Mathematics

Accelerated CCGPS Coordinate Algebra/Analytic Geometry – For students in either Math 8 or Pre-Algebra in middle school; taken first semester of 9th grade. Students will begin their preparation for college-level course work (i.e., AP Calculus AB, AP Calculus BC, and AP Statistics) by studying mathematics within the confines of the following conceptual categories:

  • Number and Quantity
    • Reason quantitatively and use units to solve problems.
  • Algebra
    • Interpret the structure of expressions.
    • Create linear and exponential equations that describe numbers or relationships.
    • Understand solving equations as a process of reasoning and explain the reasoning.
    • Solve linear equations and inequalities in one variable, including iterated equations.
    • Solve systems of linear equations.
    • Represent and solve linear and exponential equations and inequalities graphically.
  • Functions
    • Understand the concept of a function and use function notation.
    • Interpret non-periodic functions that arise in applications in terms of the context.
    • Analyze linear and exponential functions using different representations.
    • Build a function that models a relationship between two quantities using arithmetic operations. Build explicit and recursive arithmetic and geometric sequences to model situations.
    • Build new functions from existing functions using function translations.
    • Construct and compare linear and exponential functions and solve problems.
    • Interpret expressions for functions in terms of the situation they model.
  • Geometry
    • Experiment with transformations in the plane.
    • Understand congruence in terms of rigid motions.
    • Prove geometric theorems.
    • Make geometric constructions.
    • Understand similarity in terms of similarity transformations.
    • Prove theorems involving similarity.
    • Define trigonometric ratios and solve problems involving right triangles.
    • Understand and apply theorems about circles.
    • Find arc lengths and areas of sectors of circles.
    • Use coordinates to prove simple geometric theorems algebraically.
    • Explain volume formulas and use them to solve problems.
  • Statistics and Probability
    • Summarize, represent, and interpret data on a single count or measurement variable, including analysis of the mean, median, and interquartile range.
    • Summarize, represent, and interpret data on two categorical and quantitative variables, including the use of two-way frequency tables, and linear and exponential models.
    • Interpret linear models.

Honors CCGPS Analytic GeometryFor students who took Algebra I (private and home school) or whose CCSD middle school accelerated math did not include geometry taken first semester of 9th grade. Students will study the topics of the CCGPS Analytic Geometry course at a deeper level. Items marked with an asterisk (*) indicate Cobb County School District honors standards.

  • Number and Quantity
    • Extend the properties of exponents to rational exponents.
    • Use properties of rational and irrational exponents.
    • * Represent vector quantities graphically.
    • * Represent complex numbers as vectors graphically.
    • Perform arithmetic operations with complex numbers.
    • Use complex numbers in polynomial identities and equations.
  • Algebra
    • Interpret the structure of expressions.
    • Write quadratic expressions in equivalent forms to solve problems.
    • Perform arithmetic operations on polynomials.
    • Create quadratic equations that describe numbers or relationships.
    • Solve quadratic equations and inequalities in one variable.
    • Solve systems of equations involving linear and quadratic equations.
    • * Solve systems of inequalities involving linear and quadratic inequalities.
  • Functions
    • Interpret non-periodic functions that arise in applications in terms of the context.
    • Analyze quadratic functions using different representations.
    • Build a function that models a representation between two quantities using arithmetic operations.
    • Build new functions from existing functions using function translations.
    • Construct and compare linear, quadratic, and exponential models and solve problems.
  • Geometry
    • Understand congruence in terms of rigid motions.
    • * Use conjecture, inductive reasoning, deductive reasoning, counter-examples, and informal proofs to justify mathematical arguments.
    • Make geometric constructions.
    • * Classify triangles based on their properties.
    • * Determine points of concurrency for triangles.
    • Understand similarity in terms of similarity transformations.
    • Prove theorems involving similarity.
    • * Develop and understand properties of special quadrilaterals.
    • * Determine the sum of angles for polygons.
    • Define trigonometric ratios and solve problems involving right triangles.
    • * Define trigonometric ratios and solve problems involving special right triangles.
    • * Determine angles of elevation and depression.
    • Understand and apply theorems about circles.
    • * Locate, draw, and describe a locus in a plane and in space.
    • Find arc lengths and areas of sectors of circles.
    • Translate between the geometric description and the equation for circles and parabolas.
    • Use coordinates to prove simple geometric theorems algebraically.
    • Explain volume formulas and use them to solve problems.
    • * Explain surface area formulas and use them to solve problems.
    • * Develop and understand the algebraic and geometric relationships between a sphere’s volume and surface area.
  • Statistics and Probability
    • Summarize, represent, and interpret data on two categorical and quantitative variables, including the use of scatter plots and quadratic models.
    • Understand independence and conditional probability and use them to interpret data.
    • Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Accelerated CCGPS Analytic Geometry B/Advanced Algebra  – taken second semester of 9th grade
Students will continue their preparation for college-level course work (i.e., AP Calculus AB, AP Calculus BC, and AP Statistics) by studying mathematics within the confines of the following conceptual categories:

  • Number and Quantity
    • Extend the properties of exponents to rational exponents.
    • Use properties of rational and irrational numbers.
    • Perform arithmetic operations with complex numbers.
    • Use complex numbers in polynomial identities and equations.
  • Algebra
    • Interpret the structure of expressions and use the structure of an expression to identify ways to rewrite it.
    • Write expressions in equivalent forms to solve problems.
    • Perform arithmetic operations on polynomials.
    • Understand the relationship between zeros and factors of polynomials.
    • Use polynomial identities to solve problems.
    • Rewrite rational expressions.
    • Create linear, exponential, simple rational, and quadratic equations that describe numbers or relationships.
    • Understand solving equations as a process of reasoning and explain the reasoning.
    • Solve quadratic equations in one variable.
    • Solve systems of equations involving one linear and one quadratic equation.
    • Represent and solve equations graphically, including equations involving linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
  •  Functions
    • Interpret functions that arise in applications in terms of the context.
    • Analyze linear, quadratic, square root, cube root, piece-wise defined, polynomial, rational, exponential, and logarithmic functions using different representations.
    • Build a function that models a representation between two quantities using arithmetic operations and composition.
    • Build new functions from existing functions using function translations.
    • Construct and compare linear, quadratic, and exponential models and solve problems.
    • Extend the domain of trigonometric functions using the unit circle.
    • Model periodic phenomena with trigonometric functions.
    • Prove and apply trigonometric identities.
  • Geometry
    • Translate between the geometric description and the equation for circles and parabolas.
    • Use coordinates to prove simple geometric theorems algebraically.
    • Visualize relationships between two-dimensional and three-dimensional objects.
    • Apply geometric concepts in modeling situations.
  • Statistics and Probability
    • Summarize, represent, and interpret data on a single count or measurement variable, including analysis of the mean, median, interquartile range, and standard deviation.
    • Summarize, represent, and interpret data on two categorical and quantitative variables, including the use of scatter plots and quadratic models.
    • Understand and evaluate random processes underlying statistical experiments.
    • Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Accelerated CCGPS Pre-Calculus – taken either first or second semester of 9th grade
Students will complete their preparation for college-level course work (i.e., AP Calculus AB, AP Calculus BC, and AP Statistics) by studying mathematics within the confines of the following conceptual categories:

  • Number & Quantity
    • Perform arithmetic operations with complex numbers.
    • Represent complex numbers and their operations on the complex plane.
    • Represent and model with vector quantities.
    • Perform operations on vectors.
    • Perform operations on matrices and use matrices in applications.
  • Algebra
    • Solve systems of equations using matrices.
  • Functions
    • Build new functions from existing functions.
    • Extend the domain of trigonometric functions using the unit circle.
    • Model periodic phenomena with trigonometric functions.
    • Prove and apply trigonometric identities.
  • Geometry
    • Apply trigonometry to general triangles.
    • Translate between the geometric description and the equation for ellipses and hyperbolas.
  • Statistics and Probability
    • Use the rules of probability to compute probabilities of compound events in a uniform probability model.
    • Calculate expected values and use them to solve problems.
    • Use probability to evaluate outcomes of decisions.

AP Statistics, a college-level course taught on a high school campus, is divided into four major themes: exploratory analysis, planning a study, probability, and statistical inference. Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Probability is the tool used to anticipate future behavior of data associated with a given model. Statistical inference is the process used to make decisions stemming from observed. This course is designed for students who want to pursue studies or careers in the quantitative or scientific fields, or fields that rely on statistical analysis of pertinent data.
Advanced Placement Calculus AB

Advanced Placement Calculus AB. In this course, which is similar to most first-semester calculus courses in college, we investigate the fundamentals of differential and integral calculus. Along with typical lectures and assessments, students participate in lab activities and one term project that demonstrate and enrich concepts presented in class. Use of graphing utilities and computers is integrated into the course as well. The prerequisite for this course is Analysis, but students from Trigonometry and/or non-AP Calculus can be enrolled with a teacher recommendation. Completion of this course qualifies students to enroll in AP Calculus BC.

Advanced Placement Calculus BCThis course, which is similar to most second-semester calculus courses in college, continues where Calculus AB ends. New topics include the calculus of series and parametric, polar, and vector functions. Along with typical lectures and assessments, students participate in computer activities and practice for the actual AP exam in May. Use of graphing utilities and computers is integrated into the course as well. The prerequisite for this course is AB, and completion of this course qualifies students to enroll in Multivariable Calculus.
Multi-Variable Calculus

Multi-Variable Calculus involves the study of functions in several variables. Topics include functions, limits, continuity, differentials, directional derivatives, partial derivatives, chain rule, multiple integrals, and applications. This course is designed for strong math students who want to pursue studies or careers in the quantitative or scientific fields. Prerequisites are AP Calculus AB and BC.

Advanced Mathematical Topics 
In this course, students will study mathematical topics that extend beyond multivariable calculus. Students will investigate first-order, second-order, linear, and partial differential equations. Students will explore topics in discrete mathematics such as graph theory, combinatorics, and game theory. Students will apply logic, and learn and apply set theory. Finally, students will learn to utilize multiple methods for proving mathematical statements and theorems.

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