High School — Algebra

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Interpret expressions that represent a quantity in terms of its contextCCSS.Math.Content.HSA-SSE.A.1

Use the structure of an expression to identify ways to rewrite it.CCSS.Math.Content.HSA-SSE.A.2

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.CCSS.Math.Content.HSA-SSE.B.3

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.CCSS.Math.Content.HSA-SSE.B.4

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.CCSS.Math.Content.HSA-APR.A.1

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).CCSS.Math.Content.HSA-APR.B.2

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.CCSS.Math.Content.HSA-APR.B.3

Prove polynomial identities and use them to describe numerical relationships.CCSS.Math.Content.HSA-APR.C.4

(+) 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.CCSS.Math.Content.HSA-APR.C.5

Rewrite simple rational expressions in different forms; write ^a(x/_b(x) in the form q(x) + ^r(x)/_b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.CCSS.Math.Content.HSA-APR.D.6

(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.CCSS.Math.Content.HSA-APR.D.7

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.CCSS.Math.Content.HSA-CED.A.1

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.CCSS.Math.Content.HSA-CED.A.2

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.CCSS.Math.Content.HSA-CED.A.3

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.CCSS.Math.Content.HSA-CED.A.4

Explain 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.CCSS.Math.Content.HSA-REI.A.1

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.CCSS.Math.Content.HSA-REI.A.2

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.CCSS.Math.Content.HSA-REI.B.3

Solve quadratic equations in one variable.CCSS.Math.Content.HSA-REI.B.4

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.CCSS.Math.Content.HSA-REI.C.5

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.CCSS.Math.Content.HSA-REI.C.6

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.CCSS.Math.Content.HSA-REI.C.7

(+) Represent a system of linear equations as a single matrix equation in a vector variable.CCSS.Math.Content.HSA-REI.C.8

(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).CCSS.Math.Content.HSA-REI.C.9

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).CCSS.Math.Content.HSA-REI.D.10

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.CCSS.Math.Content.HSA-REI.D.11

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.CCSS.Math.Content.HSA-REI.D.12