Georgia State Standards for Mathematics: Grade 10

GA.MM1A. Mathematics 1 - Algebra: Students will explore functions and solve simple equations. Students will simplify and operate with radical, polynomial, and rational expressions.

MM1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MM1A1.a. Represent functions using function notation.

MM1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MM1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MM1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MM1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MM1A1.f. Recognize sequences as functions with domains that are whole numbers.

MM1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MM1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MM1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

MM1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MM1A2.a. Simplify algebraic and numeric expressions involving square root.

MM1A2.b. Perform operations with square roots.

MM1A2.c. Add, subtract, multiply, and divide polynomials.

MM1A2.d. Expand binomials using the Binomial Theorem.

MM1A2.e. Add, subtract, multiply, and divide rational expressions.

MM1A2.f. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3 x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

MM1A2.g. Use area and volume models for polynomial arithmetic.

MM1A3. Students will solve simple equations.

MM1A3.a. Solve quadratic equations in the form ax^2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

MM1A3.b. Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

MM1A3.c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x^2 + bx + c = 0.

MM1A3.d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA.MM1G. Mathematics 1 - Geometry: Students will explore, understand, and use the formal language of reasoning and justification. Students will apply properties of polygons and determine distances and points of concurrence.

MM1G1. Students will investigate properties of geometric figures in the coordinate plane.

MM1G1.a. Determine the distance between two points.

MM1G1.b. Determine the distance between a point and a line.

MM1G1.c. Determine the midpoint of a segment.

MM1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MM1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

MM1G2. Students will understand and use the language of mathematical argument and justification.

MM1G2.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MM1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MM1G3.a. Determine the sum of interior and exterior angles in a polygon.

MM1G3.b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

MM1G3.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MM1G3.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MM1G3.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

GA.MM1D. Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.

MM1D1. Students will determine the number of outcomes related to a given event.

MM1D1.a. Apply the addition and multiplication principles of counting.

MM1D1.b. Calculate and use simple permutations and combinations.

MM1D2. Students will use the basic laws of probability.

MM1D2.a. Find the probabilities of mutually exclusive events.

MM1D2.b. Find the probabilities of dependent events.

MM1D2.c. Calculate conditional probabilities.

MM1D2.d. Use expected value to predict outcomes.

MM1D3. Students will relate samples to a population.

MM1D3.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MM1D3.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MM1D3.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MM1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

GA.MM1P. Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM1P1. Students will solve problems (using appropriate technology).

MM1P1.a. Build new mathematical knowledge through problem solving.

MM1P1.b. Solve problems that arise in mathematics and in other contexts.

MM1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM1P1.d. Monitor and reflect on the process of mathematical problem solving.

MM1P2. Students will reason and evaluate mathematical arguments.

MM1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM1P2.b. Make and investigate mathematical conjectures.

MM1P2.c. Develop and evaluate mathematical arguments and proofs.

MM1P2.d. Select and use various types of reasoning and methods of proof.

MM1P3. Students will communicate mathematically.

MM1P3.a. Organize and consolidate their mathematical thinking through communication.

MM1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM1P4. Students will make connections among mathematical ideas and to other disciplines.

MM1P4.a. Recognize and use connections among mathematical ideas.

MM1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM1P5. Students will represent mathematics in multiple ways.

MM1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM2N. Mathematics 2 - Number and Operations: Students will use the complex number system.

MM2N1. Students will represent and operate with complex numbers.

MM2N1.a. Write square roots of negative numbers in imaginary form.

MM2N1.b. Write complex numbers in the form a + bi.

MM2N1.c. Add, subtract, multiply, and divide complex numbers.

MM2N1.d. Simplify expressions involving complex numbers.

GA.MM2A. Mathematics 2 - Algebra: Students will investigate piecewise, exponential, and quadratic functions, using numerical, analytical, and graphical approaches, focusing on the use of these functions in problem-solving situations. Students will solve equations and inequalities and explore inverses of functions.

MM2A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MM2A1.a. Write absolute value functions as piecewise functions.

MM2A1.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MM2A1.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

MM2A2. Students will explore exponential functions.

MM2A2.a. Extend properties of exponents to include all integer exponents.

MM2A2.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MM2A2.c. Graph functions as transformations of f(x) = a^x.

MM2A2.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MM2A2.e. Understand and use basic exponential functions as models of real phenomena.

MM2A2.f. Understand and recognize geometric sequences as exponential functions with domains that are whole numbers.

MM2A2.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

MM2A3.a. Convert between standard and vertex form.

MM2A3. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MM2A3.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MM2A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MM2A3.d. Explore arithmetic series and various ways of computing their sums.

MM2A3.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MM2A4. Students will solve quadratic equations and inequalities in one variable.

MM2A4.a. Solve equations graphically using appropriate technology.

MM2A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MM2A4.c. Analyze the nature of roots using technology and using the discriminant.

MM2A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MM2A5. Students will explore inverses of functions.

MM2A5.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MM2A5.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MM2A5.c. Explore the graphs of functions and their inverses.

MM2A5.d. Use composition to verify that functions are inverses of each other.

GA.MM2G. Mathematics 2 - Geometry: Students will explore right triangles and right-triangle trigonometry. They will understand and apply properties of circles and spheres, and use them in determining related measures.

MM2G1. Students will identify and use special right triangles.

MM2G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MM2G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MM2G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MM2G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MM2G2.c. Solve application problems using the trigonometric ratios.

MM2G3. Students will understand the properties of circles.

MM2G3.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MM2G3.b. Understand and use properties of central, inscribed, and related angles.

MM2G3.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MM2G3.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MM2G4. Students will find and compare the measures of spheres.

MM2G4.a. Use and apply surface area and volume of a sphere.

MM2G4.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MM2D. Mathematics 2 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. They will use regression to analyze data and to make inferences.

MM2D1. Using sample data, students will make informal inferences about population means and standard deviations.

MM2D1.a. Pose a question and collect sample data from at least two different populations.

MM2D1.b. Understand and calculate the means and standard deviations of sets of data.

MM2D1.c. Use means and standard deviations to compare data sets.

MM2D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MM2D2. Students will determine an algebraic model to quantify the association between two quantitative variables.

MM2D2.a. Gather and plot data that can be modeled with linear and quadratic functions.

MM2D2.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and 'eyeballing.'

MM2D2.c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

MM2D2.d. Investigate issues that arise when using data to explore the relationship between two variables, including confusion between correlation and causation.

GA.MM2P. Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM2P1. Students will solve problems (using appropriate technology).

MM2P1.a. Build new mathematical knowledge through problem solving.

MM2P1.b. Solve problems that arise in mathematics and in other contexts.

MM2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM2P1.d. Monitor and reflect on the process of mathematical problem solving.

MM2P2. Students will reason and evaluate mathematical arguments.

MM2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM2P2.b. Make and investigate mathematical conjectures.

MM2P2.c. Develop and evaluate mathematical arguments and proofs.

MM2P2.d. Select and use various types of reasoning and methods of proof.

MM2P3. Students will communicate mathematically.

MM2P3.a. Organize and consolidate their mathematical thinking through communication.

MM2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM2P4. Students will make connections among mathematical ideas and to other disciplines.

MM2P4.a. Recognize and use connections among mathematical ideas.

MM2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM2P5. Students will represent mathematics in multiple ways.

MM2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM3A. Mathematics 3 - Algebra: Students will investigate exponential, logarithmic and polynomial functions of degree higher than 2. Students will understand matrices and use them to solve problems.

MM3A1. Students will analyze graphs of polynomial functions of higher degree.

MM3A1.a. Graph simple polynomial functions as translations of the function f(x) = ax^n.

MM3A1.b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

MM3A1.c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

MM3A1.d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

MM3A2. Students will explore logarithmic functions as inverses of exponential functions.

MM3A2.a. Define and understand the properties of nth roots.

MM3A2.b. Extend properties of exponents to include rational exponents.

MM3A2.c. Define logarithmic functions as inverses of exponential functions.

MM3A2.d. Understand and use properties of logarithms by extending laws of exponents.

MM3A2.e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

MM3A2.f. Graph functions as transformations of f(x) = a^x, f(x) = log ax, f(x) = e^x, f(x) = ln x.

MM3A2.g. Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

MM3A3. Students will solve a variety of equations and inequalities.

MM3A3.a. Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

MM3A3.b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

MM3A3.c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

MM3A3.d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

MM3A4. Students will perform basic operations with matrices.

MM3A4.a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

MM3A4.b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.

MM3A4.c. Examine the properties of matrices, contrasting them with properties of real numbers.

MM3A5. Students will use matrices to formulate and solve problems.

MM3A5.a. Represent a system of linear equations as a matrix equation.

MM3A5.b. Solve matrix equations using inverse matrices.

MM3A5.c. Represent and solve realistic problems using systems of linear equations.

MM3A6. Students will solve linear programming problems in two variables.

MM3A6.a. Solve systems of inequalities in two variables, showing the solutions graphically.

MM3A6.b. Represent and solve realistic problems using linear programming.

MM3A7. Students will understand and apply matrix representations of vertex-edge graphs.

MM3A7.a. Use graphs to represent realistic situations.

MM3A7.b. Use matrices to represent graphs, and solve problems that can be represented by graphs.

GA.MM3G. Mathematics 3 - Geometry: Students will understand and use the analytic geometry of conic sections and of planes and spheres in space.

MM3G1. Students will investigate the relationships between lines and circles.

MM3G1.a. Find equations of circles.

MM3G1.b. Graph a circle given an equation in general form.

MM3G1.c. Find the equation of a tangent line to a circle at a given point.

MM3G1.d. Solve a system of equations involving a circle and a line.

MM3G1.e. Solve a system of equations involving two circles.

MM3G2. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MM3G2.a. Convert equations of conics by completing the square.

MM3G2.b. Graph conic sections, identifying fundamental characteristics.

MM3G2.c. Write equations of conic sections given appropriate information.

MM3G3. Students will investigate planes and spheres.

MM3G3.a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

MM3G3.b. Apply the distance formula in 3-space.

MM3G3.c. Recognize and understand equations of planes and spheres.

GA.MM3D. Mathematics 3 - Data Analysis and Probability: Students will use a normal distribution to calculate probabilities. They will organize, represent, investigate, interpret, and make inferences using data from both observational studies and experiments.

MM3D1. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

MM3D2. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

MM3D2.a. Determine intervals about the mean that include a given percent of data.

MM3D2.b. Determine the probability that a given value falls within a specified interval.

MM3D2.c. Estimate how many items in a population fall within a specified interval.

MM3D3. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

GA.MM3P. Mathematics 3 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM3P1. Students will solve problems (using appropriate technology).

MM3P1.a. Build new mathematical knowledge through problem solving.

MM3P1.b. Solve problems that arise in mathematics and in other contexts.

MM3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM3P1.d. Monitor and reflect on the process of mathematical problem solving.

MM3P2. Students will reason and evaluate mathematical arguments.

MM3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM3P2.b. Make and investigate mathematical conjectures.

MM3P2.c. Develop and evaluate mathematical arguments and proofs.

MM3P2.d. Select and use various types of reasoning and methods of proof.

MM3P3. Students will communicate mathematically.

MM3P3.a. Organize and consolidate their mathematical thinking through communication.

MM3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM3P4. Students will make connections among mathematical ideas and to other disciplines.

MM3P4.a. Recognize and use connections among mathematical ideas.

MM3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM3P5. Students will represent mathematics in multiple ways.

MM3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM4A. Mathematics 4 - Algebra: Students will analyze rational and trigonometric functions. Students will investigate and apply sequences and series and will understand and use vectors.

MM4A1. Students will explore rational functions.

MM4A1.a. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

MM4A1.b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

MM4A1.c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

MM4A2. Students will use the circle to define the trigonometric functions.

MM4A2.a. Define and understand angles measured in degrees and radians, including but not limited to 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, their multiples, and equivalences.

MM4A2.b. Understand and apply the six trigonometric functions as functions of general angles in standard position.

MM4A2.c. Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

MM4A2.d. Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

MM4A2.e. Find values of trigonometric functions using the unit circle.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

MM4A3.a. Understand and apply the six basic trigonometric functions as functions of real numbers.

MM4A3.b. Determine the characteristics of the graphs of the six basic trigonometric functions.

MM4A3.c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3.d. Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

MM4A4. Students will investigate functions.

MM4A4.a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

MM4A4.b. Investigate transformations of functions.

MM4A4.c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

MM4A5. Students will establish trigonometric identities and use them to simplify trigonometric expressions and verify equivalence statements.

MM4A6. Students will solve trigonometric equations both graphically and algebraically.

MM4A6.a. Solve trigonometric equations over a variety of domains, using technology as appropriate.

MM4A6.b. Use the coordinates of a point on the terminal side of an angle to express x and y as polar coordinates.

MM4A6.d. Apply the law of sines and the law of cosines.

MM4A7. Students will verify and apply 1/2 ab sinC to find the area of a triangle.

MM4A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

MM4A8.a. Find values of the above functions using technology as appropriate.

MM4A8.b. Determine characteristics of the above functions and their graphs.

MM4A9. Students will use sequences and series

MM4A9.a. Use and find recursive and explicit formulae for the terms of sequences.

MM4A9.b. Recognize and use simple arithmetic and geometric sequences.

MM4A9.c. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

MM4A9.d. Use summation notation to explore finite series.

MM4A10. Students will understand and use vectors.

MM4A10.a. Represent vectors algebraically and geometrically.

MM4A10.b. Convert between vectors expressed using rectangular coordinates and expressed using magnitude and direction.

MM4A10.c. Add, subtract, and compute scalar multiples of vectors.

MM4A10.d. Use vectors to solve realistic problems.

GA.MM4D. Mathematics 4 - Data Analysis and Probability: Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

MM4D1. Using simulation, students will develop the idea of the central limit theorem.

MM4D2. Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

MM4D3. Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

GA.MM4P. Mathematics 4 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM4P1. Students will solve problems (using appropriate technology).

MM4P1.a. Build new mathematical knowledge through problem solving.

MM4P1.b. Solve problems that arise in mathematics and in other contexts.

MM4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM4P1.d. Monitor and reflect on the process of mathematical problem solving.

MM4P2. Students will reason and evaluate mathematical arguments.

MM4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM4P2.b. Make and investigate mathematical conjectures.

MM4P2.c. Develop and evaluate mathematical arguments and proofs.

MM4P2.d. Select and use various types of reasoning and methods of proof.

MM4P3. Students will communicate mathematically.

MM4P3.a. Organize and consolidate their mathematical thinking through communication.

MM4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM4P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM4P4. Students will make connections among mathematical ideas and to other disciplines.

MM4P4.a. Recognize and use connections among mathematical ideas.

MM4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM4P5. Students will represent mathematics in multiple ways.

MM4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM4P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC1A. Core Mathematics 1 - Algebra: Students will explore and interpret the characteristics of functions.

MC1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MC1A1.a. Represent functions using function notation.

MC1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MC1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MC1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MC1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MC1A1.f. Recognize sequences as functions with domains that are whole numbers.

MC1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MC1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MC1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

GA.MC1G. Core Mathematics 1 - Geometry: The student will apply properties of polygons and determine distances.

MC1G1. Students will investigate properties of geometric figures in the coordinate plane.

MC1G1.a. Determine the distance between two points.

MC1G1.b. Determine the distance between a point and a line.

MC1G1.c. Determine the midpoint of a segment.

MC1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MC1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

GA.MC1D. Core Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability.

MC1D1. Students will determine the number of outcomes related to a given event

MC1D1.a. Apply addition and multiplication principles of counting.

MC1D1.b. Calculate and use simple permutations and combinations.

MC1D2. Students will use the basic laws of probability

MC1D2.a. Find the probabilities of mutually exclusive events.

MC1D2.b. Find the probabilities of dependent events.

MC1D2.c. Calculate conditional probabilities.

MC1D2.d. Use expected value to predict outcomes.

GA.MC1P. Core Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC1P1. Students will solve problems (using appropriate technology).

MC1P1.a. Build new mathematical knowledge through problem solving.

MC1P1.b. Solve problems that arise in mathematics and in other contexts.

MC1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC1P1.d. Monitor and reflect on the process of mathematical problem solving.

MC1P2. Students will reason and evaluate mathematical arguments.

MC1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC1P2.b. Make and investigate mathematical conjectures.

MC1P2.c. Develop and evaluate mathematical arguments and proofs.

MC1P2.d. Select and use various types of reasoning and methods of proof.

MC1P3. Students will communicate mathematically.

MC1P3.a. Organize and consolidate their mathematical thinking through communication.

MC1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC1P4. Students will make connections among mathematical ideas and to other disciplines.

MC1P4.a. Recognize and use connections among mathematical ideas.

MC1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC1P5. Students will represent mathematics in multiple ways.

MC1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC2A. Core Mathematics 2 - Algebra: Students will simplify and operate with radical expressions, polynomials, and rational expressions. Students will solve simple equations.

MC2A1. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MC2A1.a. Simplify algebraic and numeric expressions involving square root.

MC2A1.b. Perform operations with square roots.

MC2A1.c. Add, subtract, multiply, and divide polynomials.

MC2A1.d. Add, subtract, multiply, and divide rational expressions.

MC2A1.e. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3 x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y3

MC2A1.f. Use area and volume models for polynomial arithmetic.

MC2A2. Students will solve simple equations.

MC2A2.a. Solve quadratic equations in the form ax^2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

MC2A2.b. Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

MC2A2.c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x^2 + bx + c = 0.

MC2A2.d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA.MC2G. Core Mathematics 2 - Geometry: Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons.

MC2G1. Students will understand and use the language of mathematical argument and justification.

MC2G1.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MC2G1.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MC2G1.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MC2G1.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MC2G1.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

GA.MC2D. Core Mathematics 2 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.

MC2D1. Students will relate samples to a population.

MC2D1.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MC2D1.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MC2D1.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MC2D2. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

GA.MC2P. Core Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC2P1. Students will solve problems (using appropriate technology).

MC2P1.a. Build new mathematical knowledge through problem solving.

MC2P1.b. Solve problems that arise in mathematics and in other contexts.

MC2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC2P1.d. Monitor and reflect on the process of mathematical problem solving.

MC2P2. Students will reason and evaluate mathematical arguments.

MC2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC2P2.b. Make and investigate mathematical conjectures.

MC2P2.c. Develop and evaluate mathematical arguments and proofs.

MC2P2.d. Select and use various types of reasoning and methods of proof.

MC2P3. Students will communicate mathematically.

MC2P3.a. Organize and consolidate their mathematical thinking through communication.

MC2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC2P4. Students will make connections among mathematical ideas and to other disciplines.

MC2P4.a. Recognize and use connections among mathematical ideas.

MC2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC2P5. Students will represent mathematics in multiple ways.

MC2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC3A. Core Mathematics 3 - Algebra: Students will investigate piecewise and exponential functions from numerical, analytical and graphical approaches, focusing on the use of these functions in problem-solving situations.

MC3A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MC3A1.a. Write absolute value functions as piecewise functions.

MC3A1.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MC3A1.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

MC3A2. Students will explore exponential functions.

MC3A2.a. Extend properties of exponents to include all integer exponents.

MC3A2.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MC3A2.c. Graph functions as transformations of f(x) = a^x.

MC3A2.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MC3A2.e. Understand and use basic exponential functions as models of real phenomena.

MC3A2.f. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

MC3A2.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

GA.MC3G. Core Mathematics 3 - Geometry: Students will explore right triangles and right triangular trigonometry.

MC3G1. Students will identify and use special right triangles.

MC3G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MC3G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MC3G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MC3G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MC3G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MC3G2.c. Solve application problems using the trigonometric ratios.

GA.MC3D. Core Mathematics 3 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will use regression to analyze data, and to make inferences.

MC3D1. Using sample data, students will make informal inferences about population means and standard deviations.

MC3D1.a. Pose a question and collect sample data from at least two different populations.

MC3D1.b. Understand and calculate the means and standard deviations of sets of data.

MC3D1.c. Use means and standard deviations to compare data sets.

MC3D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MC3D2. Students will determine an algebraic model to quantify the association between two quantitative variables.

MC3D2.a. Gather and plot data that can be modeled with linear functions.

MC3D2.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and 'eyeballing.'

MC3D2.c. Understand and apply the processes of linear regression for curve fitting using appropriate technology.

GA.MC3P. Core Mathematics 3 - Process Standards: The following process standards are essential mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC3P1. Students will solve problems (using appropriate technology).

MC3P1.a. Build new mathematical knowledge through problem solving.

MC3P1.b. Solve problems that arise in mathematics and in other contexts.

MC3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC3P1.d. Monitor and reflect on the process of mathematical problem solving.

MC3P2. Students will reason and evaluate mathematical arguments.

MC3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC3P2.b. Make and investigate mathematical conjectures.

MC3P2.c. Develop and evaluate mathematical arguments and proofs.

MC3P2.d. Select and use various types of reasoning and methods of proof.

MC3P3. Students will communicate mathematically.

MC3P3.a. Organize and consolidate their mathematical thinking through communication.

MC3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC3P4. Students will make connections among mathematical ideas and to other disciplines.

MC3P4.a. Recognize and use connections among mathematical ideas.

MC3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC3P4.c. Recognize and apply mathematics in context outside of mathematics.

MC3P5. Students will represent mathematics in multiple ways.

MC3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC4N. Core Mathematics 4 - Number and Operations: Students will use the complex number system.

MC4N1. Students will represent and operate with complex numbers.

MC4N1.a. Write square roots of negative numbers in imaginary form.

MC4N1.b. Write complex numbers in the form a + bi.

MC4N1.c. Add, subtract, multiply, and divide complex numbers.

MC4N1.d. Simplify expressions involving complex numbers.

GA.MC4A. Core Mathematics 4 - Algebra: Students will investigate quadratic functions from numerical, analytical and graphical approaches, focusing on the use of these functions in problem-solving situations. Students will solve quadratic equations and inequalities and explore inverses of functions.

MC4A1. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MC4A1.a. Convert between standard and vertex form.

MC4A1.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MC4A1.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MC4A1.d. Explore arithmetic series and various ways of computing their sums.

MC4A1.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MC4A2. Students will solve quadratic equations and inequalities in one variable.

MC4A2.a. Solve equations graphically using appropriate technology.

MC4A2.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MC4A2.c. Analyze the nature of roots using technology and using the discriminant.

MC4A2.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MC4A3. Students will explore inverses of functions.

MC4A3.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MC4A3.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MC4A3.c. Explore the graphs of functions and their inverses.

MC4A3.d. Use composition to verify that functions are inverses of each other.

GA.MC4G. Core Mathematics 4 - Geometry: Students will understand and apply properties of circles and spheres and use them in determining related measures.

MC4G1. Students will understand the properties of circles.

MC4G1.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MC4G1.b. Understand and use properties of central, inscribed, and related angles.

MC4G1.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MC4G1.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MC4G2. Students will find and compare the measures of spheres.

MC4G2.a. Use and apply surface area and volume of a sphere.

MC4G2.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MC4D. Core Mathematics 4 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will use regression to analyze data, and to make inferences.

MC4D1. Students will determine an algebraic model to quantify the association between two quantitative variables.

MC4D1.a. Gather and plot data that can be modeled with quadratic functions.

MC4D1.b. Understand and apply the processes of quadratic regression for curve fitting using appropriate technology.

GA.MC4P. Core Mathematics 4 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC4P1. Students will solve problems (using appropriate technology).

MC4P1.a. Build new mathematical knowledge through problem solving.

MC4P1.b. Solve problems that arise in mathematics and in other contexts.

MC4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC4P1.d. Monitor and reflect on the process of mathematical problem solving.

MC4P2. Students will reason and evaluate mathematical arguments.

MC4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC4P2.b. Make and investigate mathematical conjectures.

MC4P2.c. Develop and evaluate mathematical arguments and proofs.

MC4P2.d. Select and use various types of reasoning and methods of proof.

MC4P3. Students will communicate mathematically.

MC4P3.a. Organize and consolidate their mathematical thinking through communication.

MC4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC4P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC4P4. Students will make connections among mathematical ideas and to other disciplines.

MC4P4.a. Recognize and use connections among mathematical ideas.

MC4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC4P5. Students will represent mathematics in multiple ways.

MC4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC4P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA1N. Accelerated Mathematics 1 - Number and Operations: Students will use the complex number system.

MA1N1. Students will represent and operate with complex numbers.

MA1N1.a. Write square roots of negative numbers in imaginary form.

MA1N1.b. Write complex numbers in the form a + bi.

MA1N1.c. Add, subtract, multiply, and divide complex numbers.

MA1N1.d. Simplify expressions involving complex numbers.

GA.MA1A. Accelerated Mathematics 1 - Algebra: Students will explore functions, solve equations and operate with radical, polynomial and rational expressions.

MA1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MA1A1.a. Represent functions using function notation.

MA1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MA1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MA1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MA1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MA1A1.f. Recognize sequences as functions with domains that are sets of whole numbers.

MA1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MA1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MA1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

MA1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MA1A2.a. Simplify algebraic and numeric expressions involving square root.

MA1A2.b. Perform operations with square roots.

MA1A2.c. Add, subtract, multiply, and divide polynomials.

MA1A2.d. Add, subtract, multiply, and divide rational expressions.

MA1A2.e. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

MA1A2.f. Use area and volume models for polynomial arithmetic.

MA1A3. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MA1A3.a. Convert between standard and vertex form.

MA1A3.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MA1A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MA1A3.d. Explore arithmetic series and various ways of computing their sums.

MA1A3.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MA1A4. Students will solve quadratic equations and inequalities in one variable.

MA1A4.a. Solve equations graphically using appropriate technology.

MA1A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MA1A4.c. Analyze the nature of roots using technology and using the discriminant.

MA1A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MA1A5. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MA1A5.a. Write absolute value functions as piecewise functions.

MA1A5.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MA1A5.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

GA.MA1G. Accelerated Mathematics 1 - Geometry: Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons, circles and spheres, and determine distances and points of concurrence.

MA1G1. Students will investigate properties of geometric figures in the coordinate plane.

MA1G1.a. Determine the distance between two points.

MA1G1.b. Determine the distance between a point and a line.

MA1G1.c. Determine the midpoint of a segment.

MA1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MA1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

MA1G2. Students will understand and use the language of mathematical argument and justification.

MA1G2.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MA1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MA1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MA1G3.a. Determine the sum of interior and exterior angles in a polygon.

MA1G3.b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

MA1G3.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MA1G3.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MA1G3.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

MA1G4. Students will understand the properties of circles.

MA1G4.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MA1G4.b. Understand and use properties of central, inscribed, and related angles.

MA1G4.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MA1G4.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MA1G5. Students will find and compare the measures of spheres.

MA1G5.a. Use and apply surface area and volume of a sphere.

MA1G5.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MA1D. Accelerated Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will determine algebraic models from data.

MA1D1. Students will determine the number of outcomes related to a given event.

MA1D1.a. Apply the addition and multiplication principles of counting.

MA1D1.b. Calculate and use simple permutations and combinations.

MA1D2. Students will use the basic laws of probability.

MA1D2.a. Find the probabilities of mutually exclusive events.

MA1D2.b. Find the probabilities of dependent events.

MA1D2.c. Calculate conditional probabilities.

MA1D2.d. Use expected value to predict outcomes.

MA1D3. Students will relate samples to a population.

MA1D3.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MA1D3.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MA1D3.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MA1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

MA1D5. Students will determine an algebraic model to quantify the association between two quantitative variables.

MA1D5.a. Gather and plot data that can be modeled with linear and quadratic functions.

MA1D5.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and .eyeballing..

MA1D5.c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

GA.MA1P. Accelerated Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA1P1. Students will solve problems (using appropriate technology).

MA1P1.a. Build new mathematical knowledge through problem solving.

MA1P1.b. Solve problems that arise in mathematics and in other contexts.

MA1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA1P1.d. Monitor and reflect on the process of mathematical problem solving.

MA1P2. Students will reason and evaluate mathematical arguments.

MA1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA1P2.b. Make and investigate mathematical conjectures.

MA1P2.c. Develop and evaluate mathematical arguments and proofs.

MA1P2.d. Select and use various types of reasoning and methods of proof.

MA1P3. Students will communicate mathematically.

MA1P3.a. Organize and consolidate their mathematical thinking through communication.

MA1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA1P4. Students will make connections among mathematical ideas and to other disciplines.

MA1P4.a. Recognize and use connections among mathematical ideas.

MA1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA1P5. Students will represent mathematics in multiple ways.

MA1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA2A. Accelerated Mathematics 2 - Algebra: Students will investigate exponential, logarithmic, and polynomial functions of higher degree; understand matrices and use them to solve problems; and solve linear programming problems in two variables.

MA2A1. Students will explore exponential functions.

MA2A1.a. Extend properties of exponents to include all integer exponents.

MA2A1.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MA2A1.c. Graph functions as transformations of f(x) = a^x.

MA2A1.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MA2A1.e. Understand and use basic exponential functions as models of real phenomena.

MA2A1.f. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

MA2A1.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

MA2A2. Students will explore inverses of functions.

MA2A2.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MA2A2.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MA2A2.c. Explore the graphs of functions and their inverses.

MA2A2.d. Use composition to verify that functions are inverses of each other.

MA2A3. Students will analyze graphs of polynomial functions of higher degree.

MA2A3.a. Graph simple polynomial functions as translations of the function f(x) = ax^n.

MA2A3.b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

MA2A3.c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

MA2A3.d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

MA2A4. Students will explore logarithmic functions as inverses of exponential functions.

MA2A4.a. Define and understand the properties of nth roots.

MA2A4.b. Extend properties of exponents to include rational exponents.

MA2A4.c. Define logarithmic functions as inverses of exponential functions.

MA2A4.d. Understand and use properties of logarithms by extending laws of exponents.

MA2A4.e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

MA2A4.f. Graph functions as transformations of f(x) = a^x, f(x) = log ax, f(x) = e^x, f(x) = ln x.

MA2A4.g. Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

MA2A5. Students will solve a variety of equations and inequalities.

MA2A5.a. Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

MA2A5.b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

MA2A5.c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

MA2A5.d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

MA2A6. Students will perform basic operations with matrices.

MA2A6.a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

MA2A6.b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.

MA2A6.c. Examine the properties of matrices, contrasting them with properties of real numbers.

MA2A7. Students will use matrices to formulate and solve problems.

MA2A7.a. Represent a system of linear equations as a matrix equation.

MA2A7.b. Solve matrix equations using inverse matrices.

MA2A7.c. Represent and solve realistic problems using systems of linear equations.

MA2A8. Students will solve linear programming problems in two variables.

MA2A8.a. Solve systems of inequalities in two variables, showing the solutions graphically.

MA2A8.b. Represent and solve realistic problems using linear programming.

MA2A9. Students will understand and apply matrix representations of vertex-edge graphs.

MA2A9.a. Use graphs to represent realistic situations.

MA2A9.b. Use matrices to represent graphs, and solve problems that can be represented by graphs.

GA.MA2G. Accelerated Mathematics 2 - Geometry: Students will explore right triangles and right triangular trigonometry. They will understand and apply properties of conic sections, planes, and spheres.

MA2G1. Students will identify and use special right triangles.

MA2G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MA2G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MA2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MA2G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MA2G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MA2G2.c. Solve application problems using the trigonometric ratios.

MA2G3. Students will investigate the relationships between lines and circles.

MA2G3.a. Find equations of circles.

MA2G3.b. Graph a circle given an equation in general form.

MA2G3.c. Find the equation of a tangent line to a circle at a given point.

MA2G3.d. Solve a system of equations involving a circle and a line.

MA2G3.e. Solve a system of equations involving two circles.

MA2G4. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MA2G4.a. Convert equations of conics by completing the square.

MA2G4.b. Graph conic sections, identifying fundamental characteristics.

MA2G4.c. Write equations of conic sections given appropriate information.

MA2G5. Students will investigate planes and spheres.

MA2G5.a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

MA2G5.b. Apply the distance formula in 3-space.

MA2G5.c. Recognize and understand equations of planes and spheres.

GA.MA2D. Accelerated Mathematics 2 - Data Analysis and Probability: Students will make informal inferences about means and standard deviations. Students will use a normal distribution to calculate probabilities. Students will organize, represent, investigate, interpret, and make inferences from both observational studies and experiments.

MA2D1. Using sample data, students will make informal inferences about population means and standard deviations.

MA2D1.a. Pose a question and collect sample data from at least two different populations.

MA2D1.b. Understand and calculate the means and standard deviations of sets of data.

MA2D1.c. Use means and standard deviations to compare data sets.

MA2D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MA2D2. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

MA2D3. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

MA2D3.a. Determine intervals about the mean that include a given percent of data.

MA2D3.b. Determine the probability that a given value falls within a specified interval.

MA2D3.c. Estimate how many items in a population fall within a specified interval.

MA2D4. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

GA.MA2P. Accelerated Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA2P1. Students will solve problems (using appropriate technology).

MA2P1.a. Build new mathematical knowledge through problem solving.

MA2P1.b. Solve problems that arise in mathematics and in other contexts.

MA2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA2P1.d. Monitor and reflect on the process of mathematical problem solving.

MA2P2. Students will reason and evaluate mathematical arguments.

MA2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA2P2.b. Make and investigate mathematical conjectures.

MA2P2.c. Develop and evaluate mathematical arguments and proofs.

MA2P2.d. Select and use various types of reasoning and methods of proof.

MA2P3. Students will communicate mathematically.

MA2P3.a. Organize and consolidate their mathematical thinking through communication.

MA2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA2P4. Students will make connections among mathematical ideas and to other disciplines.

MA2P4.a. Recognize and use connections among mathematical ideas.

MA2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA2P5. Students will represent mathematics in multiple ways.

MA2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA3A. Accelerated Mathematics 3 - Algebra: Students will explore characteristics of various functions, understand and use concepts of trigonometric functions, investigate and apply sequences and series, and use parametric and polar equations to represent functions and curves.

MA3A1. Students will explore rational functions.

MA3A1.a. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

MA3A1.b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

MA3A1.c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

MA3A2. Students will use the circle to define the trigonometric functions.

MA3A2.a. Define and understand angles measured in degrees and radians, including but not limited to 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, their multiples, and equivalences.

MA3A2.b. Understand and apply the six trigonometric functions as functions of general angles in standard position.

MA3A2.c. Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

MA3A2.d. Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

MA3A2.e. Find values of trigonometric functions using the unit circle.

MA3A3. Students will investigate and use the graphs of the six trigonometric functions.

MA3A3.a. Understand and apply the six basic trigonometric functions as functions of real numbers.

MA3A3.b. Determine the characteristics of the graphs of the six basic trigonometric functions.

MA3A3.c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MA3A3.d. Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

MA3A4. Students will investigate functions.

MA3A4.a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

MA3A4.b. Investigate transformations of functions.

MA3A4.c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

MA3A5. Students will establish trigonometric identities and use them to simplify trigonometric expressions and verify equivalence statements.

MA3A6. Students will solve trigonometric equations both graphically and algebraically.

MA3A6.a. Solve trigonometric equations over a variety of domains, using technology as appropriate.

MA3A6.b. Use the coordinates of a point on the terminal side of an angle to express x and y as polar coordinates.

MA3A6.c. Apply the law of sines and the law of cosines.

MA3A7. Students will verify and apply 1/2 ab sinC to find the area of a triangle.

MA3A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

MA3A8.a. Find values of the above functions using technology as appropriate.

MA3A8.b. Determine characteristics of the above functions and their graphs.

MA3A9. Students will use sequences and series

MA3A9.a. Use and find recursive and explicit formulae for the terms of sequences.

MA3A9.b. Recognize and use simple arithmetic and geometric sequences.

MA3A9.c. Investigate limits of sequences.

MA3A9.d. Use mathematical induction to find and prove formulae for sums of finite series.

MA3A9.e. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

MA3A9.f. Use summation notation to explore series.

MA3A9.g. Determine geometric series and their limits.

MA3A10. Students will understand and use vectors.

MA3A10.a. Represent vectors algebraically and geometrically.

MA3A10.b. Convert between vectors expressed using rectangular coordinates and vectors expressed using magnitude and direction.

MA3A10.c. Add and subtract vectors and compute scalar multiples of vectors.

MA3A10.d. Use vectors to solve realistic problems.

MA3A11. Students will use complex numbers in trigonometric form.

MA3A11.a. Represent complex numbers in trigonometric form.

MA3A11.b. Find products, quotients, powers, and roots of complex numbers in trigonometric form.

MA3A12. Students will explore parametric representations of plane curves.

MA3A12.a. Convert between Cartesian and parametric form.

MA3A12.b. Graph equations in parametric form showing direction and beginning and ending points where appropriate.

MA3A13. Students will explore polar equations.

MA3A13.a. Express coordinates of points in rectangular and polar form.

MA3A13.b. Graph and identify characteristics of simple polar equations including lines, circles, cardioids, limacons, and roses.

GA.MA3D. Accelerated Mathematics 3 - Data Analysis and Probability: Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

MA3D1. Using simulation, students will develop the idea of the central limit theorem.

MA3D2. Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

MA3D3. Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

GA.MA3P. Accelerated Mathematics 3 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA3P1. Students will solve problems (using appropriate technology).

MA3P1.a. Build new mathematical knowledge through problem solving.

MA3P1.b. Solve problems that arise in mathematics and in other contexts.

MA3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA3P1.d. Monitor and reflect on the process of mathematical problem solving.

MA3P2. Students will reason and evaluate mathematical arguments.

MA3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA3P2.b. Make and investigate mathematical conjectures.

MA3P2.c. Develop and evaluate mathematical arguments and proofs.

MA3P2.d. Select and use various types of reasoning and methods of proof.

MA3P3. Students will communicate mathematically.

MA3P3.a. Organize and consolidate their mathematical thinking through communication.

MA3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA3P4. Students will make connections among mathematical ideas and to other disciplines.

MA3P4.a. Recognize and use connections among mathematical ideas.

MA3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA3P5. Students will represent mathematics in multiple ways.

MA3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MRC. Reading Across the Curriculum: Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.

MRC1. Students will enhance reading in all curriculum areas by:

MRC1.a. Reading in all curriculum areas: Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas; Read both informational and fictional texts in a variety of genres and modes of discourse; Read technical texts related to various subject areas

MRC1.b. Discussing books: Discuss messages and themes from books in all subject areas; Respond to a variety of texts in multiple modes of discourse; Relate messages and themes from one subject area to messages and themes in another area; Evaluate the merit of texts in every subject discipline; Examine author's purpose in writing; Recognize the features of disciplinary texts.

MRC1.c. Building vocabulary knowledge: Demonstrate an understanding of contextual vocabulary in various subjects; Use content vocabulary in writing and speaking; Explore understanding of new words found in subject area texts.

MRC1.d. Establishing context: Explore life experiences related to subject area content; Discuss in both writing and speaking how certain words are subject area related; Determine strategies for finding content and contextual meaning for unknown words.