High School: Algebra
HSA.REI.C5
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.
October 1, 2018HSA.REI.C6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
October 1, 2018HSA.REI.C7
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.
October 1, 2018HSA.REI.C8
(+) Represent a system of linear equations as a single matrix equation in a vector variable.
October 1, 2018HSA.REI.D10
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).
October 1, 2018HSA.APR.D7
(+) 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.
October 1, 2018HSA.CED.A1
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.
October 1, 2018HSA.CED.A2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
October 1, 2018HSA.CED.A3
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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
October 1, 2018HSA.CED.A4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
October 1, 2018HSA.REI.A1
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.
October 1, 2018HSA.REI.A2
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
October 1, 2018