### A1: Algebra

#### A1.1: Solving Problems

A1.1.B: Solve problems that can be represented by linear functions, equations, and inequalities.

A1.1.C: Solve problems that can be represented by a system of two linear equations or inequalities.

A1.1.D: Solve problems that can be represented by quadratic functions and equations.

A1.1.E: Solve problems that can be represented by exponential functions and equations.

#### A1.2: Numbers, expressions, and operations

A1.2.B: Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables.

A1.2.C: Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions.

A1.2.E: Use algebraic properties to factor and combine like terms in polynomials.

A1.2.F: Add, subtract, multiply, and divide polynomials.

#### A1.3: Characteristics and behaviors of functions

A1.3.A: Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables.

A1.3.B: Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations.

#### A1.4: Linear functions, equations, and inequalities

A1.4.A: Write and solve linear equations and inequalities in one variable.

A1.4.B: Write and graph an equation for a line given the slope and the yintercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations.

A1.4.C: Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.

A1.4.D: Write and solve systems of two linear equations and inequalities in two variables.

A1.4.E: Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent.

#### A1.5: Quadratic functions and equations

A1.5.A: Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations.

A1.5.B: Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation.

A1.5.C: Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers.

A1.5.D: Solve quadratic equations that have real roots by completing the square and by using the quadratic formula.

#### A1.6: Data and distributions

A1.6.C: Describe how linear transformations affect the center and spread of univariate data.

A1.6.D: Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.

A1.6.E: Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative.

A1.7.A: Sketch the graph for an exponential function of the form y = abn where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.

A1.7.C: Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.

### G: Geometry

#### G.1: Logical arguments and proofs

G.1.D: Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.

#### G.2: Lines and Angles

G.2.B: Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal

G.2.C: Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines.

#### G.3: Two- and three-dimensional figures

G.3.B: Determine and prove triangle congruence, triangle similarity, and other properties of triangles.

G.3.E: Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.

G.3.F: Know, prove, and apply basic theorems about parallelograms.

G.3.H: Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles.

G.3.I: Explain and perform constructions related to the circle.

#### G.5: Geometric transformations

G.5.A: Sketch results of transformations and compositions of transformations for a given two-dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axes or the line y = x.

G.5.C: Given two congruent or similar figures in a coordinate plane, describe a composition of translations, reflections, rotations, and dilations that superimposes one figure on the other.

G.5.D: Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.

G.6.C: Apply formulas for surface area and volume of three-dimensional figures to solve problems.

G.6.D: Predict and verify the effect that changing one, two, or three linear dimensions has on perimeter, area, volume, or surface area of two- and three-dimensional figures.

G.6.E: Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose.

#### G.7: Reasoning, problem solving, and communication

G.7.H: Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.

### A2: Algebra 2

#### A2.1: Solving Problems

A2.1.C: Solve problems that can be represented by quadratic functions, equations, and inequalities.

A2.1.D: Solve problems that can be represented by exponential and logarithmic functions and equations.

A2.1.F: Solve problems involving combinations and permutations.

#### A2.3: Quadratic functions and equations

A2.3.A: Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.

A2.3.B: Determine the number and nature of the roots of a quadratic function.

A2.3.C: Solve quadratic equations and inequalities, including equations with complex roots.

#### A2.4: Exponential and logarithmic functions and equations

A2.4.A: Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.

A2.4.B: Graph an exponential function of the form f(x) = abx and its inverse logarithmic function.

#### A2.5: Additional functions and equations

A2.5.A: Construct new functions using the transformations f(x - h), f(x) + k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s).

A2.5.B: Plot points, sketch, and describe the graphs of functions of the form f (x) = a times the square root of x - c + d , and solve related equations.

A2.5.C: Plot points, sketch, and describe the graphs of functions of the form (x) = a/x + b, f(x) = a/x² + b, and f(x) = a/(bx + c), and solve related equations.

A2.5.D: Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.

#### A2.6: Probability, data, and distributions

A2.6.A: Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events).

A2.6.B: Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B.

A2.6.C: Compute permutations and combinations, and use the results to calculate probabilities.

A2.6.E: Determine if a bivariate data set can be better modeled with an exponential or a quadratic function and use the model to make predictions.

A2.7.B: Find the terms and partial sums of arithmetic and geometric series and the infinite sum for geometric series.

### M1: Mathematics 1

#### M1.1: Solving problems

M1.1.B: Solve problems that can be represented by linear functions, equations, and inequalities.

M1.1.D: Solve problems that can be represented by exponential functions and equations.

#### M1.2: Characteristics and behaviors of functions

M1.2.A: Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables.

M1.2.B: Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations.

M1.2.D: Plot points, sketch, and describe the graphs of functions of the form f(x) = a/x + b.

#### M1.3: Linear functions, equations, and relationships

M1.3.A: Write and solve linear equations and inequalities in one variable.

M1.3.B: Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent.

M1.3.C: Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.

M1.3.D: Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations.

M1.3.E: Write and solve systems of two linear equations and inequalities in two variables.

M1.3.F: Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.

M1.3.G: Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative.

#### M1.4: Proportionality, similarity, and geometric reasoning

M1.4.D: Determine and prove triangle similarity.

M1.4.F: Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal.

M1.4.G: Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines.

#### M1.5: Data and distributions

M1.5.B: Describe how linear transformations affect the center and spread of univariate data.

#### M1.6: Numbers, expressions, and operations

M1.6.C: Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables.

M1.7.A: Sketch the graph for an exponential function of the form y = ab to the n power where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.

M1.7.C: Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions.

M1.7.D: Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.

#### M1.8: Reasoning, problem solving, and communication

M1.8.H: Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.

### M2: Mathematics 2

#### M2.1: Modeling situations and solving problems

M2.1.C: Solve problems that can be represented by quadratic functions, equations, and inequalities.

M2.1.D: Solve problems that can be represented by exponential functions and equations.

M2.1.E: Solve problems involving combinations and permutations.

#### M2.2: Quadratic functions, equations, and relationships

M2.2.A: Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations.

M2.2.B: Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation.

M2.2.C: Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.

M2.2.D: Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers.

M2.2.E: Determine the number and nature of the roots of a quadratic function.

M2.2.F: Solve quadratic equations that have real roots by completing the square and by using the quadratic formula.

M2.2.G: Solve quadratic equations and inequalities, including equations with complex roots.

M2.2.H: Determine if a bivariate data set can be better modeled with an exponential or a quadratic function and use the model to make predictions.

#### M2.3: Conjectures and proofs

M2.3.C: Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.

M2.3.F: Determine and prove triangle congruence and other properties of triangles.

M2.3.H: Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.

M2.3.J: Know, prove, and apply basic theorems about parallelograms.

#### M2.4: Probability

M2.4.A: Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events).

M2.4.B: Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B.

M2.4.C: Compute permutations and combinations, and use the results to calculate probabilities.

M2.5.A: Use algebraic properties to factor and combine like terms in polynomials.

M2.5.B: Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose.

M2.5.D: Find the terms and partial sums of arithmetic and geometric series and the infinite sum for geometric series.

#### M2.6: Reasoning, problem solving, and communication

M2.6.H: Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.

### M3: Mathematics 3

#### M3.1: Solving problems

M3.1.C: Solve problems that can be represented by quadratic functions, equations, and inequalities.

M3.1.D: Solve problems that can be represented by exponential and logarithmic functions and equations.

#### M3.2: Transformations and functions

M3.2.A: Sketch results of transformations and compositions of transformations for a given two-dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axes or the line y = x.

M3.2.C: Given two congruent or similar figures in a coordinate plane, describe a composition of translations, reflections, rotations, and dilations that superimposes one figure on the other.

M3.2.D: Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.

M3.2.E: Construct new functions using the transformations f(x - h), f(x) + k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s).

#### M3.3: Functions and modeling

M3.3.A: Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.

M3.3.B: Graph an exponential function of the form f(x) = ab to the x power and its inverse logarithmic function.

M3.3.D: Plot points, sketch, and describe the graphs of functions of the form f (x) = a times the square root of x - c + d, and solve related equations.

M3.3.E: Plot points, sketch, and describe the graphs of functions of the form f(x) = a/x² + b and f(x) = a/(bx + c), and solve related equations.

M3.3.F: Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.

#### M3.5: Three-dimensional geometry

M3.5.D: Apply formulas for surface area and volume of three-dimensional figures to solve problems.

M3.5.E: Predict and verify the effect that changing one, two, or three linear dimensions has on perimeter, area, volume, or surface area of two- and three-dimensional figures.

#### M3.6: Algebraic properties

M3.6.C: Add, subtract, multiply, and divide polynomials.