Kentucky Academic Standards: Mathematics I
Skills available for Kentucky Integrated 1 math standards
Domain
Print skill plan
N
Number and Quantity
The Real Number System
Extend the properties of exponents to rational exponents.
Extend the properties of exponents to rational exponents.
KY.HS.N.1: Extend the properties of integer exponents to rational exponents, allowing for the expression of radicals in terms of rational exponents.
KY.HS.N.1: Extend the properties of integer exponents to rational exponents, allowing for the expression of radicals in terms of rational exponents.
KY.HS.N.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Rational exponents
Radical expressions
KY.HS.N.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Rational exponents
Radical expressions
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Quantities
Reason quantitatively and use units to solve problems.
Reason quantitatively and use units to solve problems.
KY.HS.N.4: Use units in context as a way to understand problems and to guide the solution of multi-step problems;
KY.HS.N.4: Use units in context as a way to understand problems and to guide the solution of multi-step problems;
KY.HS.N.4.a: Choose and interpret units consistently in formulas;
KY.HS.N.4.a: Choose and interpret units consistently in formulas;
KY.HS.N.4.b: Choose and interpret the scale and the origin in graphs and data displays.
KY.HS.N.4.b: Choose and interpret the scale and the origin in graphs and data displays.
KY.HS.N.5: Define appropriate units in context for the purpose of descriptive modeling.
Linear models
Exponential models
Quadratic models
KY.HS.N.5: Define appropriate units in context for the purpose of descriptive modeling.
Linear models
Exponential models
Quadratic models
KY.HS.N.6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Precision
Greatest possible error
Percent error
KY.HS.N.6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Precision
Greatest possible error
Percent error
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A
Algebra
Seeing Structure in Expressions
Interpret the structure of expressions.
Interpret the structure of expressions.
KY.HS.A.1: Interpret expressions that represent a quantity in terms of its context.
KY.HS.A.1: Interpret expressions that represent a quantity in terms of its context.
KY.HS.A.1.a: Interpret parts of an expression, such as terms, factors and coefficients.
KY.HS.A.1.a: Interpret parts of an expression, such as terms, factors and coefficients.
KY.HS.A.1.b: Interpret complicated expressions, given a context, by viewing one or more of their parts as a single entity.
KY.HS.A.1.b: Interpret complicated expressions, given a context, by viewing one or more of their parts as a single entity.
KY.HS.A.2: Use the structure of an expression to identify ways to rewrite it and consistently look for opportunities to rewrite expressions in equivalent forms.
Linear expressions
Numeric expressions with exponents
Exponential expressions
Polynomial expressions
Quadratic expressions
Radical expressions
KY.HS.A.2: Use the structure of an expression to identify ways to rewrite it and consistently look for opportunities to rewrite expressions in equivalent forms.
Linear expressions
Numeric expressions with exponents
Exponential expressions
Polynomial expressions
Quadratic expressions
Radical expressions
Write expressions in equivalent forms to solve problems.
Write expressions in equivalent forms to solve problems.
KY.HS.A.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
KY.HS.A.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
KY.HS.A.3.a: Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient and constant term.
KY.HS.A.3.a: Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient and constant term.
KY.HS.A.3.b: Factor a quadratic expression to reveal the zeros of the function it defines.
Factor quadratics
Zeros of a function
KY.HS.A.3.b: Factor a quadratic expression to reveal the zeros of the function it defines.
Factor quadratics
Zeros of a function
KY.HS.A.3.c: Use the properties of exponents to rewrite exponential expressions.
Exponential expressions
Evaluate an exponential function
KY.HS.A.3.c: Use the properties of exponents to rewrite exponential expressions.
Exponential expressions
Evaluate an exponential function
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Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials.
Perform arithmetic operations on polynomials.
KY.HS.A.5: Add, subtract and multiply polynomials.
Model polynomials
Add and subtract polynomials
Multiply polynomials
KY.HS.A.5: Add, subtract and multiply polynomials.
Model polynomials
Add and subtract polynomials
Multiply polynomials
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Understand the relationship between zeros and factors of polynomials.
Understand the relationship between zeros and factors of polynomials.
KY.HS.A.7: Identify roots of polynomials when suitable factorizations are available. Know these roots become the zeros (x-intercepts) for the corresponding polynomial function.
KY.HS.A.7: Identify roots of polynomials when suitable factorizations are available. Know these roots become the zeros (x-intercepts) for the corresponding polynomial function.
Creating Equations
Create equations that describe numbers or relationships.
Create equations that describe numbers or relationships.
KY.HS.A.12: Create equations and inequalities in one variable and use them to solve problems.
Linear equations
Inequalities
Exponential and quadratic equations
KY.HS.A.12: Create equations and inequalities in one variable and use them to solve problems.
Linear equations
Inequalities
Exponential and quadratic equations
KY.HS.A.13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Direct variation
Slope-intercept form
Standard form
Point-slope form
Exponential equations
Quadratic equations
Linear, quadratic, and exponential equations
KY.HS.A.13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Direct variation
Slope-intercept form
Standard form
Point-slope form
Exponential equations
Quadratic equations
Linear, quadratic, and exponential equations
KY.HS.A.14: Create a system of equations or inequalities to represent constraints within a modeling context. Interpret the solution(s) to the corresponding system as viable or nonviable options within the context.
Equations
Inequalities
KY.HS.A.14: Create a system of equations or inequalities to represent constraints within a modeling context. Interpret the solution(s) to the corresponding system as viable or nonviable options within the context.
Equations
Inequalities
KY.HS.A.15: Rearrange formulas to solve a literal equation, highlighting a quantity of interest, using the same reasoning as in solving equations.
KY.HS.A.15: Rearrange formulas to solve a literal equation, highlighting a quantity of interest, using the same reasoning as in solving equations.
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Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning.
Understand solving equations as a process of reasoning and explain the reasoning.
KY.HS.A.16: Understand each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
KY.HS.A.16: Understand each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Solve equations and inequalities in one variable.
Solve equations and inequalities in one variable.
KY.HS.A.18: Solve linear equations and inequalities in one variable, including literal equations with coefficients represented by letters.
Multi-variable equations
Equations with models
One- and two-step linear equations
Multi-step linear equations
Solutions to linear equations
Linear inequalities
Compound inequalities
KY.HS.A.18: Solve linear equations and inequalities in one variable, including literal equations with coefficients represented by letters.
Multi-variable equations
Equations with models
One- and two-step linear equations
Multi-step linear equations
Solutions to linear equations
Linear inequalities
Compound inequalities
KY.HS.A.19: Solve quadratic equations in one variable.
KY.HS.A.19: Solve quadratic equations in one variable.
KY.HS.A.19.a: Solve quadratic equations by taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Square roots
Factoring
Quadratic formula
Word problems
KY.HS.A.19.a: Solve quadratic equations by taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Square roots
Factoring
Quadratic formula
Word problems
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Solve systems of equations.
Solve systems of equations.
KY.HS.A.20: Solve systems of linear equations in two variables.
KY.HS.A.20: Solve systems of linear equations in two variables.
KY.HS.A.20.a: Understand a system of two equations in two variables has the same solution as a new system formed by replacing one of the original equations with an equivalent equation.
KY.HS.A.20.a: Understand a system of two equations in two variables has the same solution as a new system formed by replacing one of the original equations with an equivalent equation.
KY.HS.A.20.b: Solve systems of linear equations with graphs, substitution and elimination, focusing on pairs of linear equations in two variables.
Graphing
Understand solutions
Substitution
Elimination
Any method
KY.HS.A.20.b: Solve systems of linear equations with graphs, substitution and elimination, focusing on pairs of linear equations in two variables.
Graphing
Understand solutions
Substitution
Elimination
Any method
Represent and solve equations and inequalities graphically.
Represent and solve equations and inequalities graphically.
KY.HS.A.23: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
KY.HS.A.23: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
KY.HS.A.24: Justify that the solutions of the equations f(x) = g(x) are the x-coordinates of the points where the graphs of y = f(x) and y = g(x) intersect. Find the approximate solutions graphically, using technology or tables.
Tables
Graphs
KY.HS.A.24: Justify that the solutions of the equations f(x) = g(x) are the x-coordinates of the points where the graphs of y = f(x) and y = g(x) intersect. Find the approximate solutions graphically, using technology or tables.
Tables
Graphs
KY.HS.A.25: Graph linear inequalities in two variables.
KY.HS.A.25: Graph linear inequalities in two variables.
KY.HS.A.25.a: Graph the solutions to a linear inequality as a half-plane (excluding the boundary in the case of a strict inequality).
KY.HS.A.25.a: Graph the solutions to a linear inequality as a half-plane (excluding the boundary in the case of a strict inequality).
KY.HS.A.25.b: Graph the solution set to a system of linear inequalities as the intersection of the corresponding half-planes.
KY.HS.A.25.b: Graph the solution set to a system of linear inequalities as the intersection of the corresponding half-planes.
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F
Functions
Interpreting Functions
Understand the concept of a function and use function notation.
Understand the concept of a function and use function notation.
KY.HS.F.1: Understand properties and key features of functions and the different ways functions can be represented.
KY.HS.F.1: Understand properties and key features of functions and the different ways functions can be represented.
KY.HS.F.1.a: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function, x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.
Independent and dependent variables
Identify functions
Function tables and graphs
Relations
Linear functions
Exponential functions
Quadratic functions
Absolute value functions
Square root functions
KY.HS.F.1.a: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function, x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.
Independent and dependent variables
Identify functions
Function tables and graphs
Relations
Linear functions
Exponential functions
Quadratic functions
Absolute value functions
Square root functions
KY.HS.F.1.b: Using appropriate function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context.
Evaluate a function
Interpret function notation
Tables and graphs
KY.HS.F.1.b: Using appropriate function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context.
Evaluate a function
Interpret function notation
Tables and graphs
KY.HS.F.1.c: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.
Linear functions
Exponential functions
Quadratic functions
Linear, quadratic, and exponential functions
Absolute value functions
Word problems
KY.HS.F.1.c: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.
Linear functions
Exponential functions
Quadratic functions
Linear, quadratic, and exponential functions
Absolute value functions
Word problems
KY.HS.F.1.d: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Linear functions
Exponential functions
Quadratic functions
Absolute value functions
Square root functions
KY.HS.F.1.d: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Linear functions
Exponential functions
Quadratic functions
Absolute value functions
Square root functions
KY.HS.F.1.e: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
KY.HS.F.1.e: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
KY.HS.F.2: Recognize that arithmetic and geometric sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Mixed sequences
Arithmetic sequences
Geometric sequences
Recursive formulas
Explicit and recursive sequences
KY.HS.F.2: Recognize that arithmetic and geometric sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Mixed sequences
Arithmetic sequences
Geometric sequences
Recursive formulas
Explicit and recursive sequences
Interpret functions that arise in applications in terms of the context.
Interpret functions that arise in applications in terms of the context.
KY.HS.F.3: Understand average rate of change of a function over an interval.
KY.HS.F.3: Understand average rate of change of a function over an interval.
KY.HS.F.3.a: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.
Rate of change
Constant of variation
Slope
KY.HS.F.3.a: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.
Rate of change
Constant of variation
Slope
KY.HS.F.3.b: Estimate the rate of change from a graph.
KY.HS.F.3.b: Estimate the rate of change from a graph.
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Analyze functions using different representations.
Analyze functions using different representations.
KY.HS.F.4: Graph functions expressed symbolically and show key features of the graph, with and without using technology (computer, graphing calculator).
KY.HS.F.4: Graph functions expressed symbolically and show key features of the graph, with and without using technology (computer, graphing calculator).
KY.HS.F.4.a: Graph linear and quadratic functions and show intercepts, maxima and minima.
Linear functions
Quadratic functions
KY.HS.F.4.a: Graph linear and quadratic functions and show intercepts, maxima and minima.
Linear functions
Quadratic functions
KY.HS.F.5: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
KY.HS.F.5: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
KY.HS.F.5.a: Identify zeros, extreme values and symmetry of the graph within the context of a quadratic function.
Characteristics of quadratic functions
Identify zeros
KY.HS.F.5.a: Identify zeros, extreme values and symmetry of the graph within the context of a quadratic function.
Characteristics of quadratic functions
Identify zeros
KY.HS.F.5.b: Use the properties of exponents to interpret expressions for exponential functions and classify the exponential function as representing growth or decay.
KY.HS.F.5.b: Use the properties of exponents to interpret expressions for exponential functions and classify the exponential function as representing growth or decay.
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Building Functions
Build a function that models a relationship between two quantities.
Build a function that models a relationship between two quantities.
KY.HS.F.6: Write a function that describes a relationship between two quantities.
KY.HS.F.6: Write a function that describes a relationship between two quantities.
KY.HS.F.6.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
Sequences
Linear, quadratic, and exponential functions
KY.HS.F.6.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
Sequences
Linear, quadratic, and exponential functions
KY.HS.F.6.b: Combine standard function types using arithmetic operations.
KY.HS.F.6.b: Combine standard function types using arithmetic operations.
KY.HS.F.7: Use arithmetic and geometric sequences to model situations and scenarios.
KY.HS.F.7: Use arithmetic and geometric sequences to model situations and scenarios.
KY.HS.F.7.a: Use formulas (explicit and recursive) to generate terms for arithmetic and geometric sequences.
KY.HS.F.7.a: Use formulas (explicit and recursive) to generate terms for arithmetic and geometric sequences.
KY.HS.F.7.b: Write formulas to model arithmetic and geometric sequences and apply those formulas in realistic situations.
KY.HS.F.7.b: Write formulas to model arithmetic and geometric sequences and apply those formulas in realistic situations.
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Linear, Quadratic and Exponential Functions
Construct and compare linear, quadratic and exponential models and solve problems.
Construct and compare linear, quadratic and exponential models and solve problems.
KY.HS.F.11: Distinguish between situations that can be modeled with linear functions and with exponential functions.
KY.HS.F.11: Distinguish between situations that can be modeled with linear functions and with exponential functions.
KY.HS.F.11.a: Recognize and justify that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
KY.HS.F.11.a: Recognize and justify that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
KY.HS.F.11.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
KY.HS.F.11.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
KY.HS.F.11.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
KY.HS.F.11.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
KY.HS.F.12: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Arithmetic and geometric sequences
Slope-intercept form
Parallel and perpendicular lines
Point-slope form
Exponential functions
Linear and exponential functions
KY.HS.F.12: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Arithmetic and geometric sequences
Slope-intercept form
Parallel and perpendicular lines
Point-slope form
Exponential functions
Linear and exponential functions
KY.HS.F.13: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
KY.HS.F.13: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Interpret expressions for functions in terms of the situation they model.
Interpret expressions for functions in terms of the situation they model.
KY.HS.F.14: Interpret the parameters in a linear or exponential function in terms of a context.
KY.HS.F.14: Interpret the parameters in a linear or exponential function in terms of a context.
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G
Geometry
Congruence
Experiment with transformations in the plane.
Experiment with transformations in the plane.
KY.HS.G.1: Know and apply precise definitions of the language of Geometry:
KY.HS.G.1: Know and apply precise definitions of the language of Geometry:
KY.HS.G.1.a: Understand properties of line segments, angles and circle.
KY.HS.G.1.a: Understand properties of line segments, angles and circle.
KY.HS.G.1.b: Understand properties of and differences between perpendicular and parallel lines.
KY.HS.G.1.b: Understand properties of and differences between perpendicular and parallel lines.
KY.HS.G.2: Representing transformations in the plane.
KY.HS.G.2: Representing transformations in the plane.
KY.HS.G.2.a: Describe transformations as functions that take points in the plane as inputs and give other points as outputs.
Translations
Reflections
Rotations
Congruence transformations
Dilations
KY.HS.G.2.a: Describe transformations as functions that take points in the plane as inputs and give other points as outputs.
Translations
Reflections
Rotations
Congruence transformations
Dilations
KY.HS.G.2.b: Compare transformations that preserve distance and angle measures to those that do not.
KY.HS.G.2.b: Compare transformations that preserve distance and angle measures to those that do not.
KY.HS.G.2.c: Given a rectangle, parallelogram, trapezoid, or regular polygon, formally describe the rotations and reflections that carry it onto itself, using properties of these figures.
KY.HS.G.2.c: Given a rectangle, parallelogram, trapezoid, or regular polygon, formally describe the rotations and reflections that carry it onto itself, using properties of these figures.
KY.HS.G.4: Understand the effects of transformations of geometric figures.
KY.HS.G.4: Understand the effects of transformations of geometric figures.
KY.HS.G.4.a: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure.
KY.HS.G.4.a: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure.
KY.HS.G.4.b: Specify a sequence of transformations that will carry a given figure onto another.
KY.HS.G.4.b: Specify a sequence of transformations that will carry a given figure onto another.
KY.HS.G.4.c: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
KY.HS.G.4.c: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
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Understand congruence in terms of rigid motions.
Understand congruence in terms of rigid motions.
KY.HS.G.5: Know and apply the concepts of triangle congruence:
KY.HS.G.5: Know and apply the concepts of triangle congruence:
KY.HS.G.5.a: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
KY.HS.G.5.a: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
KY.HS.G.5.b: Explain how the criteria for triangle congruence (ASA, SAS and SSS) follow from the definition of congruence in terms of rigid motions.
KY.HS.G.5.b: Explain how the criteria for triangle congruence (ASA, SAS and SSS) follow from the definition of congruence in terms of rigid motions.
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Prove geometric theorems.
Prove geometric theorems.
KY.HS.G.6: Apply theorems for lines, angles, triangles, parallelograms.
Lines and angles
Triangles
Parallelograms
KY.HS.G.6: Apply theorems for lines, angles, triangles, parallelograms.
Lines and angles
Triangles
Parallelograms
KY.HS.G.7: Prove theorems about geometric figures.
KY.HS.G.7: Prove theorems about geometric figures.
KY.HS.G.7.a: Construct formal proofs to justify theorems for lines, angles and triangles.
Proofs involving angles
Proofs involving lines
Proofs involving triangles
KY.HS.G.7.a: Construct formal proofs to justify theorems for lines, angles and triangles.
Proofs involving angles
Proofs involving lines
Proofs involving triangles
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Make geometric constructions.
Make geometric constructions.
KY.HS.G.8: Create and apply geometric constructions.
KY.HS.G.8: Create and apply geometric constructions.
KY.HS.G.8.a: Make formal geometric constructions with a variety of tools and methods.
Angles
Points, lines, and segments
Regular polygons
Triangles
Circles
KY.HS.G.8.a: Make formal geometric constructions with a variety of tools and methods.
Angles
Points, lines, and segments
Regular polygons
Triangles
Circles
KY.HS.G.8.b: Apply basic construction procedures to construct more complex figures.
KY.HS.G.8.b: Apply basic construction procedures to construct more complex figures.
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Similarity, Right Triangles and Trigonometry
Understand similarity in terms of similarity transformations.
Understand similarity in terms of similarity transformations.
KY.HS.G.9: Understand properties of dilations.
KY.HS.G.9: Understand properties of dilations.
KY.HS.G.9.a: Verify the properties that result from that dilations given by a center and a scale factor.
KY.HS.G.9.a: Verify the properties that result from that dilations given by a center and a scale factor.
KY.HS.G.9.b: Verify that a dilation produces an image that is similar to the pre-image.
Similar figures
Dilations
KY.HS.G.9.b: Verify that a dilation produces an image that is similar to the pre-image.
Similar figures
Dilations
KY.HS.G.10: Apply the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
KY.HS.G.10: Apply the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
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Prove theorems involving similarity.
Prove theorems involving similarity.
KY.HS.G.11: Understand theorems about triangles.
KY.HS.G.11: Understand theorems about triangles.
KY.HS.G.11.a: Apply theorems about triangles.
Triangle midsegments
Triangle Proportionality Theorem
Pythagorean Theorem
Prove theorems about triangles
KY.HS.G.11.a: Apply theorems about triangles.
Triangle midsegments
Triangle Proportionality Theorem
Pythagorean Theorem
Prove theorems about triangles
KY.HS.G.11.c: Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Similar triangles
Proofs involving similar triangles
KY.HS.G.11.c: Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Similar triangles
Proofs involving similar triangles
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Define trigonometric ratios and solve problems involving right triangles.
Define trigonometric ratios and solve problems involving right triangles.
KY.HS.G.12: Understand properties of right triangles.
KY.HS.G.12: Understand properties of right triangles.
KY.HS.G.12.a: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles (sine, cosine and tangent).
KY.HS.G.12.a: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles (sine, cosine and tangent).
KY.HS.G.12.b: Explain and use the relationship between the sine and cosine of complementary angles.
KY.HS.G.12.b: Explain and use the relationship between the sine and cosine of complementary angles.
KY.HS.G.12.c: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Pythagorean Theorem
Trigonometric ratios
Solve a right triangle
KY.HS.G.12.c: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Pythagorean Theorem
Trigonometric ratios
Solve a right triangle
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Circles
Understand and apply theorems about circles.
Understand and apply theorems about circles.
KY.HS.G.15: Verify using dilations that all circles are similar.
KY.HS.G.15: Verify using dilations that all circles are similar.
KY.HS.G.16: Identify and describe relationships among angles and segments within the context of circles involving:
KY.HS.G.16: Identify and describe relationships among angles and segments within the context of circles involving:
KY.HS.G.16.a: Recognize differences between and properties of inscribed, central and circumscribed angles.
KY.HS.G.16.a: Recognize differences between and properties of inscribed, central and circumscribed angles.
KY.HS.G.16.b: Understand relationships between inscribed angles and the diameter of a circle.
KY.HS.G.16.b: Understand relationships between inscribed angles and the diameter of a circle.
KY.HS.G.16.c: Understand the relationship between the radius of a circle and the line drawn through the point of tangency on that radius.
KY.HS.G.16.c: Understand the relationship between the radius of a circle and the line drawn through the point of tangency on that radius.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section.
Translate between the geometric description and the equation for a conic section.
KY.HS.G.19: Understand the relationship between the algebraic form and the geometric representation of a circle.
KY.HS.G.19: Understand the relationship between the algebraic form and the geometric representation of a circle.
KY.HS.G.19.a: Write the equation of a circle of given center and radius using the Pythagorean Theorem.
KY.HS.G.19.a: Write the equation of a circle of given center and radius using the Pythagorean Theorem.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Use coordinates to prove simple geometric theorems algebraically.
Use coordinates to prove simple geometric theorems algebraically.
KY.HS.G.21: Use coordinates to justify and prove simple geometric theorems algebraically.
KY.HS.G.21: Use coordinates to justify and prove simple geometric theorems algebraically.
KY.HS.G.22: Justify and apply the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
KY.HS.G.22: Justify and apply the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
KY.HS.G.23: Find measurements among points within the coordinate plane.
KY.HS.G.23: Find measurements among points within the coordinate plane.
KY.HS.G.23.a: Use points from the coordinate plane to find the coordinates of a midpoint of a line segment and the distance between the endpoints of a line segment.
Midpoint
Distance
KY.HS.G.23.a: Use points from the coordinate plane to find the coordinates of a midpoint of a line segment and the distance between the endpoints of a line segment.
Midpoint
Distance
KY.HS.G.23.b: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
KY.HS.G.23.b: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
KY.HS.G.24: Use coordinates within the coordinate plane to calculate measurements of two dimensional figures.
KY.HS.G.24: Use coordinates within the coordinate plane to calculate measurements of two dimensional figures.
KY.HS.G.24.a: Compute the perimeters of various polygons.
KY.HS.G.24.a: Compute the perimeters of various polygons.
KY.HS.G.24.b: Compute the areas of triangles, rectangles and other quadrilaterals.
KY.HS.G.24.b: Compute the areas of triangles, rectangles and other quadrilaterals.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Geometric Measurement and Dimensions
Explain volume formulas and use them to solve problems.
Explain volume formulas and use them to solve problems.
KY.HS.G.25: Analyze and determine the validity of arguments for the formulas for the various figures and shapes.
KY.HS.G.25: Analyze and determine the validity of arguments for the formulas for the various figures and shapes.
KY.HS.G.25.a: Finding the circumference and area of a circle.
KY.HS.G.25.a: Finding the circumference and area of a circle.
KY.HS.G.25.b: Finding the volume of a sphere, prism, cylinder, pyramid and cone.
KY.HS.G.25.b: Finding the volume of a sphere, prism, cylinder, pyramid and cone.
KY.HS.G.27: Use volume formulas to solve problems for cylinders, pyramids, cones, spheres, prisms.
KY.HS.G.27: Use volume formulas to solve problems for cylinders, pyramids, cones, spheres, prisms.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Visualize relationships between two-dimensional and three-dimensional objects.
Visualize relationships between two-dimensional and three-dimensional objects.
KY.HS.G.28: Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.
KY.HS.G.28: Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Modeling with Geometry
Apply geometric concepts in modeling situations.
Apply geometric concepts in modeling situations.
KY.HS.G.29: Use geometric shapes, their measures and their properties to describe objects in real world settings.
KY.HS.G.29: Use geometric shapes, their measures and their properties to describe objects in real world settings.
KY.HS.G.30: Apply concepts of density based on area and volume in modeling situations, using appropriate units of measurement.
KY.HS.G.30: Apply concepts of density based on area and volume in modeling situations, using appropriate units of measurement.
KY.HS.G.31: Apply geometric methods to solve design problems.
KY.HS.G.31: Apply geometric methods to solve design problems.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
SP
Statistics and Probability
Interpreting Categorical and Quantitative Data
Summarize, represent and interpret data on two categorical and quantitative variables.
Summarize, represent and interpret data on two categorical and quantitative variables.
KY.HS.SP.6: Represent data on two quantitative variables on a scatter plot and describe how the explanatory and response variables are related.
KY.HS.SP.6: Represent data on two quantitative variables on a scatter plot and describe how the explanatory and response variables are related.
KY.HS.SP.6.a: Calculate an appropriate mathematical model, or use a given mathematical model, for data to solve problems in context.
KY.HS.SP.6.a: Calculate an appropriate mathematical model, or use a given mathematical model, for data to solve problems in context.
KY.HS.SP.6.b: Informally assess the fit of a model (through calculating correlation for linear data, plotting, calculating and/or analyzing residuals).
KY.HS.SP.6.b: Informally assess the fit of a model (through calculating correlation for linear data, plotting, calculating and/or analyzing residuals).
Interpret linear models.
Interpret linear models.
KY.HS.SP.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
KY.HS.SP.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
KY.HS.SP.8: Understand the role and purpose of correlation in linear regression.
KY.HS.SP.8: Understand the role and purpose of correlation in linear regression.
KY.HS.SP.8.a: Use technology to compute correlation coefficient of a linear fit.
KY.HS.SP.8.a: Use technology to compute correlation coefficient of a linear fit.
KY.HS.SP.8.b: Interpret the meaning of the correlation within the context of the data.
KY.HS.SP.8.b: Interpret the meaning of the correlation within the context of the data.
KY.HS.SP.8.c: Describe the limitations of correlation when establishing causation.
KY.HS.SP.8.c: Describe the limitations of correlation when establishing causation.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity