Algebra 1 (Virginia SOL)

Expressions and Operations (EO)

• A.EO.1 Represent verbal quantitative situations as algebraic expressions and evaluate them for given values.
• Translate between verbal situations and algebraic expressions, including in context.
• Evaluate expressions with absolute value and square/cube roots for rational replacement values.
• A.EO.2 Add, subtract, multiply, divide, and factor polynomials in one variable, using multiple representations.
• Add and subtract one-variable polynomials using concrete, pictorial, and symbolic strategies.
• Multiply one-variable polynomials using models, the distributive property, and area models.
• Factor first- and second-degree polynomials with integer coefficients completely.
• Divide polynomials by a monomial, binomial, or completely factored divisor.
• Show that quadratic expressions written in different forms are equivalent.
• A.EO.3 Derive and apply the laws of exponents to simplify expressions.
• Discover the laws of exponents for products, quotients, and powers through patterns.
• Simplify multivariable expressions and ratios of monomials with integer exponents.
• A.EO.4 Simplify and find equivalent radical expressions with square roots of whole numbers and cube roots of integers.
• Simplify square roots of whole numbers and write equivalent expressions.
• Simplify cube roots of integers and write equivalent expressions.
• Add, subtract, and multiply numerical square-root and cube-root expressions.
• Justify radical equivalences using rational exponents (1/2 and 1/3 only).

Equations and Inequalities (EI)

• A.EI.1 Represent, solve, explain, and interpret multistep linear equations, inequalities, and literal equations in one variable.
• Write a one-variable linear equation or inequality for a contextual situation.
• Solve multistep one-variable linear equations using properties of real numbers and equality.
• Solve multistep one-variable linear inequalities and graph the solution set on a number line.
• Rearrange a formula or literal equation to isolate a given variable.
• Decide whether a one-variable linear equation has one, no, or infinitely many solutions.
• Verify solutions algebraically, graphically, and with technology, and interpret them in context.
• A.EI.2 Represent, solve, explain, and interpret systems of two linear equations, linear inequalities, and systems of inequalities in two variables.
• Write a system of two linear equations in two variables for a contextual situation.
• Solve systems of two linear equations algebraically and graphically.
• Decide whether a system of two linear equations has one, no, or infinitely many solutions.
• Write a two-variable linear inequality for a contextual situation.
• Graph the solution of a two-variable linear inequality in the coordinate plane.
• Write a system of two linear inequalities for a contextual situation.
• Graph the solution set of a system of two linear inequalities.
• Verify solutions using several methods and interpret them in context.
• A.EI.3 Represent, solve, and interpret quadratic equations in one variable.
• Solve one-variable quadratic equations over the real numbers, including in context.
• Decide and justify whether a quadratic equation has no, one, or two real solutions.
• Verify quadratic solutions using several methods and interpret them in context.

Functions (F)

• A.F.1 Investigate, analyze, and compare linear functions algebraically and graphically, and model linear relationships.
• Identify domain, range, zeros, slope, and intercepts of linear functions and interpret them in context.
• Explain how transformations of y = x affect slope and y-intercept.
• Write linear functions in slope-intercept, standard, and point-slope form and interpret each.
• Write equations of lines from graphs, two points, a slope and a point, or for vertical and horizontal lines.
• Write equations of lines parallel or perpendicular to a given line through a given point.
• Graph linear functions with and without technology, including in context.
• Find f(x) for given domain values and x for given range values of a linear function.
• Compare characteristics of linear functions given in different representations.
• A.F.2 Investigate, analyze, and compare quadratic and exponential functions, and model their relationships.
• Decide whether a relation is a function and find its domain and range.
• Identify zeros, y-intercept, vertex, domain, and range of quadratics from an equation or graph.
• Graph quadratic functions using the transformations f(x) + k and kf(x).
• Connect the standard and factored forms of a quadratic to its graph.
• Interpret the y-intercept, domain, and range of exponential functions y = ab^x, including in context.
• Graph exponential functions using the transformations f(x) + k and kf(x).
• Evaluate quadratic and exponential functions and find inputs for quadratic outputs, explaining in context.
• Compare key characteristics of linear, quadratic, and exponential functions using tables and graphs.

Statistics (ST)

• A.ST.1 Apply the data cycle to bivariate data in scatterplots and find linear or quadratic curves of best fit.
• Formulate investigative questions that require collecting or acquiring bivariate data.
• Identify variables that could explain a contextual problem or answer an investigative question.
• Choose a suitable method, such as a simple random sample, to collect a representative sample.
• For up to 30 points, use technology to decide whether a linear or quadratic model fits and find its equation.
• Use technology regression for linear or quadratic models and describe their strengths and weaknesses.
• Use linear models to make predictions and judge their strength and validity.
• Explain the slope and y-intercept of a linear model in context.
• Analyze relationships between two quantitative variables shown in a scatterplot.
• Draw conclusions from bivariate data analysis and communicate the results.