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Algebra: Reasoning with Equations and Inequalities

1296 preguntas62 habilidades

HSA-REI.A.1

12 preguntas1 habilidad
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.

HSA-REI.B.3

76 preguntas3 habilidades
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

HSA-REI.B.4a

97 preguntas3 habilidades
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (xp)2 = q that has the same solutions. Derive the quadratic formula from this form.

HSA-REI.C.5

12 preguntas1 habilidad
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.

HSA-REI.C.7

12 preguntas1 habilidad
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

HSA-REI.C.8

70 preguntas3 habilidades
Represent a system of linear equations as a single matrix equation in a vector variable.

HSA-REI.C.9

57 preguntas4 habilidades
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).

HSA-REI.D.10

118 preguntas5 habilidades
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).

HSA-REI.D.11

154 preguntas9 habilidades
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.

HSA-REI.D.12

62 preguntas4 habilidades
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.