### A: Algebra

#### A.N: Number Sense and Operations

A.N.3: Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form

A.N.5: Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation

A.N.8: Determine the number of possible arrangements (permutations) of a list of items

#### A.A: Algebra

A.A.1: Translate a quantitative verbal phrase into expression

A.A.2: Write a verbal expression that matches a given mathematical expression

A.A.3: Distinguish the difference between an algebraic expression and an algebraic equation

A.A.4: Translate verbal sentences into mathematical equations or inequalities

A.A.5: Write algebraic equations or inequalities that represent a situation

A.A.6: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable

A.A.7: Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables

A.A.8: Analyze and solve verbal problems that involve quadratic equations

A.A.9: Analyze and solve verbal problems that involve exponential growth and decay

A.A.10: Solve systems of two linear equations in two variables algebraically

A.A.11: Solve a system of one linear and one quadratic equation in two variables, where only factoring is required Note: The quadratic equation should represent a parabola and the solution(s) should be integers.

A.A.12: Multiply and divide monomial expressions with a common base, using the properties of exponents Note: Use integral exponents only

A.A.13: Add, subtract, and multiply monomials and polynomials

A.A.14: Divide a polynomial by a monomial or binomial, where the quotient has no remainder

A.A.15: Find values of a variable for which an algebraic fraction is undefined

A.A.16: Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms

A.A.19: Identify and factor the difference of two perfect squares

A.A.20: Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)

A.A.21: Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable

A.A.22: Solve all types of linear equations in one variable

A.A.23: Solve literal equations for a given variable

A.A.24: Solve linear inequalities in one variable

A.A.27: Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots

A.A.28: Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression

A.A.32: Explain slope as a rate of change between dependent and independent variables

A.A.33: Determine the slope of a line, given the coordinates of two points on the line

A.A.34: Write the equation of a line, given its slope and the coordinates of a point on the line

A.A.35: Write the equation of a line, given the coordinates of two points on the line

A.A.36: Write the equation of a line parallel to the x- or y-axis

A.A.37: Determine the slope of a line, given its equation in any form

A.A.40: Determine whether a given point is in the solution set of a system of linear inequalities

A.A.41: Determine the vertex and axis of symmetry of a parabola, given its equation

A.A.42: Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides

A.A.43: Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle

A.A.44: Find the measure of a side of a right triangle, given an acute angle and the length of another side

A.A.45: Determine the measure of a third side of a right triangle using the Pythagorean theorem, given the lengths of any two sides

#### A.G: Geometry

A.G.1: Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle Note: Figures may include triangles, rectangles, squares, parallelograms, rhombuses, trapezoids, circles, semi-circles, quarter-circles, and regular polygons (perimeter only).

A.G.2: Use formulas to calculate volume and surface area of rectangular solids and cylinders

A.G.3: Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations

A.G.4: Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions

A.G.5: Investigate and generalize how changing the coefficients of a function affects its graph

A.G.6: Graph linear inequalities

A.G.7: Graph and solve systems of linear equations and inequalities with rational coefficients in two variables

A.G.8: Find the roots of a parabolic function graphically Note: Only quadratic equations with integral solutions

A.G.9: Solve systems of linear and quadratic equations graphically Note: Only use systems of linear and quadratic equations that lead to solutions whose coordinates are integers.

A.G.10: Determine the vertex and axis of symmetry of a parabola, given its graph. Note: The vertex will have an ordered pair of integers and the axis of symmetry will have an integral value.

#### A.M: Measurement

A.M.1: Calculate rates using appropriate units (e.g., rate of a space ship versus the rate of a snail)

#### A.S: Statistics and Probability

A.S.2: Determine whether the data to be analyzed is univariate or bivariate

A.S.4: Compare and contrast the appropriateness of different measures of central tendency for a given data set

A.S.5: Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given a set of data

A.S.6: Understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a boxand- whisker plot

A.S.7: Create a scatter plot of bivariate data

A.S.8: Construct manually a reasonable line of best fit for a scatter plot and determine the equation of that line

A.S.9: Analyze and interpret a frequency distribution table or histogram, a cumulative frequency distribution table or histogram, or a box-and-whisker plot

A.S.11: Find the percentile rank of an item in a data set and identify the point values for first, second, and third quartiles

A.S.12: Identify the relationship between the independent and dependent variables from a scatter plot (positive, negative, or none)

A.S.13: Understand the difference between correlation and causation

A.S.14: Identify variables that might have a correlation but not a causal relationship

A.S.16: Recognize how linear transformations of one-variable data affect the data’s mean, median, mode, and range

A.S.21: Determine empirical probabilities based on specific sample data

A.S.23: Calculate the probability of:

A.S.23.a: a series of independent events

A.S.23.b: a series of dependent events

### G: Geometry

#### G.G: Geometry

G.G.8: Know and apply that if a plane intersects two parallel planes, then the intersection is two parallel lines

G.G.9: Know and apply that if two planes are perpendicular to the same line, they are parallel

G.G.10: Know and apply that the lateral edges of a prism are congruent and parallel

G.G.11: Know and apply that two prisms have equal volumes if their bases have equal areas and their altitudes are equal

G.G.12: Know and apply that the volume of a prism is the product of the area of the base and the altitude

G.G.13: Apply the properties of a regular pyramid, including:

G.G.13.a: lateral edges are congruent

G.G.13.b: lateral faces are congruent isosceles triangles

G.G.13.c: volume of a pyramid equals one-third the product of the area of the base and the altitude

G.G.14: Apply the properties of a cylinder, including:

G.G.14.a: bases are congruent

G.G.14.b: volume equals the product of the area of the base and the altitude

G.G.14.c: lateral area of a right circular cylinder equals the product of an altitude and the circumference of the base

G.G.15: Apply the properties of a right circular cone, including:

G.G.15.a: lateral area equals one-half the product of the slant height and the circumference of its base

G.G.15.b: volume is one-third the product of the area of its base and its altitude

G.G.17: Construct a bisector of a given angle, using a straightedge and compass, and justify the construction

G.G.18: Construct the perpendicular bisector of a given segment, using a straightedge and compass, and justify the construction

G.G.19: Construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction

G.G.20: Construct an equilateral triangle, using a straightedge and compass, and justify the construction

G.G.21: Investigate and apply the concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors of triangles

G.G.25: Know and apply the conditions under which a compound statement (conjunction, disjunction, conditional, biconditional) is true

G.G.27: Write a proof arguing from a given hypothesis to a given conclusion

G.G.28: Determine the congruence of two triangles by using one of the five congruence techniques (SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two congruent triangles

G.G.29: Identify corresponding parts of congruent triangles

G.G.30: Investigate, justify, and apply theorems about the sum of the measures of the angles of a triangle

G.G.31: Investigate, justify, and apply the isosceles triangle theorem and its converse

G.G.32: Investigate, justify, and apply theorems about geometric inequalities, using the exterior angle theorem

G.G.33: Investigate, justify, and apply the triangle inequality theorem

G.G.34: Determine either the longest side of a triangle given the three angle measures or the largest angle given the lengths of three sides of a triangle

G.G.35: Determine if two lines cut by a transversal are parallel, based on the measure of given pairs of angles formed by the transversal and the lines

G.G.36: Investigate, justify, and apply theorems about the sum of the measures of the interior and exterior angles of polygons

G.G.37: Investigate, justify, and apply theorems about each interior and exterior angle measure of regular polygons

G.G.38: Investigate, justify, and apply theorems about parallelograms involving their angles, sides, and diagonals

G.G.39: Investigate, justify, and apply theorems about special parallelograms (rectangles, rhombuses, squares) involving their angles, sides, and diagonals

G.G.41: Justify that some quadrilaterals are parallelograms, rhombuses, rectangles, squares, or trapezoids

G.G.43: Investigate, justify, and apply theorems about the centroid of a triangle, dividing each median into segments whose lengths are in the ratio 2:1

G.G.44: Establish similarity of triangles, using the following theorems: AA, SAS, and SSS

G.G.45: Investigate, justify, and apply theorems about similar triangles

G.G.46: Investigate, justify, and apply theorems about proportional relationships among the segments of the sides of the triangle, given one or more lines parallel to one side of a triangle and intersecting the other two sides of the triangle

G.G.47: Investigate, justify, and apply theorems about mean proportionality:

G.G.47.a: the altitude to the hypotenuse of a right triangle is the mean proportional between the two segments along the hypotenuse

G.G.47.b: the altitude to the hypotenuse of a right triangle divides the hypotenuse so that either leg of the right triangle is the mean proportional between the hypotenuse and segment of the hypotenuse adjacent to that leg

G.G.48: Investigate, justify, and apply the Pythagorean theorem and its converse

G.G.49: Investigate, justify, and apply theorems regarding chords of a circle:

G.G.49.a: perpendicular bisectors of chords

G.G.49.b: the relative lengths of chords as compared to their distance from the center of the circle

G.G.51: Investigate, justify, and apply theorems about the arcs determined by the rays of angles formed by two lines intersecting a circle when the vertex is:

G.G.51.a: inside the circle (two chords)

G.G.51.b: on the circle (tangent and chord)

G.G.53: Investigate, justify, and apply theorems regarding segments intersected by a circle:

G.G.53.d: along two intersecting chords of a given circle

G.G.54: Define, investigate, justify, and apply isometries in the plane (rotations, reflections, translations, glide reflections) Note: Use proper function notation.

G.G.55: Investigate, justify, and apply the properties that remain invariant under translations, rotations, reflections, and glide reflections

G.G.56: Identify specific isometries by observing orientation, numbers of invariant points, and/or parallelism

G.G.57: Justify geometric relationships (perpendicularity, parallelism, congruence) using transformational techniques (translations, rotations, reflections)

G.G.58: Define, investigate, justify, and apply similarities (dilations and the composition of dilations and isometries)

G.G.59: Investigate, justify, and apply the properties that remain invariant under similarities

G.G.60: Identify specific similarities by observing orientation, numbers of invariant points, and/or parallelism

G.G.61: Investigate, justify, and apply the analytical representations for translations, rotations about the origin of 90º and 180º, reflections over the lines x = 0, y = 0 , and x = y, and dilations centered at the origin

G.G.62: Find the slope of a perpendicular line, given the equation of a line

G.G.63: Determine whether two lines are parallel, perpendicular, or neither, given their equations

G.G.64: Find the equation of a line, given a point on the line and the equation of a line perpendicular to the given line

G.G.65: Find the equation of a line, given a point on the line and the equation of a line parallel to the desired line

G.G.68: Find the equation of a line that is the perpendicular bisector of a line segment, given the endpoints of the line segment

G.G.69: Investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas

G.G.71: Write the equation of a circle, given its center and radius or given the endpoints of a diameter

G.G.72: Write the equation of a circle, given its graph Note: The center is an ordered pair of integers and the radius is an integer.

G.G.73: Find the center and radius of a circle, given the equation of the circle in center-radius form

G.G.74: Graph circles of the form (x - h)² + (j - k)² = r²

### A2: Algebra 2 and Trigonometry

#### A2.N: Number Sense and Operations

A2.N.1: Evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (when the answers are rational numbers)

A2.N.2: Perform arithmetic operations (addition, subtraction, multiplication, division) with expressions containing irrational numbers in radical form

A2.N.3: Perform arithmetic operations with polynomial expressions containing rational coefficients

A2.N.4: Perform arithmetic operations on irrational expressions

A2.N.5: Rationalize a denominator containing a radical expression

A2.N.6: Write square roots of negative numbers in terms of i

A2.N.8: Determine the conjugate of a complex number

#### A2.A: Algebra

A2.A.1: Solve absolute value equations and inequalities involving linear expressions in one variable

A2.A.2: Use the discriminant to determine the nature of the roots of a quadratic equation

A2.A.4: Solve quadratic inequalities in one and two variables, algebraically and graphically

A2.A.5: Use direct and inverse variation to solve for unknown values

A2.A.6: Solve an application which results in an exponential function

A2.A.7: Factor polynomial expressions completely, using any combination of the following techniques: common factor extraction, difference of two perfect squares, quadratic trinomials

A2.A.8: Apply the rules of exponents to simplify expressions involving negative and/or fractional exponents

A2.A.9: Rewrite algebraic expressions that contain negative exponents using only positive exponents

A2.A.10: Rewrite algebraic expressions with fractional exponents as radical expressions

A2.A.11: Rewrite algebraic expressions in radical form as expressions with fractional exponents

A2.A.20: Determine the sum and product of the roots of a quadratic equation by examining its coefficients

A2.A.21: Determine the quadratic equation, given the sum and product of its roots

A2.A.23: Solve rational equations and inequalities

A2.A.26: Find the solution to polynomial equations of higher degree that can be solved using factoring and/or the quadratic formula

A2.A.29: Identify an arithmetic or geometric sequence and find the formula for its nth term

A2.A.30: Determine the common difference in an arithmetic sequence

A2.A.31: Determine the common ratio in a geometric sequence

A2.A.32: Determine a specified term of an arithmetic or geometric sequence

A2.A.33: Specify terms of a sequence, given its recursive definition

A2.A.37: Define a relation and function

A2.A.38: Determine when a relation is a function

A2.A.39: Determine the domain and range of a function from its equation

A2.A.43: Determine if a function is one-to-one, onto, or both

A2.A.46: Perform transformations with functions and relations: f(x + a), f(x) + a, f(-x), -f(x), af(x)

A2.A.47: Determine the center-radius form for the equation of a circle in standard form

A2.A.48: Write the equation of a circle, given its center and a point on the circle

A2.A.49: Write the equation of a circle from its graph

A2.A.51: Determine the domain and range of a function from its graph

A2.A.52: Identify relations and functions, using graphs

A2.A.53: Graph exponential functions of the form y = b to the power x for positive values of b, including b = e

A2.A.54: Graph logarithmic functions, using the inverse of the related exponential function

A2.A.55: Express and apply the six trigonometric functions as ratios of the sides of a right triangle

A2.A.56: Know the exact and approximate values of the sine, cosine, and tangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles

A2.A.57: Sketch and use the reference angle for angles in standard position

A2.A.58: Know and apply the co-function and reciprocal relationships between trigonometric ratios

A2.A.59: Use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles

A2.A.60: Sketch the unit circle and represent angles in standard position

A2.A.61: Determine the length of an arc of a circle, given its radius and the measure of its central angle

A2.A.62: Find the value of trigonometric functions, if given a point on the terminal side of angle theta

A2.A.63: Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function

A2.A.64: Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent

A2.A.66: Determine the trigonometric functions of any angle, using technology

A2.A.67: Justify the Pythagorean identities

A2.A.69: Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function

A2.A.70: Sketch and recognize one cycle of a function of the form y = AsinBx = or y = AcosBx

A2.A.72: Write the trigonometric function that is represented by a given periodic graph

A2.A.76: Apply the angle sum and difference formulas for trigonometric functions

A2.A.77: Apply the double-angle and half-angle formulas for trigonometric functions

#### A2.S: Statistics and Probability

A2.S.3: Calculate measures of central tendency with group frequency distributions

A2.S.4: Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations

A2.S.6: Determine from a scatter plot whether a linear, logarithmic, exponential, or power regression model is most appropriate

A2.S.8: Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship

A2.S.9: Differentiate between situations requiring permutations and those requiring combinations

A2.S.10: Calculate the number of possible permutations of (n P r) n items taken r at a time

A2.S.11: Calculate the number of possible combinations(n C r) of n items taken r at a time

A2.S.12: Use permutations, combinations, and the Fundamental Principle of Counting to determine the number of elements in a sample space and a specific subset (event)

A2.S.13: Calculate theoretical probabilities, including geometric applications

A2.S.14: Calculate empirical probabilities

A2.S.15: Know and apply the binomial probability formula to events involving the terms exactly, at least, and at most

A2.S.16: Use the normal distribution as an approximation for binomial probabilities

Correlation last revised: 10/30/2009

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