### A1: Algebra I

#### A1.1: The student will use expressions and equations to model number relationships.

A1.1.1: Translate word phrases and sentences into expressions and equations and vice versa.

A1.1.2: Expressions

A1.1.2.a: Simplify and evaluate linear, absolute value, rational and radical expressions.

A1.1.2.b: Simplify polynomials by adding, subtracting or multiplying.

#### A1.2: The student will use relations and functions to model number relationships.

A1.2.1: Relations and Functions

A1.2.1.a: Distinguish between linear and nonlinear data.

A1.2.1.b: Distinguish between relations and functions.

A1.2.1.c: Identify dependent and independent variables, domain and range.

A1.2.1.d: Evaluate a function using tables, equations or graphs.

A1.2.2: Recognize the parent graph of the functions y = k, y = x, y = |x|, and predict the effects of transformations on the parent graph (e.g., y = |x| + 2, change slope, change intercepts, change slope and intercept).

A1.2.3: Calculate the slope of a line using a graph, an equation, two points or a set of data points.

A1.2.4: Develop the equation of a line and graph linear relationships given the following:

A1.2.4.a: slope and y-intercept

A1.2.4.b: slope and one point on the line

A1.2.4.c: two points on the line

A1.2.4.d: x-intercept and y-intercept

A1.2.4.e: a set of data points

A1.2.5: Slope Interpretation

A1.2.5.a: Use the slope to differentiate between lines that are parallel, perpendicular, horizontal, or vertical.

A1.2.5.b: Interpret the slope and intercepts within the context of everyday life (e.g., telephone charges based on base rate [y-intercept] plus rate per minute [slope]).

A1.2.6: Linear Equations and Inequalities

A1.2.6.a: Solve linear equations by graphing or using properties of equality.

A1.2.6.b: Solve linear inequalities by graphing or using properties of inequalities.

A1.2.6.c: Match appropriate equations or inequalities (with 1 or 2 variables) to a graph, table, or situation and vice versa.

A1.2.7: Solve a system of linear equations by graphing, substitution or elimination.

A1.2.8: Problem Solving

A1.2.8.a: Use the formulas from measurable attributes of geometric models (perimeter, circumference, area and volume), science, and statistics to solve problems within an algebraic context.

A1.2.8.b: Solve two-step and three-step problems using concepts such as rules of exponents, probability, rate, distance, ratio and proportion, measures of central tendency and percent.

A1.2.9: Nonlinear Functions

A1.2.9.a: Match exponential and quadratic functions to a table, graph or situation and vice versa.

A1.2.9.b: Solve quadratic equations by graphing, factoring, or using the quadratic formula.

#### A1.3: The student will use data analysis and statistics to formulate and justify predictions from a set of data.

A1.3.2: Collect data involving two variables and display on a scatter plot; interpret results using a linear model/equation and identify whether the model/equation is a line best fit for the data (e.g., given a scatter plot and several linear equations, which one is the best fit?).

### GE: Geometry

#### GE.1: The student will use deductive and inductive reasoning to solve problems.

GE.1.1: Properties and Relationships of Figures

GE.1.1.a: Identify the relationships of parallel lines with a transversal.

GE.1.1.b: Identify relationships between pairs of angles (e.g., adjacent, complementary, vertical).

GE.1.2: Determine and use the relationships of congruency and similarity to determine unknown values.

#### GE.2: The student will use the properties and formulas of geometric figures to solve problems.

GE.2.1: Polygons

GE.2.1.a: Identify and describe polygons (i.e., convex, concave, regular)

GE.2.1.b: Apply the interior and exterior angle sum of convex polygons to solve problems.

GE.2.1.c: Develop and apply the properties of quadrilaterals to solve problems (e.g., rectangles, parallelograms, rhombi, trapezoids, kites).

GE.2.2: Draw and analyze 2- and 3-dimensional figures.

GE.2.3: Use properties of 2- and 3-dimensional figures to determine unknown values (e.g., given the perimeter/circumference, find the area).

GE.2.4: Compute length, perimeter or circumference, area, volume, and surface area of geometric figures with missing information and correctly identify the appropriate unit of measure of each.

GE.2.5: Use geometric tools (e.g., protractor, compass, straight edge) to construct a variety of figures.

GE.2.7: Chords, Secants and Tangents

GE.2.7.a: Identify and describe the relationship between two chords that intersect in the interior of a circle.

#### GE.3: The student will solve problems with geometric figures in the coordinate plane.

GE.3.1: Use transformations (reflection, rotation, translation) within coordinate geometry (e.g., reflect points across the y-axis).

GE.3.2: Use coordinate geometry to find the distance between two points; the midpoint of a segment; and to calculate the slopes of parallel, perpendicular, horizontal, and vertical lines.

GE.3.3: Given a set of points determine the type of figure based on its properties (e.g., parallelogram, isosceles triangle, regular octagon).

#### GE.4: The student will use the properties of angles, right triangles and similar polygons to solve problems.

GE.4.1: Solve problems using properties of angles (e.g., interior, exterior, complementary, vertical, angle sums, 30-60-90).

GE.4.2: Use the Pythagorean Theorem and its converse to find missing side lengths and to determine acute, right, and obtuse triangles.

GE.4.4: Express the trigonometric functions as ratios and derive the relationship between sine, cosine, and tangent ratios, and use to solve real-world problems.

GE.4.5: Similar Polygons

GE.4.5.a: Use similar figures to construct ratios and solve for a missing side.

GE.4.5.b: Use ratios of similar figures to find linear distance, perimeter, area, and volume.

### A2: Algebra II

#### A2.1: The student will perform operations with real numbers, complex numbers and matrices.

A2.1.1: Define and perform operations on real and complex numbers.

A2.1.2: Convert expressions from radical notations and vice versa.

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

A2.2.1: Recognize the parent graph of the function y = x² and predict the effects of transformations on the parent graph (e.g., y = x² + 3 shifts the graph up 3, y = 3x² creates vertical stretching by a factor of 3).

A2.2.2: Solve, graph and analyze systems of linear equations and inequalities.

A2.2.3: Solve quadratic equations by graphing, factoring, completing the square and quadratic formula.

A2.2.4: Compare the relationship between the x-intercepts (zeros) of a quadratic function and the roots of a quadratic equation to solve problems.

A2.2.5: Interpret the maximum and minimum value and the y-intercept of a quadratic function.

A2.2.6: Identify, graph, and write the equations of the conic sections.

A2.2.7: Define and distinguish between relations and functions.

A2.2.8: Use functional notation and specify domain and range.

A2.2.9: Find and graph the inverse of a function.

A2.2.10: Exponential and Logarithmic Functions

A2.2.10.a: Interpret and graph exponential and logarithmic functions.

A2.2.10.b: Apply the inverse relationship between exponential and logarithmic functions.

A2.2.10.c: Use exponential and logarithmic functions to solve problems (e.g., compound interest, exponential growth or exponential decay).

A2.2.11: Solve multistep problems using concepts such as rate, distance, ratio and proportion, average, and percent.

A2.2.12: Polynomials

A2.2.12.a: Use synthetic division to find the solutions of a polynomial.

A2.2.12.b: Use factoring to find the solutions of a polynomial.

A2.2.12.c: Graph a polynomial and identify the x- and y-intercepts, relative maximums and relative minimums.

A2.2.13: Rational Expressions and Equations

A2.2.13.a: Simplify rational expressions.

A2.2.13.c: Graph rational expressions and identify x- and y-intercepts, horizontal asymptotes and vertical asymptotes.

#### A2.3: The student will use data analysis and statistics to formulate and justify predictions from a set of data.

A2.3.1: Collect data involving two variables and display on a scatter plot, interpret results using a linear, exponential or quadratic model/equation and identify whether the model/equation is a curve of best fit for the data.

A2.3.2: Analyze and synthesize data using measures of central tendency and standard deviation.

A2.3.3: Identify how given outliers affect representations of data (e.g., a regression line may be strongly affected by a few aberrant points while the same aberrant points might indicate a mistake on a scatter plot).

A2.3.4: Differentiate between arithmetic and geometric sequences and series.

Correlation last revised: 10/24/2008

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