High School Algebra (Colorado Academic Standards)

Standard 2: Algebra and Functions

• MA.HS.A-SSE.A Interpret the structure of expressions.
  • 1. Interpret expressions that stand for a quantity in context.
  • 1.a. Interpret terms, factors and coefficients in an expression.
  • 1.b. Interpret complex expressions by treating parts as single quantities, e.g. P(1 + r)ⁿ.
  • 2. Use an expression's structure to find ways to rewrite it (e.g. x⁴ − y⁴ as a difference of squares).
• MA.HS.A-SSE.B Rewrite expressions in equivalent forms to solve problems.
  • 1. Choose an equivalent form of an expression that reveals properties of the quantity.
  • 1.a. Factor a quadratic to show the zeros of its function.
  • 1.b. Complete the square to show a quadratic function's maximum or minimum.
  • 1.c. Use exponent properties to rewrite exponential expressions (e.g. annual to monthly rates).
  • 2. Use the finite geometric series sum formula to solve problems such as mortgage payments.
  • 2.a. Summary being checked: read this one in the official document.
• MA.HS.A-APR.A Do arithmetic with polynomials.
  • 1. Know polynomials are closed under addition, subtraction and multiplication like the integers; add, subtract and multiply them.
• MA.HS.A-APR.B Relate zeros and factors of polynomials.
  • 1. Use the Remainder Theorem: dividing p(x) by x − a leaves p(a), so p(a) = 0 exactly when x − a is a factor.
  • 2. Find zeros of factorable polynomials and use them to sketch a rough graph.
• MA.HS.A-APR.C Use polynomial identities to solve problems.
  • 1. (+) Prove polynomial identities and use them to show number relationships (e.g. Pythagorean triples). (being checked)
  • 2. (+) Use the Binomial Theorem to expand (x + y)ⁿ, with coefficients from Pascal's triangle.
• MA.HS.A-APR.D Rewrite rational expressions.
  • 1. Rewrite simple rational expressions as quotient plus remainder over divisor, by inspection, long division or technology.
  • 2. (+) Know rational expressions are closed under the four operations (nonzero divisor) and add, subtract, multiply and divide them.
• MA.HS.A-CED.A Write equations and inequalities that describe relationships.
  • 1. Create one-variable equations and inequalities (linear, quadratic, simple rational, exponential) and use them to solve problems.
  • 2. Create equations in two or more variables for relationships and graph them with labeled axes and scales.
  • 3. Express constraints with equations, inequalities or systems and judge whether solutions are viable in context.
  • 4. Rearrange formulas to isolate a quantity of interest (e.g. solve V = IR for R).
• MA.HS.A-REI.A Treat solving equations as reasoning and explain each step.
  • 1. Justify each step of solving a simple equation and build a viable argument for the solution method.
  • 2. Solve simple rational and radical equations and show how extraneous solutions can appear.
• MA.HS.A-REI.B Solve equations and inequalities in one variable.
  • 1. Solve one-variable linear equations and inequalities, including ones with letter coefficients.
  • 2. Solve quadratic equations in one variable.
  • 2.a. Complete the square to rewrite a quadratic as (x − p)² = q and derive the quadratic formula.
  • 2.b. Solve quadratics by inspection, square roots, completing the square, the formula or factoring; spot complex solutions.
• MA.HS.A-REI.C Solve systems of equations.
  • 1. Prove that replacing an equation by its sum with a multiple of the other keeps a system's solutions.
  • 2. Solve linear systems exactly and approximately (e.g. by graphing), mainly pairs of equations in two variables.
  • 3. Solve a system of one linear and one quadratic equation algebraically and graphically.
  • 4. (+) Write a system of linear equations as one matrix equation.
  • 5. (+) Find an inverse matrix when one exists and use it to solve linear systems.
• MA.HS.A-REI.D Represent and solve equations and inequalities with graphs.
  • 1. Know a two-variable equation's graph shows every one of its solutions on the plane.
  • 2. 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.
  • 3. Graph two-variable linear inequalities as half-planes and systems of them as overlapping half-planes.