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- Common Core MathK - 8High School

# Algebra: Reasoning with Equations and Inequalities

1309 questions62 skills

# Algebra: Reasoning with Equations and Inequalities

1309 questions62 skills

## HSA-REI.A.1

12 questions1 skill

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.A.2

168 questions7 skills

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

## HSA-REI.B.3

76 questions3 skills

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

## HSA-REI.B.4

388 questions16 skills

Solve quadratic equations in one variable.

Quadratic formula

Quadratics by factoring (intro)

Completing the square (intermediate)

Completing the square

Quadratics by factoring

Quadratics by taking square roots

Quadratic word problems (standard form)

Solve equations using structure

Number of solutions of quadratic equations

Completing the square (intro)

Quadratics by taking square roots (intro)

Solve quadratic equations: complex solutions

Quadratics by taking square roots: with steps

Quadratics by taking square roots: strategy

Zero product property

Strategy in solving quadratics

## HSA-REI.B.4a

97 questions3 skills

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.## HSA-REI.B.4b

404 questions17 skills

Solve quadratic equations by inspection, 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*.Quadratic formula

Quadratics by factoring (intro)

Completing the square (intermediate)

Completing the square

Quadratics by factoring

Quadratics by taking square roots

Quadratic word problems (standard form)

Solve equations by completing the square

Solve equations using structure

Number of solutions of quadratic equations

Completing the square (intro)

Quadratics by taking square roots (intro)

Solve quadratic equations: complex solutions

Quadratics by taking square roots: with steps

Quadratics by taking square roots: strategy

Zero product property

Strategy in solving quadratics

## HSA-REI.C.5

12 questions1 skill

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.6

221 questions11 skills

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Age word problems

Systems of equations with graphing

Systems of equations with substitution

Systems of equations with elimination

Systems of equations with elimination challenge

Elimination strategies

Systems of equations word problems

Creating systems in context

Systems of equations word problems (with zero and infinite solutions)

Combining equations

Solutions of systems of equations

## HSA-REI.C.7

12 questions1 skill

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

## HSA-REI.C.8

70 questions3 skills

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

## HSA-REI.C.9

78 questions4 skills

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 questions5 skills

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

146 questions9 skills

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.Systems of equations with graphing

Solving equations graphically: intro

Number of solutions to a system of equations graphically

Solving equations graphically: word problems

Number of solutions to a system of equations algebraically

Solving equations graphically: graphing calculator

Solve equations graphically

Interpret equations graphically

Solutions of systems of equations

## HSA-REI.D.12

62 questions4 skills

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.