Common Core Standards Plus Mathematics Grade 5 Answer Key

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Skills available for Kentucky high school math standards

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N Number and Quantity

The Real Number System
- 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.
    - Evaluate integers raised to rational exponents ( A1-V.12 )
  - KY.HS.N.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
    - Multiplication with rational exponents ( A1-V.13 )
    - Division with rational exponents ( A1-V.14 )
    - Power rule with rational exponents ( A1-V.15 )
    - Simplify expressions involving rational exponents ( A1-V.16 )
    - Simplify radical expressions ( A1-EE.1 )
    - Simplify radical expressions with variables ( A1-EE.2 )
    - Simplify radical expressions involving fractions ( A1-EE.3 )
    - Multiply radical expressions ( A1-EE.4 )
    - Add and subtract radical expressions ( A1-EE.5 )
    - Simplify radical expressions using the distributive property ( A1-EE.6 )
    - Simplify radical expressions using conjugates ( A1-EE.7 )
    - Simplify radical expressions: mixed review ( A1-EE.8 )
  - Checkpoint opportunity
    - Checkpoint: Radicals and rational exponents ( A1-EE.9 )
Quantities
- 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.a Choose and interpret units consistently in formulas;
      - Scale drawings: word problems ( A1-C.7 )
      - Convert rates and measurements: customary units ( A1-E.1 )
      - Convert rates and measurements: metric units ( A1-E.2 )
      - Unit prices with unit conversions ( A1-E.3 )
      - Multi-step problems with unit conversions ( A1-E.4 )
    - 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.
    - Solve one-step and two-step equations: word problems ( A1-J.10 )
    - Solve a system of equations using any method: word problems ( A1-U.15 )
    - Exponential growth and decay: word problems ( A1-X.5 )
  - KY.HS.N.6 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
    - Precision ( A1-E.5 )
    - Greatest possible error ( A1-E.6 )
    - Minimum and maximum area and volume ( A1-E.7 )
    - Percent error ( A1-E.8 )
    - Percent error: area and volume ( A1-E.9 )
  - Checkpoint opportunity

A Algebra

Seeing Structure in 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.a Interpret parts of an expression, such as terms, factors and coefficients.
      - Sort factors of variable expressions ( A1-I.2 )
      - Polynomial vocabulary ( A1-Z.1 )
    - KY.HS.A.1.b Interpret complicated expressions, given a context, by viewing one or more of their parts as a single entity.
      - Factor using a quadratic pattern ( A2-J.4 )
  - 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.
    - Simplify variable expressions using properties ( A1-H.3 )
    - Simplify variable expressions involving like terms and the distributive property ( A1-I.3 )
    - Evaluate expressions using properties of exponents ( A1-V.8 )
    - Identify equivalent expressions involving exponents I ( A1-V.9 )
    - Identify equivalent expressions involving exponents II ( A1-V.10 )
    - Powers of monomials ( A1-Y.5 )
    - Factor out a monomial ( A1-AA.2 )
    - Factor quadratics: special cases ( A1-AA.6 )
    - Simplify radical expressions ( A1-EE.1 )
    - Simplify radical expressions with variables ( A1-EE.2 )
    - Simplify radical expressions involving fractions ( A1-EE.3 )
    - Simplify radical expressions: mixed review ( A1-EE.8 )
- 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.a Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient and constant term.
      - Polynomial vocabulary ( A1-Z.1 )
    - KY.HS.A.3.b Factor a quadratic expression to reveal the zeros of the function it defines.
      - Factor quadratics with leading coefficient 1 ( A1-AA.4 )
      - Factor quadratics with other leading coefficients ( A1-AA.5 )
      - Factor quadratics: special cases ( A1-AA.6 )
      - Solve a quadratic equation by factoring ( A1-BB.8 )
    - KY.HS.A.3.c Use the properties of exponents to rewrite exponential expressions.
      - Evaluate expressions using properties of exponents ( A1-V.8 )
      - Identify equivalent expressions involving exponents I ( A1-V.9 )
      - Identify equivalent expressions involving exponents II ( A1-V.10 )
      - Evaluate an exponential function ( A1-X.1 )
  - Checkpoint opportunity
    - Checkpoint: Write and interpret equivalent expressions ( A1-BB.19 )
Arithmetic with Polynomials and Rational Expressions
- Perform arithmetic operations on polynomials.
  - KY.HS.A.5 Add, subtract and multiply polynomials.
    - Model polynomials with algebra tiles ( A1-Z.2 )
    - Add and subtract polynomials using algebra tiles ( A1-Z.3 )
    - Add and subtract polynomials ( A1-Z.4 )
    - Add polynomials to find perimeter ( A1-Z.5 )
    - Multiply a polynomial by a monomial ( A1-Z.6 )
    - Multiply two binomials using algebra tiles ( A1-Z.7 )
    - Multiply two binomials ( A1-Z.8 )
    - Multiply two binomials: special cases ( A1-Z.9 )
    - Multiply polynomials ( A1-Z.10 )
  - Checkpoint opportunity
    - Checkpoint: Add, subtract, and multiply polynomials ( A1 )
- 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.
    - Solve a quadratic equation using the zero product property ( A1-BB.7 )
    - Match quadratic functions and graphs ( A1-BB.15 )
  - Checkpoint opportunity
    - Checkpoint: Polynomial operations ( A1-Z.12 )
Creating Equations
- Create equations that describe numbers or relationships.
  - KY.HS.A.12 Create equations and inequalities in one variable and use them to solve problems.
    - Write variable equations ( A1-I.5 )
    - Model and solve equations using algebra tiles ( A1-J.1 )
    - Write and solve equations that represent diagrams ( A1-J.2 )
    - Solve one-step and two-step equations: word problems ( A1-J.10 )
    - Write inequalities from graphs ( A1-K.2 )
    - Write compound inequalities from graphs ( A1-K.13 )
    - Consecutive integer problems ( A1-O.3 )
    - Weighted averages: word problems ( A1-O.5 )
    - Linear inequalities: word problems ( A1-T.4 )
  - 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.
    - Write direct variation equations ( A1-R.4 )
    - Slope-intercept form: graph an equation ( A1-S.7 )
    - Slope-intercept form: write an equation from a graph ( A1-S.8 )
    - Slope-intercept form: write an equation ( A1-S.9 )
    - Slope-intercept form: write an equation from a table ( A1-S.10 )
    - Slope-intercept form: write an equation from a word problem ( A1-S.11 )
    - Write linear functions: word problems ( A1-S.13 )
    - Write equations in standard form ( A1-S.17 )
    - Standard form: graph an equation ( A1-S.19 )
    - Point-slope form: graph an equation ( A1-S.22 )
    - Point-slope form: write an equation ( A1-S.23 )
    - Graph quadratic functions in vertex form ( A1-BB.5 )
    - Graph quadratic functions in standard form ( A1-BB.14 )
    - Write a quadratic function from its vertex and another point ( A1-BB.16 )
    - Write linear, quadratic, and exponential functions ( A1-CC.6 )
    - Graph an absolute value function ( A1-DD.2 )
  - 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.
    - Linear inequalities: word problems ( A1-T.4 )
    - Solve a system of equations by graphing: word problems ( A1-U.3 )
    - Solve a system of equations using substitution: word problems ( A1-U.9 )
    - Solve a system of equations using elimination: word problems ( A1-U.11 )
    - Solve a system of equations using augmented matrices: word problems ( A1-U.13 )
    - Solve a system of equations using any method: word problems ( A1-U.15 )
  - KY.HS.A.15 Rearrange formulas to solve a literal equation, highlighting a quantity of interest, using the same reasoning as in solving equations.
    - Rearrange multi-variable equations ( A1-I.11 )
    - Rate of travel: word problems ( A1-O.4 )
    - Linear equations: solve for y ( A1-S.12 )
  - Checkpoint opportunity
    - Checkpoint: Represent constraints ( A1-U. )
    - Checkpoint: Problem solving with equations and inequalities ( A1-CC.12 )
Reasoning with Equations and Inequalities
- 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.
    - Properties of equality ( A1-H.4 )
    - Identify equivalent equations ( A1-H.5 )
    - Solve equations: complete the solution ( A1-J.7 )
- 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.
    - Rearrange multi-variable equations ( A1-I.11 )
    - Model and solve equations using algebra tiles ( A1-J.1 )
    - Write and solve equations that represent diagrams ( A1-J.2 )
    - Solve one-step linear equations ( A1-J.3 )
    - Solve two-step linear equations ( A1-J.4 )
    - Solve advanced linear equations ( A1-J.5 )
    - Solve equations with variables on both sides ( A1-J.6 )
    - Solve equations: complete the solution ( A1-J.7 )
    - Solve one-step and two-step equations: word problems ( A1-J.10 )
    - Solve linear equations: mixed review ( A1-J.11 )
    - Identify solutions to inequalities ( A1-K.3 )
    - Solve one-step linear inequalities: addition and subtraction ( A1-K.4 )
    - Solve one-step linear inequalities: multiplication and division ( A1-K.5 )
    - Solve one-step linear inequalities ( A1-K.6 )
    - Solve two-step linear inequalities ( A1-K.8 )
    - Solve advanced linear inequalities ( A1-K.10 )
    - Solve compound inequalities ( A1-K.14 )
  - 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 ± b i for real numbers a and b.
      - Solve a quadratic equation using square roots ( A1-BB.6 )
      - Solve a quadratic equation using the zero product property ( A1-BB.7 )
      - Solve a quadratic equation by factoring ( A1-BB.8 )
      - Solve a quadratic equation using the quadratic formula ( A1-BB.11 )
  - Checkpoint opportunity
    - Checkpoint: Solve linear equations and inequalities ( A1-K.16 )
- Solve systems of equations.
  - 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.b Solve systems of linear equations with graphs, substitution and elimination, focusing on pairs of linear equations in two variables.
      - Is (x, y) a solution to the system of equations? ( A1-U.1 )
      - Solve a system of equations by graphing ( A1-U.2 )
      - Solve a system of equations by graphing: word problems ( A1-U.3 )
      - Find the number of solutions to a system of equations by graphing ( A1-U.4 )
      - Find the number of solutions to a system of equations ( A1-U.5 )
      - Classify a system of equations by graphing ( A1-U.6 )
      - Solve a system of equations using substitution ( A1-U.8 )
      - Solve a system of equations using substitution: word problems ( A1-U.9 )
      - Solve a system of equations using elimination ( A1-U.10 )
      - Solve a system of equations using elimination: word problems ( A1-U.11 )
      - Solve a system of equations using any method ( A1-U.14 )
      - Solve a system of equations using any method: word problems ( A1-U.15 )
- 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.
    - Relations: convert between tables, graphs, mappings, and lists of points ( A1-Q.1 )
    - Find values using function graphs ( A1-Q.6 )
    - Complete a function table from an equation ( A1-Q.13 )
    - Interpret the graph of a function: word problems ( A1-Q.16 )
    - Complete a table and graph a linear function ( A1-S.14 )
  - 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.
    - Solve a system of equations by graphing ( A1-U.2 )
    - Solve a system of equations by graphing: word problems ( A1-U.3 )
    - Find the number of solutions to a system of equations by graphing ( A1-U.4 )
  - 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).
      - Graph a two-variable linear inequality ( A1-T.3 )
    - KY.HS.A.25.b Graph the solution set to a system of linear inequalities as the intersection of the corresponding half-planes.
      - Solve systems of linear inequalities by graphing ( A1-T.6 )
  - Checkpoint opportunity
    - Checkpoint: Solve equations using graphs and tables ( A1-Q.22 )
    - Checkpoint: Systems of equations and inequalities ( A1-U.16 )
    - Checkpoint: Quadratic equations ( A1-BB.18 )

F Functions

Interpreting Functions
- 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.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.
      - Domain and range of relations ( A1-Q.2 )
      - Identify independent and dependent variables ( A1-Q.3 )
      - Identify functions ( A1-Q.4 )
      - Identify functions: vertical line test ( A1-Q.5 )
      - Find values using function graphs ( A1-Q.6 )
      - Complete a function table from a graph ( A1-Q.12 )
      - Complete a function table from an equation ( A1-Q.13 )
      - Domain and range of exponential functions: graphs ( A1-X.3 )
      - Domain and range of exponential functions: equations ( A1-X.4 )
    - 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.
      - Find values using function graphs ( A1-Q.6 )
      - Evaluate a function ( A1-Q.7 )
      - Evaluate a function: plug in an expression ( A1-Q.8 )
      - Complete a function table from a graph ( A1-Q.12 )
      - Complete a function table from an equation ( A1-Q.13 )
      - Interpret functions using everyday language ( A1-Q.17 )
      - Evaluate an exponential function ( A1-X.1 )
      - Complete a function table: quadratic functions ( A1-BB.3 )
      - Complete a function table: absolute value functions ( A1-DD.1 )
    - 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.
      - Identify proportional relationships ( A1-R.1 )
      - Find the constant of variation ( A1-R.2 )
      - Graph a proportional relationship ( A1-R.3 )
      - Identify linear functions from graphs and equations ( A1-S.1 )
      - Identify linear functions from tables ( A1-S.2 )
      - Find the slope of a graph ( A1-S.3 )
      - Slope-intercept form: find the slope and y-intercept ( A1-S.6 )
      - Slope-intercept form: graph an equation ( A1-S.7 )
      - Complete a table and graph a linear function ( A1-S.14 )
      - Standard form: find x- and y-intercepts ( A1-S.18 )
      - Standard form: graph an equation ( A1-S.19 )
      - Point-slope form: graph an equation ( A1-S.22 )
      - Slopes of parallel and perpendicular lines ( A1-S.25 )
      - Match exponential functions and graphs ( A1-X.2 )
      - Characteristics of quadratic functions: graphs ( A1-BB.1 )
      - Characteristics of quadratic functions: equations ( A1-BB.2 )
      - Graph quadratic functions in vertex form ( A1-BB.5 )
      - Identify linear, quadratic, and exponential functions from graphs ( A1-CC.2 )
      - Identify linear, quadratic, and exponential functions from tables ( A1-CC.4 )
    - KY.HS.F.1.d Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
      - Domain and range of exponential functions: graphs ( A1-X.3 )
      - Domain and range of exponential functions: equations ( A1-X.4 )
      - Domain and range of absolute value functions: graphs ( A1-DD.3 )
      - Domain and range of absolute value functions: equations ( A1-DD.4 )
      - Domain and range of square root functions: graphs ( A1-FF.2 )
      - Domain and range of square root functions: equations ( A1-FF.3 )
    - 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).
      - Compare linear functions: graphs and equations ( A1-S.15 )
      - Compare linear functions: tables, graphs, and equations ( A1-S.16 )
  - KY.HS.F.2 Recognize that arithmetic and geometric sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
    - Identify arithmetic and geometric sequences ( A1-P.1 )
    - Arithmetic sequences ( A1-P.2 )
    - Geometric sequences ( A1-P.3 )
    - Evaluate variable expressions for number sequences ( A1-P.4 )
    - Evaluate recursive formulas for sequences ( A1-P.5 )
    - Write variable expressions for arithmetic sequences ( A1-P.7 )
    - Write variable expressions for geometric sequences ( A1-P.8 )
    - Write a formula for a recursive sequence ( A1-P.9 )
    - Number sequences: mixed review ( A1-P.12 )
- 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.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: tables ( A1-Q.18 )
      - Find the constant of variation ( A1-R.2 )
      - Find the slope from two points ( A1-S.4 )
      - Slope-intercept form: find the slope and y-intercept ( A1-S.6 )
    - KY.HS.F.3.b Estimate the rate of change from a graph.
      - Rate of change: graphs ( A1-Q.19 )
      - Find the slope of a graph ( A1-S.3 )
  - Checkpoint opportunity
    - Checkpoint: Function concepts ( A1-Q.20 )
    - Checkpoint: Average rate of change ( A1-Q.21 )
- 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.a Graph linear and quadratic functions and show intercepts, maxima and minima.
      - Slope-intercept form: graph an equation ( A1-S.7 )
      - Standard form: graph an equation ( A1-S.19 )
      - Point-slope form: graph an equation ( A1-S.22 )
      - Characteristics of quadratic functions: graphs ( A1-BB.1 )
      - Graph quadratic functions in vertex form ( A1-BB.5 )
  - 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: graphs ( A1-BB.1 )
      - Characteristics of quadratic functions: equations ( A1-BB.2 )
      - Solve a quadratic equation using the zero product property ( A1-BB.7 )
      - Solve a quadratic equation by factoring ( A1-BB.8 )
      - Solve a quadratic equation by completing the square ( A1-BB.10 )
    - 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.
      - Evaluate an exponential function ( A1-X.1 )
      - Match exponential functions and graphs ( A1-X.2 )
  - Checkpoint opportunity
    - Checkpoint: Features of functions ( A1-CC.13 )
    - Checkpoint: Graph and analyze functions ( A1-DD.13 )
Building Functions
- 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.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
      - Write variable expressions for arithmetic sequences ( A1-P.7 )
      - Write variable expressions for geometric sequences ( A1-P.8 )
      - Write a formula for a recursive sequence ( A1-P.9 )
      - Write linear functions: word problems ( A1-S.13 )
      - Write linear and exponential functions ( A1-CC.5 )
      - Write linear, quadratic, and exponential functions ( A1-CC.6 )
    - KY.HS.F.6.b Combine standard function types using arithmetic operations.
      - Add and subtract functions ( A1-Q.9 )
      - Multiply functions ( A1-Q.10 )
      - Add and subtract polynomials ( A1-Z.4 )
      - Multiply polynomials ( A1-Z.10 )
  - 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.
      - Evaluate variable expressions for number sequences ( A1-P.4 )
      - Evaluate recursive formulas for sequences ( A1-P.5 )
    - KY.HS.F.7.b Write formulas to model arithmetic and geometric sequences and apply those formulas in realistic situations.
      - Write variable expressions for arithmetic sequences ( A1-P.7 )
      - Write variable expressions for geometric sequences ( A1-P.8 )
      - Write a formula for a recursive sequence ( A1-P.9 )
  - Checkpoint opportunity
    - Checkpoint: Sequences ( A1-P.13 )
    - Checkpoint: Build functions ( A1-CC.15 )
Linear, Quadratic and Exponential Functions
- 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.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.
      - Identify linear and exponential functions from graphs ( A1-CC.1 )
      - Identify linear and exponential functions from tables ( A1-CC.3 )
      - Describe linear and exponential growth and decay ( A1-CC.9 )
    - KY.HS.F.11.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
      - Solve one-step and two-step equations: word problems ( A1-J.10 )
      - Identify linear and exponential functions from graphs ( A1-CC.1 )
      - Identify linear, quadratic, and exponential functions from tables ( A1-CC.4 )
    - 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.
      - Exponential growth and decay: word problems ( A1-X.5 )
      - Identify linear and exponential functions from graphs ( A1-CC.1 )
  - 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).
    - Write variable expressions for arithmetic sequences ( A1-P.7 )
    - Write variable expressions for geometric sequences ( A1-P.8 )
    - Slope-intercept form: write an equation from a graph ( A1-S.8 )
    - Slope-intercept form: write an equation ( A1-S.9 )
    - Slope-intercept form: write an equation from a table ( A1-S.10 )
    - Slope-intercept form: write an equation from a word problem ( A1-S.11 )
    - Write linear functions: word problems ( A1-S.13 )
    - Point-slope form: write an equation ( A1-S.23 )
    - Point-slope form: write an equation from a graph ( A1-S.24 )
    - Write an equation for a parallel or perpendicular line ( A1-S.26 )
    - Write linear and exponential functions ( A1-CC.5 )
    - Write linear, quadratic, and exponential functions ( A1-CC.6 )
  - 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.
    - Compare linear and exponential growth ( A1-CC.10 )
    - Compare linear, exponential, and quadratic growth ( A1-CC.11 )
- 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.
    - Solve one-step and two-step equations: word problems ( A1-J.10 )
    - Exponential growth and decay: word problems ( A1-X.5 )
    - Compound interest: word problems ( A1-X.6 )
  - Checkpoint opportunity
    - Checkpoint: Compare linear and exponential functions ( A1-CC.14 )

SP Statistics and Probability

Interpreting Categorical and Quantitative Data
- 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.a Calculate an appropriate mathematical model, or use a given mathematical model, for data to solve problems in context.
      - Find the equation of a regression line ( A1-LL.13 )
      - Interpret regression lines ( A1-LL.14 )
      - Analyze a regression line of a data set ( A1-LL.15 )
    - 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 a scatter plot ( A1-LL.8 )
- 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.
    - Interpret regression lines ( A1-LL.14 )
    - Analyze a regression line of a data set ( A1-LL.15 )
  - 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.
      - Match correlation coefficients to scatter plots ( A1-LL.10 )
      - Calculate correlation coefficients ( A1-LL.11 )
    - 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.
  - Checkpoint opportunity
    - Checkpoint: Linear modeling ( A1-LL.16 )

Common Core Standards Plus Mathematics Grade 5 Answer Key

Source: https://www.ixl.com/standards/kentucky/math/high-school

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Common Core Standards Plus Mathematics Grade 5 Answer Key

N Number and Quantity

The Real Number System

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.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Checkpoint opportunity

Quantities

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.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.5 Define appropriate units in context for the purpose of descriptive modeling.

KY.HS.N.6 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Checkpoint opportunity

A Algebra

Seeing Structure in 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.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.2 Use the structure of an expression to identify ways to rewrite it and consistently look for opportunities to rewrite expressions in equivalent forms.

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.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.

KY.HS.A.3.c Use the properties of exponents to rewrite exponential expressions.

Checkpoint opportunity

Arithmetic with Polynomials and Rational Expressions

Perform arithmetic operations on polynomials.

KY.HS.A.5 Add, subtract and multiply polynomials.

Checkpoint opportunity

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.

Checkpoint opportunity

Creating Equations

Create equations that describe numbers or relationships.

KY.HS.A.12 Create equations and inequalities in one variable and use them to solve problems.

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.

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.

KY.HS.A.15 Rearrange formulas to solve a literal equation, highlighting a quantity of interest, using the same reasoning as in solving equations.

Checkpoint opportunity

Reasoning with Equations and Inequalities

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.

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.

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 ± b i for real numbers a and b.

Checkpoint opportunity

Solve systems of equations.

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.b Solve systems of linear equations with graphs, substitution and elimination, focusing on pairs of linear equations in two variables.

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.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.

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.b Graph the solution set to a system of linear inequalities as the intersection of the corresponding half-planes.

Checkpoint opportunity

F Functions

Interpreting Functions

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.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.

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.

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.

KY.HS.F.1.d Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

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.

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.a Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.

KY.HS.F.3.b Estimate the rate of change from a graph.

Checkpoint opportunity

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.a Graph linear and quadratic functions and show intercepts, maxima and minima.

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.