Core Curriculum

A.N.2: Simplify radical terms (no variable in the radicand)

Operations with Radical Expressions

Simplifying Radicals - Activity A

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

Operations with Radical Expressions

Simplifying Radicals - Activity A

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

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

Percent of Change

Polling: Neighborhood

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

Permutations

Permutations and Combinations

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

Using Algebraic Equations

Using Algebraic Expressions

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

Using Algebraic Equations

Using Algebraic Expressions

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

Using Algebraic Equations

Using Algebraic Expressions

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

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Equations By Graphing Each Side

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Solving Two-Step Equations

Using Algebraic Equations

Using Algebraic Expressions

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

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Using Algebraic Equations

Using Algebraic Expressions

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

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Half-life

Using Algebraic Equations

Using Algebraic Expressions

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

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

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

Dividing Exponential Expressions

Multiplying Exponential Expressions

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

Addition of Polynomials - Activity A

Multiplying Exponential Expressions

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

Dividing Polynomials Using Synthetic Division

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

Dividing Exponential Expressions

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

Dividing Exponential Expressions

Modeling the Factorization of *x*^{2}+*bx*+*c*

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)

Factoring Special Products

Modeling the Factorization of *x*^{2}+*bx*+*c*

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

Linear Inequalities in Two Variables - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

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

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Equations By Graphing Each Side

Solving Two-Step Equations

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

Solving Formulas for any Variable

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

Linear Inequalities in Two Variables - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

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

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

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

Direct Variation

Direct and Inverse Variation

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

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

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

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

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Standard Form of a Line

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

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Standard Form of a Line

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

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Standard Form of a Line

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

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

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

Systems of Linear Inequalities (Slope-intercept form) - Activity A

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

Holiday Snowflake Designer

Parabolas - Activity A

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

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

Translating and Scaling Sine and Cosine Functions - Activity A

Unit Circle

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

Sine and Cosine Ratios - Activity A

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

Sine and Cosine Ratios - Activity A

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

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

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).

Area of Parallelograms - Activity A

Circle: Circumference and Area

Perimeter, Circumference, and Area - Activity B

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

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

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

Introduction to Functions

Linear Functions

Polynomials and Linear Factors

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

Exponential Functions - Activity A

Linear Functions

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

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

Functions Involving Square Roots

Parabolas - Activity A

Translating and Scaling Functions

A.G.6: Graph linear inequalities

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Linear Programming - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Systems of Linear Inequalities (Slope-intercept form) - Activity A

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

Linear Programming - Activity A

Point-Slope Form of a Line - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Special Types of Solutions to Linear Systems

Systems of Linear Inequalities (Slope-intercept form) - Activity A

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

Parabolas - Activity A

Roots of a Quadratic

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.

Modeling Linear Systems - Activity A

Solving Linear Systems by Graphing

Systems of Linear Equations - Activity A

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.

Holiday Snowflake Designer

Parabolas - Activity A

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

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

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

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

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

Box-and-Whisker Plots

Histograms

Populations and Samples

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

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

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

Correlation

Lines of Best Fit Using Least Squares - Activity A

Solving Using Trend Lines

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

Box-and-Whisker Plots

Describing Data Using Statistics

Histograms

Populations and Samples

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)

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

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

Correlation

Solving Using Trend Lines

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

Correlation

Solving Using Trend Lines

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

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

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

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

A.S.23: Calculate the probability of:

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

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

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

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

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

Investigating Parallel Lines and Planes

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

Investigating Parallel Lines and Planes

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

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

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

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

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

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

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

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

Pyramids and Cones - Activity A

Surface and Lateral Area of Pyramids and Cones

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

Pyramids and Cones - Activity A

Surface and Lateral Area of Pyramids and Cones

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

Pyramids and Cones - Activity A

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

G.G.14.a: bases are congruent

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

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

Prisms and Cylinders - Activity A

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

Circle: Circumference and Area

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

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

Pyramids and Cones - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

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

Pyramids and Cones - Activity A

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

Constructing Congruent Segments and Angles

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

Constructing Congruent Segments and Angles

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

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles

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

Constructing Congruent Segments and Angles

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

Concurrent Lines, Medians, and Altitudes

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

Biconditional Statement

Conditional Statement

Proving Triangles Congruent

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

Congruence in Right Triangles

Proving Triangles Congruent

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

Congruence in Right Triangles

Proving Triangles Congruent

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

Investigating Angle Theorems - Activity A

Triangle Angle Sum - Activity A

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

Classifying Triangles

Isosceles and Equilateral Triangles

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

Classifying Triangles

Isosceles and Equilateral Triangles

Triangle Angle Sum - Activity A

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

Investigating Angle Theorems - Activity A

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

Polygon Angle Sum - Activity A

Triangle Angle Sum - Activity A

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

Triangle Angle Sum - Activity A

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

Parallelogram Conditions

Special Quadrilaterals

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

Classifying Quadrilaterals - Activity B

Parallelogram Conditions

Special Quadrilaterals

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

Area of Parallelograms - Activity A

Classifying Quadrilaterals - Activity B

Parallelogram Conditions

Special Quadrilaterals

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

Concurrent Lines, Medians, and Altitudes

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

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

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

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

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

Perimeters and Areas of Similar Figures

Similarity in Right Triangles

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

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity B

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.

Dilations

Reflections

Rotations, Reflections and Translations

Translations

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

Reflections

Rotations, Reflections and Translations

Translations

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

Dilations

Reflections

Rotations, Reflections and Translations

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

Reflections

Rotations, Reflections and Translations

Translations

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

Dilations

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

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

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

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

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

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

Dilations

Reflections

Rotations, Reflections and Translations

Translations

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

Point-Slope Form of a Line - Activity A

Slope - Activity B

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

Point-Slope Form of a Line - Activity A

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

Point-Slope Form of a Line - Activity A

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

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Standard Form of a 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

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Standard Form of a Line

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

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Slope - Activity B

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

Dividing Exponential Expressions

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

Operations with Radical Expressions

Simplifying Radicals - Activity A

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

Addition of Polynomials - Activity A

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

Operations with Radical Expressions

Simplifying Radicals - Activity A

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

Simplifying Radicals - Activity A

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

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

Points in the Complex Plane - Activity A

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

Inequalities Involving Absolute Values

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

Linear Inequalities in Two Variables - Activity A

Quadratic Inequalities - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

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

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

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

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

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

Factoring Special Products

Modeling the Factorization of *x*^{2}+*bx*+*c*

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

Dividing Exponential Expressions

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

Dividing Exponential Expressions

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

Simplifying Radicals - Activity A

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

Simplifying Radicals - Activity A

A2.A.13: Simplify radical expressions

Operations with Radical Expressions

Simplifying Radicals - Activity A

A2.A.14: Perform addition, subtraction, multiplication and division of radical expressions

Operations with Radical Expressions

Simplifying Radicals - Activity A

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

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

A2.A.25: Solve quadratic equations, using the quadratic formula

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

Dividing Polynomials Using Synthetic Division

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

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

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

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

Arithmetic Sequences

Arithmetic and Geometric Sequences

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

Arithmetic and Geometric Sequences

Geometric Sequences

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

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

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

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

A2.A.37: Define a relation and function

Introduction to Functions

Linear Functions

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

Introduction to Functions

Linear Functions

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

Functions Involving Square Roots

Introduction to Functions

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)

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

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

Functions Involving Square Roots

Introduction to Functions

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

Cosine Function

Cubic Function Activity

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

General Form of a Rational Function

Introduction to Functions

Linear Functions

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Sine Function

Tangent Function

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

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

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

Exponential Functions - Activity A

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

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

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

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

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

Translating and Scaling Sine and Cosine Functions - Activity A

Unit Circle

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

Cosine Function

Sine Function

Tangent Function

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

Cosine Function

Simplifying Trigonometric Expressions

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

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

Simplifying Trigonometric Expressions

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

Cosine Function

Sine Function

Tangent Function

Unit Circle

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

Cosine Function

Sine Function

Tangent Function

Unit Circle

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

Sine, Cosine and Tangent

Tangent Ratio

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

Sine, Cosine and Tangent

Tangent Ratio

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

Cosine Function

Sine Function

Tangent Function

Unit Circle

A2.A.67: Justify the Pythagorean identities

Simplifying Trigonometric Expressions

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

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

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

Translating and Scaling Sine and Cosine Functions - Activity A

Unit Circle

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

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions - Activity A

Unit Circle

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

Sum and Difference Identities for Sine and Cosine

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

Sum and Difference Identities for Sine and Cosine

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

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

Populations and Samples

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

Box-and-Whisker Plots

Describing Data Using Statistics

Line Plots

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

Correlation

Lines of Best Fit Using Least Squares - Activity A

Solving Using Trend Lines

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

Binomial Probabilities

Permutations

Permutations and Combinations

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

Permutations

Permutations and Combinations

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

Binomial Probabilities

Permutations and Combinations

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)

Binomial Probabilities

Permutations

Permutations and Combinations

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

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

A2.S.14: Calculate empirical probabilities

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

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