High School Math Arkansas Standards

Statistical Experiments & Studies: Students evaluate processes for statistical experiments, make inferences, and justify conclusions from statistical studies.

Systems of Equations: Students solve systems of equations.

Rational Expressions: Students perform operations on rational expressions.

Factor Polynomials: Students factor polynomials.

Graph & Key Features: Students graph and identify key features of functions.

Create & Solve: Students create and solve rational and polynomial equations.

Graph & Key Features: Students graph and interpret key features of exponential and logarithmic models.

Logarithms: Students define and use logarithms.

Create & Solve: Students create and solve problems that model exponential and logarithmic relationships.

Exponential & Logarithmic Functions & Equations

Systems of Equations: Students solve systems of equations.

Graph & Key Features: Students graph and interpret key features of equations that model quadratic relationships.

Create & Solve: Students create and solve problems that model quadratic relationships.

Systems of Equations: Students solve systems of equations.

Matrices: Students perform operations and matrices.

Arithmetic Sequences: Students use arithmetic sequences to model problems.

Transformations: Students perform transformations in the coordinate plane.

Compositions: Students compose and compare functions.

Complex Numbers: Students apply properties to complex numbers.

Radical Expressions and Rational Exponents: Students apply properties to radical expressions and rational exponents.

Use the properties of exponents to find equivalent expressions and to solve equations, including those involving rational exponents.

Sketch the graph of an exponential function given a verbal description and show key features.

Calculate and interpret the average rate of change of an exponential function represented in a table, graph, or as an equation in the context of mathematical and real-world problems.

Graph exponential and logarithmic functions with and without context, identifying key features, and determining constraints in a given context.

Graph and generalize the effect of transformations on exponential and logarithmic functions.

Transformations include: stretches, compressions, vertical shifts, and horizontal shifts

Given the graphs of exponential and logarithmic functions, explain the effects of the transformation from the parent function.

Exponentials: 𝑦 = 𝑎𝑏 𝑥 , 𝑎 ≠ 0, 𝑏 > 0, and 𝑏 ≠ 1

Logarithms: 𝑦 = 𝑙𝑜𝑔𝑏(𝑥), 𝑏 > 0, 𝑥 > 0 and 𝑏 ≠ 1

Write and solve equations from real-world problems that can be represented as a logarithmic or exponential function in one variable.

Write exponential equations that model the relationship between two quantities when given a graph, a written description, or a table of values within a mathematical or real-world context.

Write and use geometric sequences recursively and explicitly to model situations; translate between the two forms when given a graph, a description of the relationship, or two input-output pairs.

Translate between logarithmic and exponential forms of an equation.

Use properties of logarithms to simplify and evaluate logarithmic expressions, with or without technology.

Use the inverse relationship between exponents and logarithms to solve problems.

Determine the domain and range of logarithmic functions in mathematical problems.

Determine reasonable domain and range values of logarithmic functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.

Combine functions by addition, subtraction, multiplication, division, and composition to model the relationship between two quantities in mathematical and real-world contexts.

Decide if a function is even or odd from a graph or an algebraic expression.

Explain how restricting the domain of a function allows the creation of its inverse.

Write and graph the inverse of a given function; understand that the graph of an inverse function is a reflection of the function over the line 𝑦 = 𝑥.

Write and use arithmetic sequences recursively and explicitly to model situations; translate between the two forms when given a graph, a description of the relationship, or two input-output pairs.

Multiply a matrix by a scalar.

Add and subtract matrices.

Solve systems of linear equations in three variables using matrices; use Gaussian elimination or technology.

Write and solve equations from real-world problems that can be represented as a rational or square root function in one variable.

Sketch the graph of a polynomial function given a verbal description and show key features.

Calculate and interpret the average rate of change of polynomial functions represented in a table, graph, or as an equation in context of mathematical and real-world problems.

Graph functions with and without context, identifying key features and determining constraints in a given context.

Functions include: polynomial, rational, square root, and piecewise-defined

Graph and generalize the effect of transformations on square root, cubic, and rational functions.

Transformations include: stretches, compressions, vertical shifts, and horizontal shifts

Given a graph, explain the effects of the transformation from the parent function.

Square Roots: 𝑦 = √�

Cubics: 𝑦 = 𝑥 3

Rationals: 𝑦 = 1 �

Apply the Remainder Theorem to factor and create equivalent forms of polynomial functions.

Verify polynomial identities and use them to describe numerical relationships.

Apply understanding of rational number operations to add, subtract, multiply, and divide by nonzero rational expressions.

Rewrite simple rational expressions in different forms.

Divide polynomial expressions using inspection, long division, and synthetic division, with and without a remainder.

Solve non-linear formulas for a specified variable.

Explain why a solution to the equation 𝑓(𝑥) = 𝑔(𝑥) is the x-coordinate where the y-coordinate of 𝑓(𝑥)and 𝑔(𝑥) are the same using graphs, tables, or approximations.

Include cases where 𝑓(𝑥) and/or 𝑔(𝑥) are linear, polynomial, exponential, logarithmic, or rational and where at least one of the functions is not linear.

Find zeros of polynomial functions with a degree of 3 or higher when suitable factorizations are available in a real-world and mathematical context.

Use zeros and an understanding of multiplicity to sketch a graph of a polynomial function with a degree of 3 or higher.

Apply the Fundamental Theorem of Algebra to determine the number and potential types of roots of polynomial functions based on the degree of the polynomial.

Solve rational and radical equations containing one variable specifying extraneous solutions.

Determine the domain and range of polynomial and rational functions in mathematical problems.

Determine reasonable domain and range values of polynomial and rational functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.

Interpret the key features of polynomial functions that model a relationship between two quantities in a given context; translate between different representations of the function, especially graphs, tables, and equations.

Calculate and interpret the average rate of change of a quadratic function represented in a table, graph, or as an equation in the context of mathematical and real-world problems.

Solve quadratic equations with complex number solutions.

Represent and solve real-world problems using quadratic inequalities.

Use the discriminant to determine the number and type of solutions of a quadratic equation.

Sketch the graph of a quadratic function given a verbal description and show key features.

Solve a system of equations consisting of a linear equation and a nonlinear equation in two variables by choosing substitution or graphically (with or without technology) as appropriate for the system of equations.

Explain how extending the properties of integer exponents to rational exponents provides an alternative notation for radicals.

Apply the properties of exponents to translate between radical and exponential forms of expressions.

Simplify and perform operations with radical expressions with and without variables; rationalizing denominators should include conjugates.

Know there is a complex number 𝑖 and describe contexts from which complex numbers appear.

Perform the operations of addition, subtraction, multiplication, and conjugation of complex numbers.

Use polynomial identities with complex numbers.

Use data from a random sample to make inferences about a population.

Compare theoretical and empirical probabilities using simulations.

Distinguish between sample surveys, experiments, and observational studies and explain the purpose of randomization in statistical studies.

Read and explain, in context, the validity of data from outside reports by:

Identifying the variables as quantitative or categorical.

Describing how the data was collected.

Indicating any potential biases or flaws.

Identifying inferences the author of the report made from sample data.

Functions

Linear Functions and Equations

Polynomial, Rational, & Other Functions & Equations

Quadratic Functions, Equations and Inequalities

Radicals and Complex Numbers

Statistics & Probability

Triangle Congruence

Similarity

Similarities & Congruence

Plane

Coordinate Plane

Transformations

Parallel & Perpendicular Lines

Coordinate Geometry

Define & Construct

Lines & Angles

Geometric Probability

Two-Dimensional

Three-Dimensional

Geometric Figures

Equation of a Circle

Circle Relationships

Circles

Trigonometry Ratios

Special Right Triangles & Pythagorean Theorem

Right Triangles

Geometry

Bivariate Data

Numerical Data

Statistics & Probability

Statistical Relationships

Graphing

Interpret Key Features

Create & Solve

Exponential Functions & Equations

Statistical Relationships

Graphing & Transformations

Interpret Key Features

Create & Solve

Quadratic Functions & Equations

Statistical Relationships

Graphing & Transformations

Systems of Equations & Inequalities

Interpret Key Features

Create & Solve

Linear Functions, Equations, & Inequalities

Construct & Compare

Domain & Range, Function Notation

Functions

Polynomials, Roots, & Exponent Laws

Expressions

Algebra I

Represent and solve real-world problems, using exponential equations in one variable.

Write exponential functions that provide a reasonable fit to data and use them to make predictions with technology.

Represent real-world problems (growth, decay, and compound interest), using exponential equations.

Construct exponential equations from geometric sequences with and without context.

Determine the domain and range of exponential functions in mathematical problems.

Determine reasonable domain and range values of exponential functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.

Interpret the key features of an exponential function that models a relationship between two quantities in a given context.

Flexibly use different representations of an exponential function, including graphs, tables, and equations.

Interpret the quantities in an exponential equation in the context of a real-world problem, including growth, decay, and compound interest.

Graph exponential functions that model real-world problems (growth, decay, and compound interest), showing key attributes.

Students create and solve problems that model exponential relationships.

Students interpret key features of equations that model exponential relationships.

Students graph exponential functions.

Students explore exponential statistical relationships.

Students simplify algebraic and numerical expressions.

Add, subtract, and multiply polynomials; compare the system of polynomials to the system of integers when performing operations.

Simplify and perform operations with radical expressions without variables; rationalizing denominators should not include conjugates.

Simplify algebraic expressions using the laws of exponents.

Interpret the parts of expressions such as terms, factors, and coefficients in terms of a real-world context.

Explain that a function assigns each element in the domain to exactly one element in the range.

Use function notation to represent functions, understanding that if f is a function and x is an element of its domain, then f(x) represents the output of f corresponding to the input x.

Graph functions given in function notation, understanding that the graph contains the points (x,f(x)).

Evaluate functions expressed in function notation for one or more elements in their domains (inputs); use function notation to describe a contextual situation.

Differentiate between real-world scenarios that can be modeled by exponential or linear functions by determining whether the relationship has a common difference or a common ratio.

Compare the growth pattern of exponential to linear or quadratic functions using graphs and tables and recognize how exponential growth exceeds other functions.

Students understand the concept of a function, domain and range, and use function notation; students use function notation to solve problems.

Students construct and compare linear, quadratic, and exponential models and solve problems.

Represent and solve real-world problems, using linear expressions, equations, and inequalities in one variable.

Translate among equivalent forms of equations for linear functions, including standard, point-slope, and slope-intercept forms; recognize that each form reveals key features in a given context.

Solve systems of linear equations by substitution, elimination, and graphing with and without a real-world context; understand that the solutions will be the same regardless of the method for solving.

Solve a system of equations consisting of a linear equation and a quadratic equation in two variables graphically with the assistance of technology.

Explain why a solution to the equation f(x) = g(x) is the x-coordinate where the y-coordinate of f(x) and g(x) are the same using graphs, tables, or approximations. Include cases where f(x) and/or g(x) are linear, quadratic, absolute value, and exponential.

Solve linear inequalities and systems of linear inequalities in two variables by graphing.

Write linear equations that model the relationship between two quantities and produce a graph of the equation.

Graph linear functions expressed as an equation and show intercepts of the graph without technology.

Graph absolute value functions expressed as an equation with and without technology, showing intercepts and end behavior.

Graph and generalize the effect of transformations on linear and absolute value functions.<ul><li>Transformations include: stretches, compressions, vertical, and horizontal</li></ul>

Given the graph of a linear function, explain the effects of the transformation from the parent function, y=x.

Construct linear functions from arithmetic sequences with and without context.

Write linear functions that provide a reasonable fit to data and use them to make predictions, with and without technology; interpret the slope and y-intercept in context.

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

Compare and contrast correlation and causation in real-world problems.

Solve linear formulas for a specified variable.

Solve linear equations, linear inequalities, and absolute value equations in one variable, including those with rational number coefficients, and variables on both sides of the equal or inequality sign; solve them fluently, explaining the process used.

Determine the domain and range of linear functions in mathematical problems.

Determine reasonable domain and range values of linear functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.

Interpret the key features of a linear and absolute value functions that models a relationship between two quantities in a given context.

Flexibly use different representations of a linear function, including graphs, tables, and equations.

Calculate and interpret the rate of change of a linear function represented in a table, graph, or as an equation in context of real-world and mathematical problems.

Students create and solve equations that model linear relationships.

Students interpret key features of equations that model linear relationships.

Students solve systems of equations and inequalities.

Students graph linear functions, equations, and inequalities.

Students explore linear statistical relationships.

Represent and solve real-world problems using quadratic expressions and equations in one variable.

Graph quadratic functions given as an equation or in function notation, labeling key attributes, without technology.

Graph and describe the effect of transformations on quadratic functions.<ul><li>Transformations include: stretches, compressions, vertical, and horizontal</li></ul>

Given the graph of a quadratic function, explain the effects of the transformation from the parent function, y = x².

Write quadratic functions that provide a reasonable fit to data and use them to make predictions with technology.

Write quadratic equations with real number solutions that model the relationship between two quantities and produce a graph of the equation.

Solve quadratic equations with real number solutions, containing one variable, including those with variables on both sides of the equal sign. Equations should be solved by:<ul><li>Graphing,</li><li>Factoring (including perfect square trinomials and difference of squares binomials),</li><li>Using the quadratic formula,</li><li>Completing the square, or</li><li>Taking the square root.</li></ul>

Determine the domain and range of quadratic functions in mathematical problems.

Determine reasonable domain and range values of quadratic functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.

Interpret the key features of a quadratic function that models a relationship between two quantities in a given context.

Flexibly use different representations of a quadratic function, including graphs, tables, and equations.

Explain how each form of a quadratic expression (standard, factored, and vertex form) identifies different key attributes, using the different forms to interpret quantities in context.

Use factoring and completing the square to create equivalent forms of quadratic functions to reveal key attributes.

Students create and solve equations that model quadratic relationships.

Students interpret key features of equations that model quadratic relationships.

Students graph quadratic functions and explore different transformations of f(x) = x².

Students explore quadratic statistical relationships.

Use box plots and histograms to determine the statistics appropriate to the shape of the data distribution; compare the center and spread of two or more data sets.

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points.

Summarize data from two categorical variables in a frequency table; interpret relative frequencies in the context of the data, recognizing data trends and associations.

Students summarize and describe distributions.

Students will investigate patterns of association in bivariate data.

Apply the precise definition and standard geometric notation for a circle to understand geometric relationships.

Recognize and apply relationships between angles, radii, and chords, tangents, and secants including:<ul><li>The relationship between central, inscribed, and circumscribed angles,</li><li>Inscribed angles on a diameter are right angles,</li><li>The radius of a circle is perpendicular to the tangent where the radius intersects the circle, and</li><li>The relationship of angles and segments formed by chords, secants and/or tangents to a circle.</li></ul>

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

Use the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems.

Explain why the formulas for the area and circumference of a circle work using dissection and informal limit arguments.

Write the equation of a circle, given the radius and center, where the center is at the origin or another point.

Identify the center and radius of a circle, given the equation of a circle, where the center is at the origin or another point.

Apply the equation of a circle to solve real-world problems.

Students explore and use circle relationships to solve problems.

Students solve problems involving the equation of a circle.

Find the volume and surface area of complex three-dimensional figures composed of prisms, pyramids, cones, cylinders, and spheres.

Calculate the area of triangles and rectangles when given the vertices, including using the distance formula and decomposing figures.

Describe reflectional and rotational symmetry as they apply to a rectangle, parallelogram, trapezoid, or regular polygon.

Calculate probabilities as a proportion of area in a geometric context.

Use three-dimensional geometric figures and their measures to model real-world objects and solve problems.

Explain why the formulas for the volume and surface area of a cylinder, pyramid, and cone work.

Apply the Pythagorean Theorem to determine missing measurements in a three-dimensional figure.

Identify the three-dimensional figure generated by rotating a two-dimensional figure.

Apply theorems about quadrilaterals, including those involving angles, diagonals, and sides to solve problems.

Prove that a given quadrilateral is a parallelogram, rhombus, rectangle, square, kite, or trapezoid, and apply these relationships to solve problems.

Prove and apply theorems about triangles including:<ul><li>Angle-Sum Theorem,</li><li>Exterior Angle Theorem,</li><li>Isosceles Triangle Theorem and its converse,</li><li>Midsegment Theorem,</li><li>Proportionality Theorem,</li><li>Inequality Theorem and its converse, and</li><li>Geometric Mean Theorem.</li></ul>

Calculate the perimeter of polygons when given the vertices, including using the distance formula.

Students explore and solve problems involving three-dimensional figures.

Students explore and solve problems involving two-dimensional figures.

Students determine probability in geometric contexts.

Use precise definitions and standard geometric notation for angles, perpendicular lines, parallel lines, and line segments based on the undefined notions of point, line, and distance along a line.

Make formal geometric constructions with a variety of tools and methods including:<ul><li>Congruent segments and angles,</li><li>Segment and angle bisectors,</li><li>Perpendicular lines and perpendicular bisectors of a line segment,</li><li>Parallel lines, and</li><li>An equilateral triangle, a square, and a regular hexagon inscribed in a circle.</li></ul>

Determine the point that cuts a line segment into a specified ratio on a number line and a coordinate plane, including finding the midpoint.

Derive the distance and midpoint formulas and use the formulas, including the slope formula, to verify geometric relationships on a coordinate plane.

Prove and apply slope criteria of parallel and perpendicular lines to solve problems.

Write an equation of a line that is parallel or perpendicular to a given line and passing through a given point.

Prove and apply theorems about lines and angles including:<ul><li>Vertical angles,</li><li>Angles formed by parallel lines cut by a transversal, and</li><li>Points on a perpendicular bisector.</li></ul>

Students use precise definitions and various construction tools to create geometric figures.

Students reason about geometric figures using the coordinate plane.

Students solve problems involving parallel and perpendicular lines.

Apply the properties of special right triangles (30°-60°-90° and 45°-45°-90°) to solve real-world and mathematical problems.

Prove and apply the Pythagorean Theorem and its converse.

Explain how the definitions for trigonometric ratios are developed by similarity and how the side ratios in right triangles are properties of the angles in the triangle.

Explain the relationship between the sine and cosine of complementary angles and use them to solve problems.

Determine the sine, cosine, and tangent ratios of acute angles given the side lengths of right triangles.

Use trigonometric ratios (sine, cosine, and tangent) to calculate missing side lengths and angle measures in a right triangle, including applications of angles of elevation and depression; include real-world and mathematical problems.

Students explore right triangles and apply the Pythagorean Theorem.

Students apply trigonometric ratios to solve problems.

Given two figures, apply the definition of similarity in terms of a dilation to identify similar figures, proportional sides, and corresponding congruent angles.

Develop and apply the criteria of similarity for triangles (AA~, SAS~, and SSS~) to solve problems and prove geometric relationships.

Use transformations to prove all circles are similar.

Explain, using rigid motion transformations, why two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Develop and apply the criteria for triangle congruence (ASA, SAS, AAS, SSS, and HL) to solve problems and prove geometric relationships.

Students use similarity criteria to solve problems.

Students apply congruence criteria to solve problems.

Describe rotations, reflections, and translations as functions that take points in the coordinate plane as inputs and give other points as outputs; write in prime notation.

Compare transformations that preserve distance and angle (rotations, reflections, and translations) to those that do not (dilations) to develop definitions for congruence and similarity.

Apply understanding of angles, circles, perpendicular lines, parallel lines, and line segments to develop definitions for rotations, reflections, and translations.

Use geometric constructions to represent rotations, reflections, translations, and dilations in the plane with a variety of tools and methods.

Given two congruent figures, identify the sequence of transformations that maps one figure to another.

Students transform figures on the coordinate plane.

Students transform figures and make geometric constructions.