Algebra I (Arizona Mathematics Standards)

Number and Quantity

• A1.N-RN.B.3 Explain why sums and products of rationals are rational and why mixing a rational and an irrational (nonzero) gives an irrational.
• A1.N-Q.A.1 Use units to understand and guide multistep problems, read units in formulas and choose scales and origins for graphs and data displays.
• A1.N-Q.A.2 Define suitable quantities when building a descriptive model.
• A1.N-Q.A.3 Report quantities with a level of accuracy that fits the limits of measurement.

Algebra

• A1.A-SSE.A.1 Interpret expressions that stand for a quantity in context.
  • a. Interpret terms, factors and coefficients in an expression.
  • b. Interpret complex expressions by treating parts as single quantities, e.g. P(1 + r)ⁿ.
• A1.A-SSE.A.2 Use the structure of numerical and polynomial expressions to rewrite them, especially with multiplication and factoring patterns.
• A1.A-SSE.B.3 Choose an equivalent form of an expression that reveals properties of the quantity.
  • a. Factor a quadratic to show the zeros of its function.
  • b. Complete the square to show a quadratic function's maximum or minimum.
• A1.A-APR.A.1 Know polynomials are closed under addition, subtraction and multiplication like the integers; add, subtract and multiply them.
• A1.A-APR.B.3 Find zeros of factorable polynomials and use them to sketch rough graphs of quadratic and cubic functions.
• A1.A-CED.A.1 Create one-variable equations and inequalities (linear, quadratic, exponential, piecewise) and use them to solve problems.
• A1.A-CED.A.2 Create equations in two or more variables for relationships and graph them with labeled axes and scales.
• A1.A-CED.A.3 Express constraints with equations, inequalities or systems and judge whether solutions are viable in context.
• A1.A-CED.A.4 Rearrange formulas to isolate a quantity of interest (e.g. solve V = IR for R).
• A1.A-REI.A.1 Justify each step of solving linear or quadratic equations from the equality before it.
• A1.A-REI.B.3 Solve one-variable linear equations and inequalities, including ones with letter coefficients.
• A1.A-REI.B.4 Solve quadratic equations in one variable.
  • a. Complete the square to rewrite a quadratic as (x − p)² = q and derive the quadratic formula.
  • b. Solve quadratics by inspection, square roots, completing the square, the formula or factoring; spot complex solutions.
• A1.A-REI.C.5 Prove that replacing an equation by its sum with a multiple of the other keeps a system's solutions.
• A1.A-REI.C.6 Solve pairs of linear equations exactly and approximately, including in real-world contexts.
• A1.A-REI.D.10 Know a two-variable equation's graph shows every one of its solutions on the plane.
• A1.A-REI.D.11 Explain why intersections of y = f(x) and y = g(x) solve f(x) = g(x) and find them approximately with graphs, tables or technology.
• A1.A-REI.D.12 Graph two-variable linear inequalities as half-planes and systems of them as overlapping half-planes.

Functions

• A1.F-IF.A.1 Know a function assigns each domain element exactly one range element; f(x) is the output for input x.
• A1.F-IF.A.2 Use function notation, evaluate functions and interpret notation in context.
• A1.F-IF.A.3 Recognize sequences as functions on the integers, sometimes defined recursively.
• A1.F-IF.B.4 Interpret key graph and table features in context (intercepts, increase/decrease, maxima, symmetry, end behavior) and sketch graphs.
• A1.F-IF.B.5 Link a function's domain to its graph and to the situation it models.
• A1.F-IF.B.6 Calculate and interpret average rate of change over an interval and estimate it from a graph.
• A1.F-IF.C.7 Graph functions from equations and show key features, by hand for simple cases and with technology for harder ones. (being checked)
• A1.F-IF.C.8 Rewrite a function in equivalent forms to reveal different properties.
  • a. Factor or complete the square in a quadratic to show zeros, extreme values and symmetry, and interpret them.
• A1.F-IF.C.9 Compare properties of two functions shown in different ways.
• A1.F-BF.A.1 Write a function for a relationship between two quantities using an explicit expression, a recursive rule or calculation steps.
• A1.F-BF.B.3 Describe how f(x) + k, k f(x) and f(x + k) change a graph and find k from graphs.
• A1.F-LE.A.1 Tell situations modeled by linear functions from those modeled by exponential functions.
  • a. Prove linear functions grow by equal differences and exponential functions by equal factors over equal intervals.
  • b. Recognize situations with a constant rate of change per unit.
  • c. Recognize situations with a constant percent rate of growth or decay per unit.
• A1.F-LE.A.2 Build linear and exponential functions, including sequences, from a graph, a description or two input-output pairs.
• A1.F-LE.A.3 Use graphs and tables to see that exponential growth eventually overtakes linear and quadratic growth.
• A1.F-LE.B.5 Interpret the parameters of linear functions and exponential functions with integer exponents in context.

Statistics and Probability

• A1.S-ID.A.1 Show real-number data on plots to compare two or more data sets.
• A1.S-ID.A.2 Compare center (median, mean) and spread (IQR, standard deviation) of data sets using statistics suited to their shape.
• A1.S-ID.A.3 Interpret how data sets differ in shape, center and spread in context, allowing for outliers.
• A1.S-ID.B.5 Summarize two categorical variables in two-way tables and interpret joint, marginal and conditional relative frequencies.
• A1.S-ID.B.6 Make a scatter plot of two quantitative variables, describe their relationship and fit a function.
  • a. Fit a function to data, with the emphasis on linear models, and use it to solve problems in context.
  • b. Judge the fit of a function informally by plotting and analyzing residuals.
• A1.S-ID.C.7 Interpret the slope and intercept of a linear model in context.
• A1.S-ID.C.8 Use technology to find the correlation coefficient of a linear fit and interpret it.
• A1.S-ID.C.9 Tell correlation apart from causation.
• A1.S-CP.A.1 Describe events as subsets of the set of outcomes and with unions, intersections and complements ("or", "and", "not").
• A1.S-CP.A.2 Know events A and B are independent when P(A and B) = P(A) × P(B) and use this.