This is a list of all Virtual Nerd tutorials in Texas Standards, organized by topic.

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### Algebra 1

#### Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.

##### Decide whether relations represented verbally, tabularly, graphically, and symbolically define a function

##### Identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes

##### Evaluate functions, expressed in function notation, given one or more elements in their domains

- What's an Arithmetic Sequence?
- How Do You Find the Common Difference in an Arithmetic Sequence?
- How Do You Write a Quadratic Equation in Vertex Form if You Have the Vertex and Another Point?
- What is Function Notation?
- How Do You Find f(x) If You Have a Value For x?
- How Do You Write a Rule for a Geometric Sequence?
- What's an Exponential Function?
- How Do You Graph an Exponential Function Using a Table?

##### Solve mathematic and scientific formulas, and other literal equations, for a specified variable

- What's Point-Slope Form of a Linear Equation?
- How Do You Solve a Quadratic Equation with Two Solutions by Graphing?
- How Do You Use the Square Root Method to Solve a Quadratic Equation with Two Solutions?
- How Do You Use the Formula for Direct Variation?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- What's the Direct Variation or Direct Proportionality Formula?
- How Do You Solve a Formula For a Variable?
- What is a Literal Equation?

##### Write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms

#### Linear functions, equations, and inequalities. The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations.

##### Calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems

- How Do You Find the Slope of a Line from a Graph?
- What's the Direct Variation or Direct Proportionality Formula?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- What's Slope-Intercept Form of a Linear Equation?
- What's the Formula for Slope?
- What's Point-Slope Form of a Linear Equation?
- How Do You Write and Use a Prediction Equation?
- How Do You Make a Scatter Plot?
- How Do You Use the Formula for Direct Variation?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- How Do You Make an Approximate Graph From a Word Problem?

##### Determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, ax + by = c, and y - y1 = m(x - x1)

- What's the Direct Variation or Direct Proportionality Formula?
- What's Standard Form of a Linear Equation?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- How Do You Write and Use a Prediction Equation?
- What's a Function?
- How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
- How Do You Make a Scatter Plot?
- What's a Function?
- What's Slope-Intercept Form of a Linear Equation?
- How Do You Use the Graph of a Linear Equation to Solve a Word Problem?
- How Do You Know if Two Lines Are Perpendicular?
- How Do You Graph a Linear Equation by Making a Table?
- How Do You Find the Slope of a Line from a Graph?
- What's Point-Slope Form of a Linear Equation?
- How Do You Know if Two Lines are Parallel?
- How Do You Use the Formula for Direct Variation?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- What's the Formula for Slope?

##### Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems

- How Do You Graph a Linear Equation by Making a Table?
- What's Point-Slope Form of a Linear Equation?
- How Do You Use the Formula for Direct Variation?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- What's the Direct Variation or Direct Proportionality Formula?
- What's Standard Form of a Linear Equation?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
- What's Slope-Intercept Form of a Linear Equation?
- How Do You Use the Graph of a Linear Equation to Solve a Word Problem?

##### Graph the solution set of linear inequalities in two variables on the coordinate plane

##### Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane

##### Estimate graphically the solutions to systems of two linear equations with two variables in real-world problems

##### Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist

#### Linear functions, equations, and inequalities. The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations.

##### Write linear equations in two variables in various forms, including y = mx + b, ax + by = c, and y - y1 = m(x - x1), given one point and the slope and given two points

- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- What's Standard Form of a Linear Equation?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- How Do You Know if Two Lines Are Perpendicular?
- How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
- What's Slope-Intercept Form of a Linear Equation?
- How Do You Know if Two Lines are Parallel?
- What's Point-Slope Form of a Linear Equation?
- How Do You Write and Use a Prediction Equation?
- How Do You Make a Scatter Plot?

##### Write the equation of a line that contains a given point and is parallel to a given line

##### Determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities

- What is Function Notation?
- What's Standard Form of a Linear Equation?
- How Do You Find f(x) If You Have a Value For x?
- How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
- How Do You Use the Graph of a Linear Equation to Solve a Word Problem?
- How Do You Graph a Linear Equation by Making a Table?

##### Write linear equations in two variables given a table of values, a graph, and a verbal description

- What's Slope-Intercept Form of a Linear Equation?
- How Do You Write an Equation from a Word Problem?
- How Do You Know if Two Lines are Parallel?
- What's Point-Slope Form of a Linear Equation?
- How Do You Write and Use a Prediction Equation?
- How Do You Make a Scatter Plot?
- How Do You Use the Formula for Direct Variation?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- What's the Direct Variation or Direct Proportionality Formula?
- What's Standard Form of a Linear Equation?
- What's a Function?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- What's a Function?
- How Do You Know if Two Lines Are Perpendicular?
- How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?

##### Write and solve equations involving direct variation

- How Do You Solve a Proportion Using Cross Products?
- How Do You Use the Formula for Direct Variation?
- What's the Direct Variation or Direct Proportionality Formula?
- What are Similar Figures?
- How Do You Find Missing Measurements of Similar Figures Using a Proportion?
- How Do You Solve a Proportion Using the Multiplication Property of Equality?

##### Write systems of two linear equations given a table of values, a graph, and a verbal description

- How Do You Solve a Word Problem Using Two Equations?
- How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
- How Do You Graph a System of Equations With No Solution?
- How Do You Solve Two Equations with Two Variables?
- How Do You Solve a System of Equations Using the Substitution Method?
- How Do You Solve a System of Equations Using the Elimination by Addition Method?
- How Do You Solve a Word Problem Using the Elimination by Subtraction Method?
- How Do You Solve a System of Equations by Graphing?

##### Write linear inequalities in two variables given a table of values, a graph, and a verbal description

##### Write an equation of a line that is parallel or perpendicular to the x or y axis and determine whether the slope of the line is zero or undefined

##### Write the equation of a line that contains a given point and is perpendicular to a given line

#### Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.

##### Simplify numerical radical expressions involving square roots

##### Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents

- What are Rational Exponents?
- What's the Power of a Power Rule?
- How Do You Find the Product of Powers?
- What's the Power of a Product Rule?
- What's the Quotient of Powers Rule?
- What's the Product of Powers Rule?
- What Do You Do With a Zero Exponent?
- What Do You Do With a Negative Exponent?
- What's the Power of a Quotient Rule?

#### Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.

##### Determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend

##### Add and subtract polynomials of degree one and degree two

##### Multiply polynomials of degree one and degree two

- How Do You Figure Out What Factoring Strategy to Use?
- How Do You Factor a 4-Term Polynomial by Grouping?
- How Do You Multiply a Monomial by a Polynomial?
- What's the Grid Method of FOILing?
- How Do You Factor the Greatest Common Factor out of a Polynomial?
- What's the Formula for the Square of a Sum?
- How Do You Use the Formula for the Product of a Sum and a Difference?
- How Do You Multiply Binomials Using FOIL?

##### Factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two

- How Do You Divide Two Polynomials by Factoring and Canceling?
- How Do You Find Excluded Values?
- How Do You Factor a Trinomial?
- How Do You Factor a Polynomial Using Difference of Squares?
- How Do You Factor a Polynomial by Guessing and Checking?
- How Do You Use a Shortcut to Factor a Perfect Square Trinomial?
- How Do You Factor a Polynomial Using the A-C Method?
- How Do You Figure Out What Factoring Strategy to Use?
- How Do You Factor a 4-Term Polynomial by Grouping?
- How Do You Figure Out a Template for Factoring a Trinomial?

##### Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial

##### Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property

- What's the Grid Method of FOILing?
- How Do You Factor a Polynomial by Guessing and Checking?
- How Do You Factor a Polynomial Using the A-C Method?
- How Do You Factor the Greatest Common Factor out of a Polynomial?
- How Do You Figure Out What Factoring Strategy to Use?
- How Do You Factor a 4-Term Polynomial by Grouping?
- How Do You Multiply Binomials Using FOIL?
- How Do You Divide Two Polynomials by Factoring and Canceling?
- How Do You Find Excluded Values?
- How Do You Multiply a Monomial by a Polynomial?

#### Linear functions, equations, and inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.

##### Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

- How Do You Solve an Equation with Variables on Both Sides?
- How Do You Solve a Multi-Step Equation Using the Distributive Property?
- How Do You Find Missing Measurements of Similar Figures Using a Proportion?
- How Do You Solve a Proportion Using the Multiplication Property of Equality?
- How Do You Solve a Proportion Using Cross Products?
- How Do You Solve an Identity Equation?
- How Do You Solve a Multi-Step Equation with Fractions by Multiplying Away the Fraction?
- What are Similar Figures?

##### Solve systems of two linear equations with two variables for mathematical and real-world problems

- How Do You Solve a System of Equations Using the Substitution Method?
- How Do You Solve a System of Equations Using the Elimination by Addition Method?
- How Do You Solve a Word Problem Using the Elimination by Subtraction Method?
- How Do You Solve a System of Equations by Graphing?
- How Do You Solve a Word Problem Using Two Equations?
- How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
- How Do You Graph a System of Equations With No Solution?
- How Do You Solve Two Equations with Two Variables?

##### Solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

#### Quadratic functions and equations. The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations.

##### Determine the domain and range of quadratic functions and represent the domain and range using inequalities

##### Write quadratic functions when given real solutions and graphs of their related equations

##### Write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)2+ k), and rewrite the equation from vertex form to standard form (f(x) = ax2+ bx + c)

#### Exponential functions and equations. The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

##### Determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities

##### Write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

- How Do You Graph an Exponential Function Using a Table?
- What Do You Do With a Zero Exponent?
- How Can You Tell if a Function is Linear or Nonlinear From a Graph?
- What Do You Do With a Negative Exponent?
- What is Exponential Growth?
- What is exponential decay?
- How Can You Tell if a Function is Linear or Nonlinear From a Table?
- What's an Exponential Function?

##### Interpret the meaning of the values of a and b in exponential functions of the form f(x) = abx in real-world problems

##### Graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems

#### Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

##### Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

- What's the Zero Product Property?
- What is the Converse of the Pythagorean Theorem?
- How Do You Solve a Quadratic Equation with Two Solutions by Graphing?
- How Do You Use the Square Root Method to Solve a Quadratic Equation with Two Solutions?
- How Do You Solve a Quadratic Equation by Factoring?
- What is the Quadratic Formula?
- How Do You Solve a Quadratic Equation by Completing the Square?
- What is the Discriminant?
- What is the Pythagorean Theorem?

##### Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems

#### Linear functions, equations, and inequalities. The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.

##### Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association

##### Write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems

##### Compare and contrast association and causation in real-world problems

#### Quadratic functions and equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.

##### Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

- What is a Quadratic Function?
- How Do You Write a Quadratic Equation in Vertex Form if You Have the Vertex and Another Point?
- How Do You Graph the Parent Quadratic Function y=x2?
- How Do You Graph a Quadratic Function?
- How Do You Solve a Quadratic Equation with Two Solutions by Graphing?
- How Do You Use the Square Root Method to Solve a Quadratic Equation with Two Solutions?
- How Do You Find the Axis of Symmetry for a Quadratic Function?

##### Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d

##### Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions

### Geometry

#### Probability. The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events.

##### Develop strategies to use permutations and combinations to solve contextual problems

##### Identify whether two events are independent and compute the probability of the two events occurring together with or without replacement

##### Determine probabilities based on area to solve contextual problems

##### Apply independence in contextual problems

##### Apply conditional probability in contextual problems

#### Two-dimensional and three-dimensional figures. The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures.

##### Identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes

##### Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change

- How Do You Find the Volume of a Cone?
- How Do You Find the Lateral and Surface Areas of a Cylinder?
- How Do You Find the Lateral and Surface Areas of a Regular Pyramid?
- How Do You Find the Lateral and Surface Areas of a Cone?
- What is a Circle?
- How Do You Find the Surface Area of a Sphere?
- What is the Formula for the Volume of a Pyramid?
- How Do You Find the Volume of a Sphere?
- What is the Relationship Between the Surface Areas of Similar Solids?
- How Do You Use Similar Figures to Find the Area of a Polygon?
- How Do You Find the Lateral and Surface Areas of a Rectangular Prism?
- What is Circumference?
- How Do You Find the Area of a Sector of a Circle?
- What is the Formula for the Area of a Circle?

#### Circles. The student uses the process skills to understand geometric relationships and apply theorems and equations about circles.

##### Apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems

- How Do You Determine Whether a Line is Tangent to a Circle?
- What is a Tangent Line to a Circle?
- How Do You Find Missing Measures of Angles in Quadrilaterals Inscribed in Circles?
- How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
- How Do You Use Intersecting Chords to Find Arc Measures in a Circle?
- How Do You Find The Measure of an Inscribed Angle When You Know the Measure of the Intercepted Arc?
- How Do You Find the Measure of an Angle Created by Intersecting Chords in a Circle?

##### Apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems

##### Apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems

##### Show that the equation of a circle with center at the origin and radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)2 + (y - k)2 =r2

#### Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity).

##### Describe and perform transformations of figures in a plane using coordinate notation

- How Do You Make a Figure Larger Using a Dilation?
- What is a Dilation?
- What is a Congruence Transformation, or Isometry?
- How Do You Rotate a Figure 180 Degrees Around the Origin?
- How Do You Identify a Congruence Transformation?
- How Do You Use a Graph to Reflect a Figure Over the Y-Axis?
- What is a Translation?
- What is a Rotation?
- How Do You Identify Corresponding Parts in Congruent Triangles?
- How Do You Use a Graph to Translate a Figure Diagonally?
- How Do You Graph a Glide Reflection?
- What is a Reflection?
- How Do You Identify a Similarity Transformation?

##### Identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane

- What is a Translation?
- What is a Rotation?
- How Do You Identify Corresponding Parts in Congruent Triangles?
- How Do You Use a Graph to Translate a Figure Diagonally?
- How Do You Identify a Similarity Transformation?
- How Do You Rotate a Figure 180 Degrees Around the Origin?
- How Do You Identify a Congruence Transformation?

##### Determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane

- How Do You Identify a Similarity Transformation?
- How Do You Graph a Glide Reflection?
- How Do You Identify a Congruence Transformation?
- How Do You Make a Figure Larger Using a Dilation?
- What is a Dilation?
- What is a Congruence Transformation, or Isometry?
- How Do You Identify Corresponding Parts in Congruent Triangles?

##### Identify and distinguish between reflectional and rotational symmetry in a plane figure

#### Two-dimensional and three-dimensional figures. The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures.

##### Apply the formula for the area of regular polygons to solve problems using appropriate units of measure

- How Do You Use Similar Figures to Find the Area of a Polygon?
- How Do You Find the Area of a Regular Polygon When You Know the Length of the Apothem?
- What is the Formula for the Area of a Triangle Using Sines?
- What is the Formula for the Area of a Triangle?
- How Do You Find the Area of a Sector of a Circle?
- What is the Formula for the Area of a Circle?
- What is the Formula for the Area of a Parallelogram?

##### Apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

- How Do You Find the Lateral and Surface Areas of a Rectangular Prism?
- How Do You Find the Lateral and Surface Areas of a Cylinder?
- How Do You Find the Lateral and Surface Areas of a Regular Pyramid?
- How Do You Find the Lateral and Surface Areas of a Cone?
- How Do You Find the Surface Area of a Sphere?
- How Do You Find the Volume of a Sphere?

##### Determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure

##### Apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

#### Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures.

##### Determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint

##### Determine an equation of a line parallel or perpendicular to a given line that passes through a given point

##### Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines

- What are Equilateral, Isosceles, and Scalene Triangles?
- What Is the Distance Formula?
- What are Skew Lines?
- How Do You Know if Two Lines are Parallel?
- What are Parallel Lines?
- What is a Circle?
- How Do You Find the Distance Between Two Points?
- What's the Midpoint Formula?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- What's Slope-Intercept Form of a Linear Equation?
- How Do You Know if Two Lines Are Perpendicular?
- How Do You Write a Coordinate Proof?

#### Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures.

##### Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools

- How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?
- How Do You Use the Diagonals of a Rectangle to Find the Value of a Variable?
- What is the Incenter of a Triangle?
- What is the Triangle Sum Theorem?
- How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
- How Do You Find Missing Angles in a Triangle With Variables?
- How Do You Use Intersecting Chords to Find Arc Measures in a Circle?
- How Do You Determine if Triangles on the Coordinate Plane are Congruent?
- How Do You Find Missing Angles in a Transversal Diagram?
- How Do You Find the Measure of an Angle Created by Intersecting Chords in a Circle?
- What is Inductive Reasoning?
- What are Skew Lines?
- What is the Circumcenter of a Triangle?
- What is a Rectangle?
- How Do You Find Missing Angles in an Isosceles Triangle?
- How Do You Use the Triangle Proportionality Theorem to Find Missing Lengths in a Diagram?
- What is a Trapezoid?
- What are Parallel Lines?
- What is the Corresponding Angles Postulate?
- How Do You Find the Sum of the Interior Angles of a Polygon?
- What is the Side-Angle-Side Postulate for Triangle Congruence?

##### Use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships

- How Do You Determine if Triangles on the Coordinate Plane are Congruent?
- How Do You Construct a Perpendicular Bisector?
- What is the Circumcenter of a Triangle?
- What are Vertical Angles?
- How Can You Tell if a Point is on the Perpendicular Bisector of a Line Segment?
- How Do You Find Missing Angles in an Isosceles Triangle?
- What is the Converse of the Corresponding Angles Postulate?
- What are Supplementary Angles?
- What is the Side-Angle-Side Postulate for Triangle Congruence?
- How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?
- How Do You Find a Value for x that Makes Two Lines Parallel?
- What is the Incenter of a Triangle?
- How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
- What are Perpendicular Lines?

##### Construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge

##### Verify the triangle inequality theorem using constructions and apply the theorem to solve problems

#### Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships.

##### Distinguish between undefined terms, definitions, postulates, conjectures, and theorems

##### Verify that a conjecture is false using a counterexample

##### Identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse

##### Compare geometric relationships between euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle

#### Proof and congruence. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.

##### Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems

- What is a Theorem?
- How Do You Use Intersecting Chords to Find Arc Measures in a Circle?
- How Do You Find Missing Angles in a Transversal Diagram?
- How Do You Find the Measure of an Angle Created by Intersecting Chords in a Circle?
- What are Supplementary Angles?
- What are Parallel Lines?
- How Do You Find a Value for x that Makes Two Lines Parallel?
- What is the Incenter of a Triangle?
- How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
- What is the Corresponding Angles Postulate?
- How Do You Determine Whether a Line is Tangent to a Circle?
- How Do You Write an Indirect Proof?
- What is a Tangent Line to a Circle?
- What is the Circumcenter of a Triangle?
- What are Vertical Angles?
- How Can You Tell if a Point is on the Perpendicular Bisector of a Line Segment?
- What are Skew Lines?
- How Do You Use Parallel and Perpendicular Theorems to Prove a Relationship Between Two Lines?
- What is the Converse of the Corresponding Angles Postulate?

##### Apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles

- How Do You Identify a Congruence Transformation?
- What is the Distributive Property?
- What is the Substitution Property of Equality?
- What is a Congruence Transformation, or Isometry?
- How Do You Rotate a Figure 180 Degrees Around the Origin?
- How Do You Identify Corresponding Parts in Congruent Triangles?
- What is a Translation?
- What is a Rotation?
- How Do You Use a Graph to Translate a Figure Diagonally?
- How Do You Graph a Glide Reflection?

##### Prove two triangles are congruent by applying the side-angle-side, angle-side-angle, side-side-side, angle-angle-side, and hypotenuse-leg congruence conditions

- What are the Legs and Hypotenuse of a Right Triangle?
- What is the Angle-Side-Angle Postulate for Triangle Congruence?
- How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?
- What is the Hypotenuse-Leg Congruence Theorem?
- How Do You Identify Common Parts in Overlapping Triangles?
- How Do You Prove that Two Overlapping Triangles are Congruent?
- How Do You Use the Law of Detachment to Draw a Valid Conclusion?
- What is the Law of Syllogism?
- How Do You Show that Corresponding Parts of Congruent Triangles are Congruent?
- How Do You Use a Congruence Postulate to Prove Triangles are Congruent?
- What is the Distributive Property?
- How Do You Find Missing Angles in an Isosceles Triangle?
- What is the Substitution Property of Equality?
- What is CPCTC?

##### Prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems

- How Do You Use the Law of Detachment to Draw a Valid Conclusion?
- What is the Law of Syllogism?
- How Do You Find the Value for a Variable in the Angles of a Quadrilateral To Make it a Rhombus?
- What is the Distributive Property?
- What is the Substitution Property of Equality?
- How Do You Find Values for Variables in the Angles of a Quadrilateral To Make it a Parallelogram?
- What are Equilateral, Isosceles, and Scalene Triangles?
- What is a Parallelogram?
- How Do You Find the Distance Between Two Points?

##### Verify theorems about the relationships in triangles, including proof of the pythagorean theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems

- How Do You Find Missing Angles in a Triangle With Variables?
- How Do You Use the Hinge Theorem to Compare Side Lengths in Two Triangles?
- What is a 45Ã‚Â°-45Ã‚Â°-90Ã‚Â° Triangle?
- What is a Rectangle?
- How Do You Determine Whether a Triangle Can Be Formed Given Three Side Lengths?
- How Do You Write an Indirect Proof?
- How Do You Put the Sides of a Triangle in Order According to Size if You Know Two Angles of the Triangle?
- What is the Circumcenter of a Triangle?
- What are Vertical Angles?
- How Do You Find Missing Angles in an Isosceles Triangle?
- What is the Hinge Theorem?
- What is a Median of a Triangle?
- How Do You Write a Coordinate Proof?
- What is the Triangle Midsegment Theorem?
- How Do You Find the Sum of the Interior Angles of a Polygon?
- What is the Pythagorean Theorem?
- How Do You Use the Diagonals of a Rectangle to Find the Value of a Variable?
- How Do You Use the Law of Detachment to Draw a Valid Conclusion?
- What is the Law of Syllogism?
- What are Supplementary Angles?
- How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?
- How Do You Use the Centroid to Find Segment Lengths in a Triangle?
- What is a 30-60-90 Degree Triangle?
- What is an Angle?
- What are Acute, Obtuse, Right, and Straight Angles?
- What is the Converse of the Pythagorean Theorem?
- How Do You Find the Value for a Variable in the Angles of a Quadrilateral To Make it a Rhombus?
- What is the Triangle Sum Theorem?
- What is the Distributive Property?
- What is the Substitution Property of Equality?
- What is the Incenter of a Triangle?

#### Similarity, proof, and trigonometry. The student uses the process skills to understand and apply relationships in right triangles.

##### Determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems

##### Apply the relationships in special right triangles 30Â°-60Â°-90Â° and 45Â°-45Â°-90Â° and the pythagorean theorem, including pythagorean triples, to solve problems

- How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
- What is the Pythagorean Theorem?
- How Do You Determine Whether a Line is Tangent to a Circle?
- What is a Tangent Line to a Circle?
- What is a 30-60-90 Degree Triangle?
- What is the Converse of the Pythagorean Theorem?
- How Do You Find the Area of a Trapezoid?
- What is the Formula for the Area of a Trapezoid?
- How Do You Find the Area of a Regular Polygon When You Know the Length of the Apothem?
- How Do You Find the Lateral and Surface Areas of a Regular Pyramid?
- What is a 45Ã‚Â°-45Ã‚Â°-90Ã‚Â° Triangle?
- How Do You Find the Lateral and Surface Areas of a Cone?
- How Do You Find the Area of a Sector of a Circle?
- What is the Formula for the Area of a Circle?

#### Similarity, proof, and trigonometry. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.

#### Similarity, proof, and trigonometry. The student uses the process skills in applying similarity to solve problems.

### Algebra 2

#### Exponential and logarithmic functions and equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.

##### Determine the effects on the key attributes on the graphs of f(x) = bx and f(x) = logb(x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d

##### Rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations

##### Formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation

##### Determine the reasonableness of a solution to a logarithmic equation

##### Solve exponential equations of the form y = abx where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions

#### Systems of equations and inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions.

##### Solve systems of three linear equations in three variables by using gaussian elimination, technology with matrices, and substitution

##### Formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic

##### Solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation

##### Formulate systems of at least two linear inequalities in two variables

##### Solve systems of two or more linear inequalities in two variables

##### Determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables

##### Determine possible solutions in the solution set of systems of two or more linear inequalities in two variables

#### Attributes of functions and their inverses. The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse.

##### Graph the functions f(x)=âˆšx, f(x)=1/x, f(x)=x3, f(x)= 3âˆšx, f(x)=bx, f(x)=|x|, and f(x)=logb (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval

- What is a Natural Logarithm?
- How Do You Convert From Exponential Form to Logarithmic Form?
- How Do You Translate a Function?
- How Do You Graph a Square Root Function Using a Table?
- What is a Cubic Function?
- What is Domain?
- What is an Absolute Value Function?
- What is Exponential Growth?
- How Do You Convert From Exponential Form to Natural Logarithmic Form?
- How Do You Graph the Natural Base Exponential Function?
- What is the Natural Base Exponential Function?
- What Does the Constant 'k' do in y = |x|+k?
- How Do You Graph an Absolute Value Function?
- What's an Exponential Function?
- What is a Logarithm?
- How Do You Find the Degree of a Polynomial?

##### Describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range

##### Graph and write the inverse of a function using notation such as f -1 (x)

##### Use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other

#### Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions.

##### Determine the effect on the graph of f(x) = âˆšx when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d

##### Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening

##### Write the quadratic function given three specified points in the plane

##### Formulate quadratic and square root equations using technology given a table of data

##### Transform a quadratic function f(x) = ax2 + bx + c to the form f(x) = a(x - h)2 + k to identify the different attributes of f(x)

##### Solve quadratic and square root equations

- What is the Imaginary Unit i?
- How Do You Convert a Quadratic from Standard Form to Vertex Form by Completing the Square?
- What is the Discriminant?
- How Do You Solve a Quadratic Equation by Using the Quadratic Formula?
- How Do You Add Complex Numbers?
- How Do You Solve a Quadratic Equation with Two Solutions by Graphing?
- How Do You Solve a Quadratic Equation by Completing the Square?
- How Do You Solve a Radical Equation?
- How Do You Solve a Quadratic Equation by Factoring?

##### Solve quadratic inequalities

##### Identify extraneous solutions of square root equations

#### Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions.

##### Analyze data to select the appropriate model from among linear, quadratic, and exponential models

##### Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models

##### Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data

#### Number and algebraic methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations.

##### Determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two

##### Add, subtract, and multiply polynomials

##### Add, subtract, and multiply complex numbers

- What is Exponential Growth?
- How Do You Find All the Rational Zeros of a Polynomial Function?
- How Do You Add Complex Numbers?
- What's an Exponential Function?
- How Do You Solve a Quadratic Equation with Two Solutions by Graphing?
- What's a Function?
- How Do You Graph a Quadratic Function?
- How Do You Solve a Quadratic Equation by Factoring?
- How Do You Graph the Natural Base Exponential Function?
- What is the Natural Base Exponential Function?
- What's the Inverse of a Relation?
- What is a Logarithm?
- How Do You Translate a Function?
- What is the Imaginary Unit i?
- What is the Standard Form of a Quadratic?
- What is Domain?
- What is an Absolute Value Function?
- How Do You Convert From Exponential Form to Logarithmic Form?
- How Can You Tell if a Relation is Not a Function?

##### Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping

- What is the Fundamental Theorem of Algebra?
- What is the Factor Theorem?
- How Do You Factor a Polynomial Using Sum of Cubes?
- How Do You Find All the Rational Zeros of a Polynomial Function?
- How Do You Factor a Trinomial?
- How Do You Factor a Polynomial Using the A-C Method?
- How Do You Graph a Square Root Function Using a Table?

##### Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods

##### Determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two

##### Solve equations involving rational exponents

##### Rewrite radical expressions that contain variables to equivalent forms

#### Cubic, cube root, absolute value and rational functions, equations, and inequalities. The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions.

##### Analyze the effect on the graphs of f(x) = |x| when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d

##### Analyze the effect on the graphs of f(x) = x3 and f(x) = 3âˆšx when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d

##### Solve absolute value linear equations

##### Solve absolute value linear inequalities

##### Determine the reasonableness of a solution to a rational equation

##### Formulate rational equations that model real-world situations

- How Do You Find the Least Common Denominator of Two Rational Expressions?
- What's the Inverse Variation or Indirect Proportionality Formula?
- How Do You Use the Formula for Inverse Variation to Write an Equation?
- How Do You Solve a Rational Equation by Adding Fractions?
- How Do You Divide Two Polynomials by Factoring and Canceling?
- How Do You Add Two Rational Expressions with Different Denominators?
- How Do You Multiply Two Rational Expressions?
- How Do You Solve a Rational Equation by LCD Multiplication?