High School Algebra (Alaska Standards)

Seeing Structure in Expressions

• A-SSE.1 Interpret expressions that stand for a quantity in context.
• A-SSE.2 Use an expression's structure to find ways to rewrite it (e.g. x⁴ − y⁴ as a difference of squares).
• A-SSE.3 Choose an equivalent form of an expression that reveals properties of the quantity.
• A-SSE.4 Derive the finite geometric series sum formula (ratio not 1) and use it, e.g. for mortgage payments.

Arithmetic with Polynomials & Rational Expressions

• A-APR.1 Know polynomials are closed under addition, subtraction and multiplication like the integers; add, subtract and multiply them.
• A-APR.2 Use the Remainder Theorem: dividing p(x) by x − a leaves p(a), so p(a) = 0 exactly when x − a is a factor.
• A-APR.3 Find zeros of factorable polynomials and use them to sketch a rough graph.
• A-APR.4 Prove polynomial identities and use them to show number relationships (e.g. Pythagorean triples).
• A-APR.5 (+) Use the Binomial Theorem to expand (x + y)ⁿ, with coefficients from Pascal's triangle.
• A-APR.6 Rewrite simple rational expressions as quotient plus remainder over divisor, by inspection, long division or technology.
• A-APR.7 (+) Know rational expressions are closed under the four operations (nonzero divisor) and add, subtract, multiply and divide them.

Creating Equations

• A-CED.1 Create one-variable equations and inequalities (linear, quadratic, simple rational, exponential) and use them to solve problems.
• A-CED.2 Create equations in two or more variables for relationships and graph them with labeled axes and scales.
• A-CED.3 Express constraints with equations, inequalities or systems and judge whether solutions are viable in context.
• A-CED.4 Rearrange formulas to isolate a quantity of interest (e.g. solve V = IR for R).

Reasoning with Equations & Inequalities

• A-REI.1 Use properties of mathematics to justify the steps in solving one-variable equations.
• A-REI.2 Solve simple rational and radical equations and show how extraneous solutions can appear.
• A-REI.3 Solve one-variable linear equations and inequalities, including ones with letter coefficients.
• A-REI.4 Solve quadratic equations in one variable.
• A-REI.5 Show that replacing one equation in a system by its sum with a multiple of the other keeps the same solutions.
• A-REI.6 Solve linear systems, mainly pairs in two variables, exactly or approximately, by graphing or by algebra.
• A-REI.7 Solve a system of one linear and one quadratic equation algebraically and graphically.
• A-REI.8 (+) Write a system of linear equations as one matrix equation.
• A-REI.9 (+) Find an inverse matrix when one exists and use it to solve linear systems.
• A-REI.10 Know a two-variable equation's graph shows every one of its solutions on the plane.
• A-REI.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.
• A-REI.12 Graph two-variable linear inequalities as half-planes and systems of them as overlapping half-planes.