NDSA Grade 8 Expressions and Equations Practice

Expressions and Equations skills

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p.

Solve linear equations in one variable.

Analyze and solve pairs of simultaneous linear equations.

Work with radicals and integer exponents; understand the connections between proportional relationships, lines, and linear equations.

Standards basis

North Dakota State Content Standards for Mathematics — North Dakota

How the NDSA reports it

North Dakota administered its own state assessment program (the NDSA, a Cambium computer-adaptive test in grades 3-8 and 10; replaced by ND A+ beginning spring 2025). An official NDSA mathematics public-facing CAT blueprint (Cambium/NDDPI, Oct 2020) does exist and lists per-grade reporting categories with percentage ranges, but its full per-grade table could not be retrieved character-for-character from a citable primary source for transcription here (the Cambium content CDN blocks programmatic access). The NDSA reporting categories are the CCSS-M grade-level domains: the assessment was built on North Dakota's 2017 math standards, which are verbatim CCSS-M organized by grade-level domains. The coverage map below uses North Dakota's 2023-standards-style domain/standard codes (e.g. 3.AR.OA) but the skill content is CCSS-M.

Blueprint & weighting

An official NDSA mathematics CAT blueprint (Cambium/NDDPI public-facing CAT version, Oct 2020) publishes per-grade reporting-category percentage ranges (e.g. grade 3 Operations and Algebraic Thinking ~31-34%, Number and Operations in Base Ten ~22-24%; grade 6 groups Ratios & Proportional Relationships and The Number System ~28-34% and Expressions and Equations ~25-29%). The complete per-grade table could not be retrieved verbatim from a citable primary source (the Cambium content CDN returns HTTP 403 to programmatic fetches), so domain weights in the mapping are left null rather than transcribing partial/uncertain figures or splitting blueprint percentages across the grade-6+ domain groupings.

Official sources

North Dakota DPI – State Assessment page
North Dakota DPI – Home
North Dakota Department of Agriculture – Ag Mag teacher guide with ND math standards references

8 free questions · 0/0 correct

Practice playeasy

Rewrite $a^{-2}$ with a positive exponent.

The Negative Exponent Property says that a nonzero base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent, written $a^{-n} = \dfrac{1}{a^{n}}\textsf{.}$ Applying the property, $a^{-2} = \dfrac{1}{a^{2}}\textsf{.}$

Practice playeasy

What is $\sqrt{64}$ ?

$8 \times 8 = 64$ , so $\sqrt{64} = 8$ .

Practice playeasy

Which of the following systems of linear equations has no solution?

Both equations have slope $2$ but different $y$ -intercepts ( $3$ and $-1$ ), so the lines are parallel and the system has no solution.

Practice playeasy

$\begin{cases} x + y = 5 \\ 3x - y = 3 \end{cases}$

How many solutions does the given system of equations have?

Rewrite in slope-intercept form: $y = -x + 5$ and $y = 3x - 3$ . The slopes $-1$ and $3$ are different, so the lines intersect at exactly one point.

Practice playmedium

Solve $\dfrac{1}{3}(6x - 9) + 2x = 11$ for $x$ .

Distribute $\dfrac{1}{3}$ : $2x - 3 + 2x = 11$ . Combine like terms: $4x - 3 = 11$ . Add $3$ to both sides: $4x = 14$ . Divide by $4$ : $x = \dfrac{7}{2}\textsf{.}$

Practice playmedium

If $-2y = 4x + 8$ , which expression is equal to $x$ ?

Subtract $8$ from both sides: $-2y - 8 = 4x$ . Divide both sides by $4$ : $x = \dfrac{-2y - 8}{4}$ .

Practice playeasy

What is the $y$ -intercept of the graph of $y = 5x + 27$ in the coordinate plane?

In $y = mx + b$ , the $y$ -intercept is the point $(0, b)$ . Here $b = 27$ , so the $y$ -intercept is $(0, 27)\textsf{.}$

Practice playeasy

$(3 \cdot 7)^{4} = 3^{a} \cdot 7^{a}\textsf{.}$ What is $a\textsf{?}$

The Power of a Product Property says that a product raised to a power equals each factor raised to that power, written $(ab)^{n} = a^{n} \cdot b^{n}\textsf{.}$ Here $(3 \cdot 7)^{4} = 3^{4} \cdot 7^{4}$ , so $a = 4\textsf{.}$

NDSA Grade 8 Expressions and Equations. Practice it free.

Expressions and Equations skills

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p.

Solve linear equations in one variable.

Analyze and solve pairs of simultaneous linear equations.

Work with radicals and integer exponents; understand the connections between proportional relationships, lines, and linear equations.

Topics mapped to this domain

Exponent rules

Square roots and cube roots

Inconsistent linear systems (ACT/SAT/PSAT 8/9/10)

Linear Algebra Basics: Systems

Multi-step linear equations

Solve linear equation for x (ACT)

Y-intercept as a point

8 free questions · 0/0 correct

Turn expressions and equations into game time.

More Grade 8 domains