PARCC Algebra II Reasoning with Equations and Inequalities Practice

What the test measures

Reasoning with Equations and Inequalities skills

Understand solving equations as a process of reasoning and explain the reasoning
Solve equations and inequalities in one variable
Solve systems of equations
Represent and solve equations and inequalities graphically

Standards basis

Common Core State Standards for Mathematics (CCSS-M) / PARCC Model Content Frameworks — national

How the PARCC reports it

PARCC was a multistate assessment system built around the Common Core-era PARCC mathematics model content frameworks rather than a separate proprietary standards set. Its math structure is organized by grade/course and aligned to CCSS-M content categories and model content frameworks.

Blueprint & weighting

No single published PARCC weighting table was located in the accessible sources used here.

Official sources

PARCC Assessment
Common Core State Standards Initiative

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

$|x - 6| = 18$

Which of the following gives both solutions to the given equation?

The equation means $x - 6 = 18$ or $x - 6 = -18$ . So $x = 24$ or $x = -12$ . Both solutions are $-12$ and $24\textsf{.}$

Practice playeasy

If $|x - 7| = 15$ , what is the positive value of $x$ ?

Either $x - 7 = 15$ , giving $x = 22$ , or $x - 7 = -15$ , giving $x = -8$ . The positive value of $x$ is $22\textsf{.}$

Practice playeasy

How many distinct real roots does $x^{2} + 1 = 0$ have?

Here $a = 1$ , $b = 0$ , and $c = 1$ . Substituting into $b^{2} - 4ac$ gives $0^{2} - 4(1)(1) = -4\textsf{,}$ so there are $0$ distinct real roots.

Practice playeasy

How many distinct real solutions does $x^{2} + x + 1 = 0$ have?

Here $a = 1$ , $b = 1$ , and $c = 1$ . Substituting into $b^{2} - 4ac$ gives $1^{2} - 4(1)(1) = -3$ , so there are $0$ real solutions.

Practice playeasy

If $2x + 8 = 22$ , what is the value of $3x$ ?

Subtract $8$ from both sides: $2x = 14$ , so $x = 7$ . Then $3x = 3 \cdot 7 = 21\textsf{.}$

Practice playeasy

What is the least integer value of $x$ for which $-3x \le 12$ ?

Divide both sides by $-3$ and flip the inequality: $x \ge -4$ . The least integer that satisfies this is $-4$ .

Practice playeasy

$\begin{cases} y \ge 2x + 1 \\ y \le x + 5 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $x = 0$ , which of the following could be a value of $y$ ?

Substitute $x = 0$ . From $y \ge 2x + 1$ , $y \ge 1$ . From $y \le x + 5$ , $y \le 5$ . The value $y = 3$ satisfies $1 \le 3 \le 5$ .

Practice playmedium

If $f(x)=2x+3$ and $g(x)=x^{2}-x+3$ , which point is on the graph of both functions?

Set $f(x)=g(x)$ : $2x+3=x^{2}-x+3$ , so $0=x^{2}-3x$ . Then $x(x-3)=0$ , and $x=0$ or $x=3$ . For $x=0$ , $f(0)=3$ , so one intersection point is $(0,3)\textsf{.}$