#### A.1: Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots, radical form, or decimal approximations.

A.1.1: Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents

#### A.2: Analyze linear functions from their equations, slopes, and intercepts.

A.2.1: Finding the slope of a line from its equation or by applying the slope formula

A.2.2: Determining the equations of linear functions given two points, a point and the slope, tables of values, graphs, or ordered pairs

A.2.3: Graphing two-variable linear equations and inequalities on the Cartesian plane

#### A.3: Determine characteristics of a relation, including its domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs.

A.3.1: Finding the range of a function when given its domain

#### A.4: Represent graphically common relations, including x = constant, y = constant, y = x, y = square root of x , y = x² , and y = |x|.

A.4.1: Identifying situations that are modeled by common relations, including x = constant, y = constant, y = x, y = square root of x , y = x², and y = |x|

#### A.5: Perform operations of addition, subtraction, and multiplication on polynomial expressions.

A.5.1: Dividing by a monomial

#### A.7: Solve multistep equations and inequalities including linear, radical, absolute value, and literal equations.

A.7.1: Writing the solution of an equation or inequality in set notation

A.7.2: Graphing the solution of an equation or inequality

A.7.3: Modeling real-world problems by developing and solving equations and inequalities, including those involving direct and inverse variation

#### A.8: Solve systems of linear equations and inequalities in two variables graphically or algebraically.

A.8.1: Modeling real-world problems by developing and solving systems of linear equations and inequalities

#### A.9: Solve quadratic equations using the zero product property.

A.9.1: Approximating solutions graphically and numerically

#### A.10: Calculate length, midpoint, and slope of a line segment when given coordinates of its endpoints on the Cartesian plane.

A.10.1: Deriving the distance, midpoint, and slope formulas

#### A.15: Estimate probabilities given data in lists or graphs.

A.15.1: Comparing theoretical and experimental probabilities

#### G.3: Verify the relationships among different classes of polygons by using their properties.

G.3.1: Determining the missing lengths of sides or measures of angles in similar polygons

#### G.4: Determine the measure of interior and exterior angles associated with polygons.

G.4.1: Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively

#### G.5: Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes.

G.5.1: Determining the equation of a circle given its center and radius

#### G.7: Use the ratios of the sides of special right triangles to find lengths of missing sides.

G.7.1: Deriving the ratios of the sides of 30-60-90 and 45-45-90 triangles

#### G.8: Deduce relationships between two triangles, including proving congruence or similarity of the triangles from given information, using them to solve problems and to establish other relationships.

G.8.1: Determining the geometric mean to find missing lengths in right triangles

#### G.14: Classify polyhedrons according to their properties, including the number of faces.

G.14.1: Identifying Euclidean solids

#### G.16: Calculate surface areas and volumes of solid figures, including spheres, cones, and pyramids.

G.16.1: Developing formulas for surface area and volume of spheres, cones, and pyramids

G.16.2: Calculating specific missing dimensions of solid figures from surface area or volume

G.16.3: Determining the relationship between the surface areas of similar figures and volumes of similar figures

#### G.17: Analyze sets of data from geometric contexts to determine what, if any, relationships exist.

G.17.1: Distinguishing between conclusions drawn when using deductive and statistical reasoning

G.17.2: Calculating probabilities arising in geometric contexts

#### G.18: Construct with precision a circle graph to represent data from given tables or classroom experiments.

G.1.1: Generating, manually or with technological tools, graphs and tables related to personal finance and economics

#### AII.3: Analyze families of functions, including shifts, reflections, and dilations of y = k/x (inverse variation), y = kx (direct variation/linear), y = x² (quadratic), y = a to the x power (exponential), and y = log to base a of x (logarithmic).

AII.3.1: Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains

#### AII.4: Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions.

AII.4.1: Using completing the square, the zero product property, and the quadratic formula

#### AII.5: Identify the characteristics of quadratic functions from their roots, graphs, or equations.

AII.5.1: Writing an equation when given its roots or graph

AII.5.3: Determining the nature of the solutions of a quadratic equation

AII.5.4: Determining the maximum or minimum values of quadratic functions both graphically and algebraically

#### AII.6: Perform operations on functions, including addition, subtraction, multiplication, division, and composition.

AII.6.2: Performing operations on polynomial and rational expressions containing variables

#### AII.7: Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as exponential and logarithmic functions.

AII.7.2: Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation

#### AII.11: Determine an equation of linear regression from a set of data.

AII.11.1: Examining data to determine if a linear or quadratic relationship exists and to predict outcomes

#### AII.12: Calculate probabilities of events using the laws of probability.

AII.12.1: Using permutations and combinations to calculate probabilities

AII.12.3: Calculating probabilities of mutually exclusive events, independent events, and dependent events

#### AIIT.3: Analyze families of functions, including shifts, reflections, and dilations of y = k/x (inverse variation), y = kx (direct variation/linear), y = [x] (greatest integer), y = x² (quadratic), y = a to the x power (exponential), and y = log to the base a of x (logarithmic).

AIIT.3.1: Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains

#### AIIT.4: Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions.

AIIT.4.1: Using the zero product property, completing the square, and the quadratic formula

#### AIIT.5: Identify the characteristics of quadratic functions from their roots, graphs, or equations.

AIIT.5.1: Generating an equation when given its roots or graph

AIIT.5.3: Determining the maximum or minimum values of quadratic functions both graphically and algebraically

#### AIIT.6: Perform operations on functions, including addition, subtraction, multiplication, division, and composition.

AIIT.6.2: Performing operations on polynomial and rational expressions containing variables

AIIT.6.3: Constructing graphs by analyzing their functions as sums, differences, or products

#### AIIT.7: Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as simple trigonometric, exponential, and logarithmic functions.

AIIT.7.1: Solving equations using laws of exponents, including rational and irrational exponents

AIIT.7.2: Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation

#### AIIT.9: Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y=a tan(bx).

AIIT.9.1: Determining period and amplitude of sine, cosine, and tangent functions from graphs or basic equations

AIIT.9.2: Determining specific unit circle coordinates associated with special angles

#### AIIT.10: Solve general triangles, mathematical problems, and real-world applications using the Law of Sines and the Law of Cosines.

AIIT.10.2: Determining area of oblique triangles

#### AIIT.14: Determine an equation of linear regression from a set of data.

AIIT.14.1: Examining data to determine if a linear, quadratic, or exponential relationship exists and to predict outcomes

#### AIIT.15: Calculate probabilities of events using the laws of probability.

AIIT.15.1: Using permutations and combinations to calculate probabilities

AIIT.15.2: Calculating conditional probability

AIIT.15.3: Calculating probabilities of mutually exclusive events, independent events, and dependent events

#### AIII.3: Graph conic sections, centered at and rotated about the origin, given the equations.

AIII.3.1: Determining equations of conic sections from their graphs

#### AIII.4: Graph polynomial functions.

AIII.4.1: Approximating zeros using Descartes’ Rule of Signs and the bisection method

AIII.4.2: Describing the end behavior of a polynomial function given its degree and leading coefficient

#### AIII.10: Calculate descriptive statistics of univariate data, including measures of central tendency, measures of dispersion, and measures of position.

AIII.10.1: Defining vocabulary associated with probability and statistics, including descriptive and inferential statistics

AIII.10.2: Comparing descriptive statistics for samples of varying sizes generated by simulation

#### AIII.11: Interpret relationships of bivariate data using linear or quadratic regression and linear correlation.

AIII.11.1: Testing a hypothesis by displaying a scatterplot of experimental data, determining the regression coefficient and equation, and determining the correlation coefficient

#### AIII.14: Determine the probability of an event using a frequency distribution curve.

AIII.14.1: Comparing the terms of a binomial expansion to the terms of a binomial probability distribution

#### P.3: Graph conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.

P.3.1: Formulating equations of conic sections from their determining characteristics

#### P.5: Analyze the effects of parameter changes on the graphs of trigonometric, logarithmic, and exponential functions.

P.5.1: Determining the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses

#### P.7: Solve trigonometric equations and inequalities using sum, difference, and half-and double-angle identities.

P.7.1: Verifying trigonometric identities

#### P.9: Solve applied problems involving sequences with recurrence relations.

P.9.1: Determining characteristics of arithmetic and geometric sequences and series, including those defined with recurrence relations, first terms, common differences or ratios, n th terms, limits, or statements of convergence or divergence

#### P.11: Convert coordinates, equations, and complex numbers in Cartesian form to polar form and from polar form to Cartesian form.

P.11.1: Graphing simple polar equations in the polar coordinate plane

P.11.2: Graphing polar coordinates and complex numbers

#### P.12: Determine the equation of a curve of best fit from a set of data by using exponential, quadratic, or logarithmic functions.

Correlation last revised: 11/30/2009

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.