII.1.17 Inverses: Relationships/Inverse
The learner will be able to
use appropriate tools to determine special relationships between functions and their inverses.
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M.ALGIII.1.18 Conic Sections: Recognize
The learner will be able to
identify each conic section, including degenerates, as the intersection of a conical surface and a plane.
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M.ALGIII.1.19 Logarithmic/Exponential:
The learner will be able to
define, graph, and show the inverse relationship between logarithmic and exponential functions.
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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.ALGIII.2.1 Problem Solving: Relate
The learner will be able to
solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
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M.ALGIII.2.2 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.
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M.ALGIII.2.3 Linear Programming: Solve
The learner will be able to
apply linear programming strategies to solve systems of inequalities (using feasible regions and critical points).
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M.ALGIII.2.4 Conic Sections: Solve/Systems
The learner will be able to
solve systems of equations involving conics and other types of equations.
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M.ALGIII.2.5 Matrices: Recognize/Applications
The learner will be able to
identify uses and applications of matrices in practical situations, such as use of arrays to organize data in computer programming or transformations.
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M.ALGIII.2.6 Exponents/Logarithmic: Solve
The learner will be able to
solve logarithmic and exponential equations and problems.
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M.ALGIII.2.7 Logarithmic/Exponential
The learner will be able to
solve problems involving application of exponential and logarithmic functions, using appropriate techniques and tools.
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M.ALGIII.2.8 Predictions: Regression Techniques
The learner will be able to
make predictions from collected data using applying regression techniques.
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M.ALGIII.2.9 Strategies: Choose/Tools
The learner will be able to
select appropriate approaches and tools.
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M.ALGIII.2.10 Problem Solving: Estimate
The learner will be able to
use estimating strategies to predict computational results.
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M.ALGIII.2.11 Calculator: Approximation
The learner will be able to
uses approximate numbers appropriately in calculator computations and recognizes error introduced by the use of approximate numbers.
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M.ALGIII.2.12 Solution: Accuracy
The learner will be able to
find solutions to problems accurate to a given number of decimal places, and recognize situations such as measurement where approximations are appropriate.
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M.ALGIII.2.13 Strategies: Choose/Suitable
The learner will be able to
solve problems throughout this course.
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M.ALGIII.2.14 Solution: Reasonableness
The learner will be able to
judge reasonableness of results.
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PS3: NUMBER SENSE
The learner will be able to
represent, interpret, and compare real numbers.
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M.ALGIII.3.1 Exponential/Logarithmic: Common
The learner will be able to
determine values of common and natural logarithms and antilogs using a calculator.
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PS4: 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.ALGIII.4.1 Matrices: Evaluate/Operations
The learner will be able to
evaluate the results of matrix operations (such as addition, multiplication, and scalar operations) when defined.
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M.ALGIII.4.2 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.ALGIII.4.3 Matrices: Inverse
The learner will be able to
determine the inverses of matrices, if it exists, for 2x2 and/or 3x3 cases.
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M.ALGIII.4.4 Complex Numbers: Define/Apply
The learner will be able to
define and/or use the basic operations and properties of complex numbers.
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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.ALGIII.5.1 Angle Measures: Degree/Radians
The learner will be able to
converts measures of angles between radians and degrees.
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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.ALGIII.6.1 Trigonometric Functions: Evaluate
The learner will be able to
use the calculator to evaluate trigonometric ratios for given angles in either degrees or radians and to find an angle when a trigonometric ratio is known.
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M.ALGIII.6.2 Trig. Ratios: Right Triangle
The learner will be able to
solves problems involving applications of right triangle ratios.
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M.ALGIII.6.3 Trigonometric Functions: Define
The learner will be able to
define the six trigonometric functions as both circular functions and ratios of side of right triangles, and shows relationships between these functions.
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M.ALGIII.6.4 Angle: Standard Position
The learner will be able to
sketches an angle in standard position and determines 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.ALGIII.7.1 Data Management: Practical
The learner will be able to
organize, summarize, characterize, and interpret data from practical situations using relevant sets by constructing tables, graphs, and charts including frequency distributions, histograms, line plots, stem-and-leaf plots, box plots, and scatter plots for bivariate data.
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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.ALGIII.8.1 Statistics: Apply/Methods
The learner will be able to
use statistical reasoning techniques appropriately and recognizes common misuses of statistics.
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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.ALGIII.9.1 Probability: Determine/Exclusive
The learner will be able to
find the probability of mutually-exclusive events occurring.
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M.ALGIII.9.2 Counting Methods: Counting
The learner will be able to
apply fundamental counting principles.
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M.ALGIII.9.3 Combinations: Determine
The learner will be able to
find the number of permutations and number of combinations of n things taken r at a time.
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M.ALGIII.9.4 Probability: Odd/Chance
The learner will be able to
distinguish between odds, probabilities, and chance and finds the odds associated with given events.
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M.ALGIII.9.5 Probability: Sample Space
The learner will be able to
finds the probability of an event by determining the sample space of all possible outcomes and the number of successful outcomes.
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M.ALGIII.9.6 Permutations: Recognize
The learner will be able to
identify and discriminate between permutations and combinations.
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M.ALGIII.9.7 Probability Distribution:
The learner will be able to
identify common statistical distributions such as 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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