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Algebra I: Expressions and Equations

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you read the structure of an algebraic expression and rewrite it to reveal what it means?

Interpret the parts of an expression (terms, factors, coefficients) in context, and rewrite expressions using structure, including factoring and the properties of exponents, to reveal meaning such as a zero, a rate, or a percent change.
A NY Regents Algebra I answer on reading and rewriting expressions: identifying terms, factors and coefficients in context, factoring to reveal zeros, and using exponent properties to reveal a growth rate or percent change.
9 min answer →

How do you create and solve linear equations and inequalities, including literal equations and contextual models?

Create equations and inequalities in one variable and use them to solve problems; solve linear equations and inequalities including those with variables on both sides; rearrange literal equations (formulas) to isolate a chosen variable; and graph the solution set of an inequality on a number line.
A NY Regents Algebra I answer on creating and solving linear equations and inequalities: variables on both sides, literal equations, contextual modeling, the sign-flip rule for inequalities, and graphing solutions on a number line.
9 min answer →

How do you add, subtract, and multiply polynomials, and how do you factor them?

Add, subtract, and multiply polynomials (closure), and factor quadratic and higher expressions using common factors, the difference of two squares, and trinomial factoring, including a leading coefficient other than 1.
A NY Regents Algebra I answer on polynomial arithmetic and factoring: adding and subtracting like terms, multiplying with the distributive property, the difference of two squares, and factoring trinomials with leading coefficient 1 and other than 1.
9 min answer →

How do you solve a quadratic equation, and how do you choose between factoring, completing the square, and the quadratic formula?

Solve quadratic equations in one variable by factoring (zero-product property), completing the square, and the quadratic formula; recognize when a method is required by the problem; and interpret the solutions in a real-world context.
A NY Regents Algebra I answer on solving quadratics by factoring, completing the square, and the quadratic formula, when each is required, the zero-product property, and interpreting solutions in context.
10 min answer →

How do you solve a system of equations or inequalities, and how do you build one from a word problem?

Solve systems of linear equations algebraically (substitution and elimination) and graphically; solve a linear-quadratic system; create and solve systems from contexts; and graph the solution region of a system of linear inequalities.
A NY Regents Algebra I answer on systems: solving by substitution, elimination, and graphing, solving a linear-quadratic system, building a system from a word problem, and graphing the solution region of linear inequalities.
9 min answer →