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- Common Core MathK - 8High School

1121 questions48 skills

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.

Skills for this standard are coming soon.

156 questions6 skills

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

76 questions3 skills

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

331 questions12 skills

Solve quadratic equations in one variable.

Solve equations using structure

Completing the square (intro)

Quadratics by factoring

Completing the square

Quadratics by taking square roots

Quadratic word problems (standard form)

Quadratic formula

Quadratics by taking square roots: strategy

Number of solutions of quadratic equations

Quadratics by factoring (intro)

Completing the square (intermediate)

Solve quadratic equations: complex solutions

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.

331 questions12 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*.

Solve equations using structure

Completing the square (intro)

Quadratics by factoring

Completing the square

Quadratics by taking square roots

Quadratic word problems (standard form)

Quadratic formula

Quadratics by taking square roots: strategy

Number of solutions of quadratic equations

Quadratics by factoring (intro)

Completing the square (intermediate)

Solve quadratic equations: complex solutions

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.

186 questions9 skills

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

Solutions of systems of equations

Systems of equations word problems

Systems of equations with elimination challenge

Systems of equations with substitution

Linear systems of equations capstone

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

Systems of equations with elimination

Systems of equations with graphing

Age word problems

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

Skills for this standard are coming soon.

70 questions3 skills

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

66 questions3 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).

142 questions6 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).

106 questions6 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.

46 questions3 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.