HS.A

Conceptual Category Algebra

HS.A.1Interpret expressions that represent a quantity in terms of its context. (MP.2, MP.6)HS.A.10(+)Rewrite simple rational expressions in different forms. (MP.7, MP.8)HS.A.11(+)Add, subtract, multiply and divide rational algebraic expressions. (MP.2, MP.3)HS.A.12Create equations and inequalities in one variable and use them to solve problems. (MP.1, MP.4)HS.A.13Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (MP.2, MP.5)HS.A.14Create a system of equations or inequalities to represent constraints within a modeling context. Interpret the solution(s) to the corresponding system as viable or nonviable options within the context. (MP.4, MP.5)HS.A.15Rearrange formulas to solve a literal equation, highlighting a quantity of interest, using the same reasoning as in solving equations. (MP.2, MP.7)HS.A.16Understand each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (MP.1, MP.3)HS.A.17Solve and justify equations in one variable. Justify the solutions and give examples showing how extraneous solutions may arise. (MP.3, MP.5, MP.7)HS.A.18Solve linear equations and inequalities in one variable, including literal equations with coefficients represented by letters. (MP.2, MP.7)HS.A.19Solve quadratic equations in one variable. (MP.1, MP.8)HS.A.2Use the structure of an expression to identify ways to rewrite it and consistently look for opportunities to rewrite expressions in equivalent forms. (MP.7, MP.8)HS.A.20Solve systems of linear equations in two variables. (MP.3, MP.6)HS.A.21Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. (MP.3, MP.6)HS.A.22(+)Use matrices to solve a system of equations. (MP.4, MP.7)HS.A.23Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. (MP.1, MP.4)HS.A.24Justify that the solutions of the equations f(x)=g(x) are the x-coordinates of the points where the graphs of y=f(x) and y=g(x) intersect. Find the approximate solutions graphically, using technology or tables. (MP.3, MP.5)HS.A.25Graph linear inequalities in two variables. (MP.5, MP.6)HS.A.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (MP.5, MP.7)HS.A.4(+)Derive the formula for the sum of a finite geometric series (when the common ratio is not 1) and use the formula to solve problems. (MP.1, MP.4)HS.A.5Add, subtract and multiply polynomials. (MP.7, MP.8)HS.A.6(+)Know and apply the Remainder Theorem. (MP.1, MP.8)HS.A.7Identify roots of polynomials when suitable factorizations are available. Know these roots become the zeros (x-intercepts) for the corresponding polynomial function. (MP.2, MP.5, MP.7)HS.A.8(+)Prove polynomial identities and use them to describe numerical relationships. (MP.2, MP.3, MP.6)HS.A.9(+)Know and apply the Binomial Theorem for the expansion of (x+y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. (MP.7, MP.8)
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