Algebra I (Kentucky Academic Standards)

Number and Quantity (N)

• KY.HS.N.1 Extend the properties of integer exponents to rational exponents and radicals.
• KY.HS.N.2 Rewrite expressions with radicals and rational exponents using exponent properties.
• KY.HS.N.4 Use units to understand and solve multi-step problems (modeling).
  • a. Choose and interpret units consistently in formulas.
  • b. Choose and interpret the scale and origin of graphs.
• KY.HS.N.5 Choose suitable quantities for descriptive modeling (modeling).
• KY.HS.N.6 Report quantities to a level of accuracy that suits the limits of measurement (modeling).

Algebra (A)

• KY.HS.A.1 Interpret expressions that stand for quantities in context (modeling).
  • a. Interpret terms, factors and coefficients.
  • b. Treat complicated parts of an expression as single quantities.
• KY.HS.A.2 Use the structure of an expression to find ways to rewrite it.
• KY.HS.A.3 Write equivalent expressions that reveal properties of a quantity (modeling).
  • a. Write polynomials in standard form and name their parts and degree.
  • b. Factor a quadratic to reveal the zeros of its function.
  • c. Use exponent properties to rewrite exponential expressions.
• KY.HS.A.5 Add, subtract and multiply polynomials.
• KY.HS.A.7 Find the roots of a polynomial from its factors and link them to the zeros of the function.
• KY.HS.A.12 Write and solve one-variable equations and inequalities for problems.
• KY.HS.A.13 Write equations in two or more variables and graph them on labeled axes.
• KY.HS.A.14 Write equations, inequalities and systems for constraints and judge solutions as viable or not.
• KY.HS.A.15 Rearrange formulas to make a chosen quantity the subject.
• KY.HS.A.16 Justify each step in solving an equation to build a valid argument.
• KY.HS.A.18 Solve linear equations and inequalities in one variable, including literal equations.
• KY.HS.A.19 Solve quadratic equations in one variable.
  • a. Solve by square roots, the quadratic formula or factoring, as suits the equation.
• KY.HS.A.20 Solve systems of two linear equations in two variables.
  • a. Know that replacing an equation with an equivalent one keeps the same solutions.
  • b. Solve by graphing, substitution and elimination.
• KY.HS.A.23 Understand that the graph of a two-variable equation is the set of all its solutions.
• KY.HS.A.24 Explain why the x-coordinates where two graphs meet solve f(x) = g(x) and estimate them (modeling).
• KY.HS.A.25 Graph linear inequalities and systems of inequalities as half-planes.
  • a. Graph the solutions of an inequality as a half-plane, leaving out strict boundaries.
  • b. Graph a system as the overlap of the matching half-planes.

Functions (F)

• KY.HS.F.1 Understand functions and their different representations.
  • a. Know a function gives each input exactly one output and use function notation.
  • b. Evaluate functions and interpret notation in context.
  • c. Interpret key features of graphs and tables and sketch graphs from descriptions.
  • d. Relate a function's domain to its graph and the situation.
  • e. Compare two functions shown in different ways.
• KY.HS.F.2 Recognize arithmetic and geometric sequences as functions on the integers.
• KY.HS.F.3 Understand average rate of change over an interval.
  • a. Calculate and interpret average rate of change from symbols or tables.
  • b. Estimate rate of change from a graph (modeling).
• KY.HS.F.4 Graph functions from their equations and show key features, with or without technology (modeling).
  • a. Graph linear and quadratic functions showing intercepts, maximums and minimums.
• KY.HS.F.5 Write functions in equivalent forms that show different properties.
  • a. Find the zeros, extreme values and symmetry of quadratic graphs.
  • (unlettered). Use exponent properties to read exponential functions as growth or decay.
• KY.HS.F.6 Write functions that describe a relationship between two quantities (modeling).
  • a. Write an explicit expression, recursive process or steps for calculation.
  • b. Combine standard function types using arithmetic operations.
• KY.HS.F.7 Use arithmetic and geometric sequences to model situations.
  • a. Generate terms using explicit and recursive formulas.
  • b. Write sequence formulas and use them in real situations (modeling).
• KY.HS.F.11 Tell apart situations modeled by linear and by exponential functions.
  • a. Justify equal differences versus equal factors over equal intervals.
  • b. Recognize a constant rate of change per unit interval.
  • c. Recognize a constant percent growth or decay per unit interval.
• KY.HS.F.12 Build linear and exponential functions from graphs, descriptions or pairs of values.
• KY.HS.F.13 Show that exponential growth eventually overtakes linear and polynomial growth.
• KY.HS.F.14 Interpret the parameters of linear or exponential functions in context.

Statistics and Probability (SP)

• KY.HS.SP.6 Show two-variable data on scatter plots and describe how the variables are related.
  • a. Fit or use a given model to solve problems in context.
  • b. Judge the fit of a model informally using correlation, plots or residuals.
• KY.HS.SP.7 Interpret the slope and intercept of a linear model in context.
• KY.HS.SP.8 Understand the role of correlation in linear regression.
  • a. Use technology to find the correlation coefficient.
  • b. Interpret correlation in the context of the data.
  • c. Describe why correlation alone does not show causation.