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- Understand Solving Equations As A Process Of Reasoning And Explain The Reasoning
A.REI.1Explain each step in solving a simpl...more
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.
A.REI.2Solve simple rational and radical eq...more
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
- Solve Equations And Inequalities In One Variable
A.REI.3Solve linear equations and inequalit...more
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
A.REI.4Solve quadratic equations in one var...more
Solve quadratic equations in one variable.
A.REI.4.aUse the method of completing the squ...more
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
A.REI.4.bSolve quadratic equations by inspect...more
Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
- Solve Systems Of Equations
A.REI.5Prove that, given a system of two eq...more
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.
A.REI.6Solve systems of linear equations ex...more
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
A.REI.7Solve a simple system consisting of ...more
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
A.REI.8(+) Represent a system of linear equ...more
(+) Represent a system of linear equations as a single matrix equation in a vector variable.
A.REI.9(+) Find the inverse of a matrix if ...more
(+) 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).
- Represent And Solve Equations And Inequalities Graphically
A.REI.10Understand that the graph of an equa...more
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).
A.REI.11Explain why the x-coordinates of the...more
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.★
A.REI.12Graph the solutions to a linear ineq...more
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.
Major cluster will be a majority of the assessment, Supporting clusters will be assessed through their success at supporting the Major Clusters and Additional Clusters will be assessed as well. The assessments will strongly focus where the standards strongly focus.
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