### IM: Introductory Mathematics

#### IM.1: The learner will understand and compute with real numbers.

IM.1.01: Develop number sense for the real numbers.

IM.1.01.b: Compare and order.

#### IM.2: The learner will use properties and relationships in geometry and measurement concepts to solve problems.

IM.2.01: Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.

IM.2.04: Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.

IM.2.05: Identify, predict, and describe dilations in the coordinate plane.

#### IM.3: The learner will understand and use graphs and data analysis.

IM.3.01: Collect, organize, analyze, and display data (including scatterplots) to solve problems.

IM.3.02: Approximate a line of best fit for a given scatterplot; explain the meaning of the line as it relates to the problem and make predictions.

#### IM.4: The learner will understand and use linear relations and functions.

IM.4.01: Develop an understanding of function.

IM.4.01.a: Translate among verbal, tabular, graphic, and algebraic representations of functions.

IM.4.01.b: Identify relations and functions as linear or nonlinear.

IM.4.01.c: Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.

IM.4.01.d: Interpret and compare properties of linear functions from tables, graphs, or equations.

IM.4.02: Write an equation of a linear relationship given: two points, the slope and one point on the line, or the slope and y-intercept.

IM.4.03: Solve problems using linear equations and inequalities; justify symbolically and graphically.

IM.4.04: Solve problems using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots.

### A1: Algebra 1

#### A1.1: The learner will perform operations with numbers and expressions to solve problems.

A1.1.01: Write equivalent forms of algebraic expressions to solve problems.

A1.1.01.a: Apply the laws of exponents.

A1.1.01.b: Operate with polynomials.

A1.1.01.c: Factor polynomials.

A1.1.03: Model and solve problems using direct variation.

#### A1.2: The learner will describe geometric figures in the coordinate plane algebraically.

A1.2.01: Find the lengths and midpoints of segments to solve problems.

A1.2.02: Use the parallelism or perpendicularity of lines and segments to solve problems.

#### A1.4: The learner will use relations and functions to solve problems.

A1.4.01: Use linear functions or inequalities to model and solve problems; justify results.

A1.4.01.a: Solve using tables, graphs, and algebraic properties.

A1.4.01.b: Interpret constants and coefficients in the context of the problem.

A1.4.02: Graph, factor, and evaluate quadratic functions to solve problems.

A1.4.03: Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify results.

A1.4.04: Graph and evaluate exponential functions to solve problems.

### GE: Geometry

#### GE.1: The learner will perform operations with real numbers to solve problems.

GE.1.01: Use the trigonometric ratios to model and solve problems involving right triangles.

GE.1.02: Use length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

GE.1.03: Use length, area, and volume to model and solve problems involving probability.

#### GE.2: The learner will use geometric and algebraic properties of figures to solve problems and write proofs.

GE.2.02: Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.

GE.2.03: Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:

GE.2.03.a: Triangles.

GE.2.04: Develop and apply properties of solids to solve problems.

#### GE.3: The learner will transform geometric figures in the coordinate plane algebraically.

GE.3.01: Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms.

### A2: Algebra 2

#### A2.1: The learner will perform operations with complex numbers, matrices, and polynomials.

A2.1.02: Define and compute with complex numbers.

A2.1.05: Model and solve problems using direct, inverse, combined and joint variation.

#### A2.2: The learner will use relations and functions to solve problems.

A2.2.01: Use the composition and inverse of functions to model and solve problems; justify results.

A2.2.02: Use quadratic functions and inequalities to model and solve problems; justify results.

A2.2.02.a: Solve using tables, graphs, and algebraic properties.

A2.2.02.b: Interpret the constants and coefficients in the context of the problem.

A2.2.03: Use exponential functions to model and solve problems; justify results.

A2.2.03.a: Solve using tables, graphs, and algebraic properties.

A2.2.03.b: Interpret the constants, coefficients, and bases in the context of the problem.

A2.2.04: Create and use best-fit mathematical models of linear, exponential, and quadratic functions to solve problems involving sets of data.

A2.2.04.a: Interpret the constants, coefficients, and bases in the context of the data.

A2.2.04.b: Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

A2.2.05: Use rational equations to model and solve problems; justify results.

A2.2.05.b: Interpret the constants and coefficients in the context of the problem.

A2.2.05.c: Identify the asymptotes and intercepts graphically and algebraically.

A2.2.06: Use cubic equations to model and solve problems.

A2.2.06.a: Solve using tables and graphs.

A2.2.06.b: Interpret constants and coefficients in the context of the problem.

A2.2.07: Use equations with radical expressions to model and solve problems; justify results.

A2.2.07.a: Solve using tables, graphs, and algebraic properties.

A2.2.07.b: Interpret the degree, constants, and coefficients in the context of the problem.

A2.2.08: Use equations and inequalities with absolute value to model and solve problems; justify results.

A2.2.08.a: Solve using tables, graphs, and algebraic properties.

A2.2.08.b: Interpret the constants and coefficients in the context of the problem.

A2.2.09: Use the equations of parabolas and circles to model and solve problems; justify results.

A2.2.09.a: Solve using tables, graphs, and algebraic properties.

A2.2.09.b: Interpret the constants and coefficients in the context of the problem.

A2.2.10: Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties.

### T1: Technical Mathematics 1

#### T1.1: The learner will apply various strategies to solve problems.

T1.1.01: Apply various techniques and strategies to solve problems.

T1.1.01.b: Identify and represent patterns using appropriate algebraic notation.

#### T1.2: The learner will measure and apply geometric concepts to solve problems.

T1.2.01: Select and use appropriate tools to measure two- and three-dimensional figures; interpret and communicate results with regard to precision.

T1.2.03: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

T1.2.04: Use the trigonometric ratios to model and solve problems involving right triangles.

#### T1.3: The learner will describe the transformation of polygons in the coordinate plane algebraically.

T1.3.02: Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms.

### T2: Technical Mathematics 2

#### T2.1: The learner will use properties of geometric figures to solve problems.

T2.1.02: Apply the properties and definitions of plane figures to model and solve problems:

T2.1.02.a: Triangles.

#### T2.2: The learner will use relations and functions to solve problems.

T2.2.02: Use exponential functions to model and solve problems; justify results.

T2.2.02.a: Solve using tables, graphs, and algebraic properties.

T2.2.02.b: Interpret the constants, coefficients, and bases in the context of the problem.

T2.2.03: Create, interpret, and analyze best-fit models of linear, exponential, and quadratic functions to solve problems.

T2.2.03.a: Interpret the constants, coefficients, and bases in the context of the data.

T2.2.04: Use systems of equations and inequalities to model and solve problems using tables, graphs, matrix operations, and algebraic properties; justify results.

### AF: Advanced Functions and Modeling

#### AF.1: The learner will analyze data and apply probability concepts to solve problems.

AF.1.01: Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, and logarithmic functions of bivariate data to solve problems.

AF.1.01.a: Interpret the constants, coefficients, and bases in the context of the data.

AF.1.01.b: Check models for goodness-of-fit; use the most appropriate model to draw conclusions and make predictions.

AF.1.02: Summarize and analyze univariate data to solve problems.

AF.1.02.c: Determine measures of central tendency and spread.

AF.1.02.e: Interpret graphical displays of univariate data.

AF.1.02.f: Compare distributions of univariate data.

AF.1.03: Use theoretical and experimental probability to model and solve problems.

AF.1.03.b: Calculate and apply permutations and combinations.

AF.1.03.c: Create and use simulations for probability models.

AF.1.03.f: Apply the Binomial Theorem.

#### AF.2: The learner will use functions to solve problems.

AF.2.01: Use logarithmic (common, natural) functions to model and solve problems; justify results.

AF.2.01.a: Solve using tables, graphs, and algebraic properties.

AF.2.01.b: Interpret the constants, coefficients, and bases in the context of the problem.

AF.2.02: Use piecewise-defined functions to model and solve problems; justify results.

AF.2.02.a: Solve using tables, graphs, and algebraic properties.

AF.2.02.b: Interpret the constants, coefficients, and bases in the context of the problem.

AF.2.03: Use power functions to model and solve problems; justify results.

AF.2.03.a: Solve using tables, graphs, and algebraic properties.

AF.2.03.b: Interpret the constants, coefficients, and bases in the context of the problem.

AF.2.04: Use trigonometric (sine, cosine) functions to model and solve problems; justify results.

AF.2.04.a: Solve using tables, graphs, and algebraic properties.

AF.2.04.b: Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.

AF.2.04.c: Develop and use the law of sines and the law of cosines.

AF.2.05: Use recursively-defined functions to model and solve problems.

AF.2.05.d: Translate between recursive and explicit representations.

### DM: Discrete Mathematics

#### DM.1: The learner will use matrices and graphs to model relationships and solve problems.

DM.1.01: Use matrices to model and solve problems.

DM.1.01.a: Display and interpret data.

#### DM.2: The learner will analyze data and apply probability concepts to solve problems.

DM.2.01: Describe data to solve problems.

DM.2.01.c: Determine measures of central tendency and spread.

DM.2.01.e: Interpret graphical displays of data.

DM.2.01.f: Compare distributions of data.

DM.2.02: Use theoretical and experimental probability to model and solve problems.

DM.2.02.b: Calculate and apply permutations and combinations.

DM.2.02.c: Create and use simulations for probability models.

DM.2.02.f: Apply the Binomial Theorem.

#### DM.3: The learner will describe and use recursively-defined relationships to solve problems.

DM.3.01: Use recursion to model and solve problems.

DM.3.01.d: Write explicit definitions using iterative processes, including finite differences and arithmetic and geometric formulas.

### PC: Pre-Calculus

#### PC.1: The learner will describe geometric figures in the coordinate plane algebraically.

PC.1.01: Transform relations in two dimensions; describe the results algebraically and geometrically.

PC.1.02: Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results.

PC.1.02.a: Solve using tables, graphs, and algebraic properties.

PC.1.02.b: Interpret the constants and coefficients in the context of the problem.

#### PC.2: The learner will use relations and functions to solve problems.

PC.2.01: Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise-defined, and greatest integer) to model and solve problems; justify results.

PC.2.01.a: Solve using graphs and algebraic properties.

PC.2.01.b: Interpret the constants, coefficients, and bases in the context of the problem.

PC.2.02: Use trigonometric and inverse trigonometric functions to model and solve problems; justify results.

PC.2.02.a: Solve using graphs and algebraic properties.

PC.2.02.b: Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.

PC.2.03: For sets of data, create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions.

PC.2.03.a: Interpret the constants, coefficients, and bases in the context of the data.

PC.2.04: Use the composition and inverse of functions to model and solve problems.

PC.2.05: Use polar equations to model and solve problems.

PC.2.05.a: Solve using graphs and algebraic properties.

PC.2.06: Use parametric equations to model and solve problems.

PC.2.07: Use recursively-defined functions to model and solve problems.

PC.2.07.d: Translate between recursive and explicit representations.

### I1: Integrated Mathematics 1

#### I1.1: The learner will perform operations with numbers and expressions to solve problems.

I1.1.01: Write equivalent forms of algebraic expressions to solve problems.

I1.1.01.a: Apply the laws of exponents.

I1.1.01.b: Operate with polynomials.

I1.1.01.c: Factor polynomials.

I1.1.02: Use algebraic expressions, including iterative and recursive forms, to model and solve problems.

#### I1.2: The learner will use properties of geometric figures to solve problems.

I1.2.01: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

I1.2.02: Develop and apply properties of solids to solve problems.

#### I1.3: The learner will analyze data and apply probability concepts to solve problems.

I1.3.02: Use theoretical and experimental probability to model and solve problems.

I1.3.02.b: Calculate and apply permutations and combinations.

I1.3.02.c: Create and use simulations for probability models.

I1.3.03: Create linear and exponential models, for sets of data, to solve problems.

I1.3.03.a: Interpret the constants, coefficients, and bases in the context of the data.

I1.3.03.b: Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

#### I1.4: The learner will use relations and functions to solve problems.

I1.4.01: Use linear functions or inequalities to model and solve problems; justify results.

I1.4.01.a: Solve using tables, graphs, and algebraic properties.

I1.4.01.b: Interpret the constants and coefficients in the context of the problem.

I1.4.02: Use exponential functions to model and solve problems; justify results.

I1.4.02.a: Solve using tables, graphs, and algebraic properties.

I1.4.02.b: Interpret the constants, coefficients, and bases in the context of the problem.

I1.4.03: Use systems of linear equations or inequalities in two variables to model problems and solve graphically.

### I2: Integrated Mathematics 2

#### I2.1: The learner will perform operations with numbers, algebraic expressions, and matrices to solve problems.

I2.1.03: Model and solve problems using direct variation.

#### I2.2: The learner will describe geometric figures in the coordinate plane algebraically.

I2.2.01: Find the lengths and midpoints of segments to solve problems.

I2.2.03: Use the trigonometric ratios to model and solve problems.

I2.2.04: Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms.

#### I2.3: The learner will collect, organize, and interpret data to solve problems.

I2.3.01: Describe data to solve problems.

I2.3.01.c: Determine measures of central tendency and spread.

I2.3.01.f: Compare distributions of data.

I2.3.02: Create and use, for sets of data, calculator-generated models of linear, exponential, and quadratic functions to solve problems.

I2.3.02.a: Interpret the constants, coefficients, and bases in the context of the data.

#### I2.4: The learner will use relations and functions to solve problems.

I2.4.01: Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify steps used.

I2.4.02: Use quadratic functions to model and solve problems; justify results.

I2.4.02.a: Solve using tables, graphs, and algebraic properties.

I2.4.02.b: Interpret the constants and coefficients in the context of the problem.

I2.4.03: Use power models to solve problems.

I2.4.03.a: Solve using tables, graphs, and algebraic properties.

### I3: Integrated Mathematics 3

#### I3.1: The learner will perform operations with numbers and algebraic expressions to solve problems.

I3.1.02: Use algebraic expressions, including iterative and recursive forms, to model and solve problems.

I3.1.04: Model and solve problems using direct, inverse, combined and joint variation.

#### I3.2: The learner will use properties of geometric figures to solve problems.

I3.2.02: Apply the properties, definitions, and theorems of angles and lines to solve problems and write proofs.

I3.2.03: Apply the properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:

I3.2.03.a: Triangles.

I3.2.03.c: Other polygons.

I3.2.03.d: Circles.

I3.2.04: Use the law of sines and law of cosines to solve problems.

#### I3.3: The learner will use relations and functions to solve problems.

I3.3.01: Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties.

I3.3.02: Use quadratic functions and inequalities to model and solve problems; justify results.

I3.3.02.a: Solve using tables, graphs, and algebraic properties.

I3.3.02.b: Interpret the constants and coefficients in the context of the problem.

I3.3.03: Use rational equations to model and solve problems; justify results.

I3.3.03.a: Solve using tables, graphs, and algebraic properties.

I3.3.03.b: Interpret the constants and coefficients in the context of the problem.

I3.3.03.c: Identify the asymptotes and intercepts graphically and algebraically.

I3.3.04: Use equations and inequalities with absolute value to model and solve problems; justify results.

I3.3.04.a: Solve using tables, graphs, and algebraic properties.

I3.3.04.b: Interpret the constants and coefficients in the context of the problem.

I3.3.05: Transform functions in two dimensions; describe the results algebraically and geometrically.

### I4: Integrated Mathematics 4

#### I4.1: The learner will operate with complex numbers and vectors to solve problems.

I4.1.02: Define and compute with complex numbers.

#### I4.2: The learner will describe geometric figures in the coordinate plane algebraically.

I4.2.01: Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results.

I4.2.01.a: Solve using tables, graphs, and algebraic properties.

I4.2.01.b: Interpret the constants and coefficients in the context of the problem.

I4.2.02: Estimate the area and volume of continuously varying quantities.

#### I4.3: The learner will analyze data to solve problems.

I4.3.01: Analyze univariate data to solve problems.

I4.3.01.c: Determine measures of central tendency and spread.

I4.3.01.e: Interpret graphical displays of distributions of univariate data.

I4.3.01.f: Compare distributions of univariate data.

I4.3.02: Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions of bivariate data to solve problems.

I4.3.02.a: Interpret the constants, coefficients, and bases in the context of the data.

#### I4.4: The learner will use relations and functions to solve problems.

I4.4.01: Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise-defined, and greatest integer) to model and solve problems; justify results.

I4.4.01.a: Solve using graphs and algebraic properties.

I4.4.01.b: Interpret the constants, coefficients, and bases in the context of the problem.

I4.4.02: Use recursively-defined functions to model and solve problems.

I4.4.02.d: Translate between recursive and explicit representations.

I4.4.03: Use the composition and inverse of functions to model and solve problems.

I4.4.04: Use trigonometric and inverse trigonometric functions to model and solve problems.

I4.4.04.a: Solve using graphs and algebraic properties.

I4.4.04.b: Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.

I4.4.05: Use polar equations to model and solve problems.

I4.4.05.a: Solve using graphs and algebraic properties.

I4.4.06: Use parametric equations to model and solve problems.

I4.4.07: Find the rate of change at any point of a function.

#### AS.1: The learner will analyze univariate data to solve problems.

AS.1.01: Summarize distributions of univariate data by determining and interpreting measures of center, spread, position, boxplots, and effects of changing units on summary measures.

#### AS.2: The learner will construct and interpret displays of univariate data to solve problems.

AS.2.01: Construct and interpret graphical displays of univariate data.

AS.2.02: Compare distributions among sets of univariate data.

#### AS.3: The learner will collect and analyze date to solve problems.

AS.3.07: Simulate sampling distributions.

AS.3.08: Use simulations to develop an understanding of the Central Limit Theorem and its importance in confidence intervals and tests of significance.

#### AS.4: The learner will analyze bivariate data to solve problems.

AS.4.01: Analyze bivariate data.

AS.4.01.a: Recognize and analyze correlation and linearity.

#### AC.1: The learner will demonstrate an understanding of the behavior of functions.

AC.1.02: Recognize and describe the nature of aberrant behavior caused by asymptotes and unboundedness.

AC.1.02.c: Compare relative magnitudes of functions and their rates of change.

AC.1.03: Identify and demonstrate an understanding of continuity of functions.

AC.1.03.a: Develop an intuitive understanding of continuity. (Close values of the domain lead to close values of the range.)

#### AC.2: The learner will use derivatives to solve problems.

AC.2.02: Apply the concept of the derivative at a point.

AC.2.02.c: Find the instantaneous rate of change as the limit of average rate of change.

AC.2.02.d: Approximate a rate of change from graphs and tables of values.

AC.2.03: Interpret the derivative as a function.

AC.2.03.d: Translate between verbal and algebraic descriptions of equations involving derivatives.

AC.2.06: Apply the derivative in graphing and modeling contexts.

AC.2.06.d: Use implicit differentiation to find the derivative of an inverse function.

AC.2.06.e: Interpret the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.

#### AC.3: The learner will use integrals to solve problems.

AC.3.01: Explore and interpret the concept of the definite integral.

AC.3.01.a: Compute Riemann sums using left, right, and midpoint evaluation points.

AC.3.01.b: Find the definite integral as a limit of Riemann sums over equal subdivisions.

AC.3.04: Define and use appropriate integrals in a variety of applications.

AC.3.04.c: Set up and use an approximating Riemann sum or trapezoidal sum and represent its limit as a definite integral.

AC.3.04.d: Find the area of a region.

AC.3.04.g: Find the distance traveled by a particle along a line.

Correlation last revised: 11/2/2009

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