VTCAP Grade 8 Expressions and Equations Practice

VTCAP Grade 8 Expressions and Equations. Practice it free.

Grade 8 Expressions and Equations standards; reported jointly with the number system as 'The Number System, Expressions and Equations' performance indicator. Blueprint target: 11-17 points (20-31% of the grade 8 test). This Grade 8 reporting domain maps to 10 practice skills and 8 representative questions from the playable bank.

Grade 88.EE10 mapped skills

Expressions and Equations skills

Work with radicals and integer exponents

Understand the connections between proportional relationships, lines, and linear equations

Analyze and solve linear equations and pairs of simultaneous linear equations

Standards basis

Common Core State Standards for Mathematics (CCSS-M) — Vermont

How the VTCAP reports it

Vermont administered the Smarter Balanced summative through spring 2022, then replaced it with the Cognia-developed Vermont Comprehensive Assessment Program (VTCAP) beginning spring 2023 — this landing slug predates the switch. VTCAP mathematics is an adaptive, CCSS-M-aligned assessment in grades 3-9. It is NOT a Smarter Balanced administration: its reporting categories are groupings of the CCSS grade-level domains (e.g. 'The Number System, Expressions and Equations'), not SBAC claims, though two cross-grade Mathematical Practices indicators ('Problem Solving, Reasoning, and Argument'; 'Modeling, Patterns, and Structure') echo the old claim structure. Per the test specifications, the grades 3-8 test may assess any CCSS-M standard at the grade; the grade 9 test assesses a prioritized subset of the high school CCSS-M within the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability (the assessed focus areas are published in the grade 9 Performance Level Descriptors).

Blueprint & weighting

VTCAP Test Specifications (Spring 2026) operational test blueprint, target percent of points per grade — Grade 3: OA 24-35%, NBT 10-14%, NF 16-20%, MD 22-29%, G 6-10%, constructed-response Mathematical Practices 12%. Grade 4: OA 20-31%, NBT 16-20%, NF 20-31%, MD 12-20%, G 6-10%, practices 12%. Grade 5: OA 14-22%, NBT 14-25%, NF 22-29%, MD 20-27%, G 8-16%, practices 12%. Grade 6: RP 15-22%, NS 15-22%, EE 15-22%, G 11-19%, SP 11-19%, practices 11%. Grade 7: RP 15-22%, NS 11%, EE 15-30%, G 11-19%, SP 19-22%, practices 11%. Grade 8: F 18-29%, NS 7%, EE 20-31%, G 18-29%, SP 18-22%, practices 11%. Grade 9 (all machine-scored): Number and Quantity/Algebra 18-27%, Algebra/Functions 31-40%, Geometry 20-29%, Statistics and Probability 13-20%; the two practices indicators are dual-aligned targets of >18% of points each. Identical figures appear in the Spring 2025 specifications.

Official sources

VTCAP Test Specifications, Spring 2026 (Vermont AOE / Cognia)
VTCAP Test Specifications, Spring 2025 (Vermont AOE / Cognia)
VTCAP Performance Level Descriptors: Mathematics, Grades 3-9 (Vermont AOE)

8 free questions · 0/0 correct

Practice playeasy

What is the $y$ -intercept of the graph of $y = 15x + 4$ in the coordinate plane?

In $y = mx + b$ , the $y$ -intercept is the point $(0, b)$ . Here $b = 4$ , so the $y$ -intercept is $(0, 4)\textsf{.}$

Practice playeasy

Simplify: $\dfrac{b^{8}}{b^{4}}$ .

The Quotient of Powers Property says that powers with the same nonzero base are divided by subtracting the exponents, written $\dfrac{b^{m}}{b^{n}} = b^{m-n}\textsf{.}$ Here both the numerator and the denominator have base $b$ , so $\dfrac{b^{8}}{b^{4}} = b^{8-4} = b^{4}\textsf{.}$

Practice playhard

Let $f(t) = 3e^{2t} + 10$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(5)$ ?

Substitute $t = 5$ : $f(5) = 3e^{10} + 10$ . Since $e^{10} \approx 22{,}026$ , $f(5) \approx 3(22{,}026) + 10 = 66{,}088 \approx 7 \times 10^{4}$ .

Practice playeasy

Which system of equations has no solution?

Both equations have slope $6$ but different $y$ -intercepts ( $1$ and $-4$ ), so the lines are parallel and the system has no solution.

Practice playeasy

$\begin{cases} x + 3y = 4 \\ 2x + 6y = 8 \end{cases}$

How many solutions does the given system of equations have?

Rewrite in slope-intercept form: $y = -\dfrac{1}{3}x + \dfrac{4}{3}$ and $y = -\dfrac{1}{3}x + \dfrac{4}{3}$ . The slopes and $y$ -intercepts match, so the equations describe the same line and the system has infinitely many solutions.

Practice playmedium

What value of $x$ solves $\dfrac{1}{2}x + 4 = x - 1$ ?

Multiply every term by $2$ to clear the fraction: $x + 8 = 2x - 2$ . Subtract $x$ from both sides: $8 = x - 2$ . Add $2$ to both sides: $x = 10\textsf{.}$

Practice playeasy

Write $720{,}000$ as $a \times 10^n$ where $1 \le a < 10$ . What is $n$ ?

$720{,}000 = 7.2 \times 10^5$ , so $n = 5$ .

Practice playmedium

What is $\dfrac{9 \times 10^{-6}}{3 \times 10^{2}}$ ?

Divide coefficients and subtract exponents: $9 \div 3 = 3$ and $-6-2=-8$ . So $\dfrac{9 \times 10^{-6}}{3 \times 10^{2}}=3 \times 10^{-8}\textsf{.}$

VTCAP Grade 8 Expressions and Equations. Practice it free.

Expressions and Equations skills

Work with radicals and integer exponents

Understand the connections between proportional relationships, lines, and linear equations

Analyze and solve linear equations and pairs of simultaneous linear equations

Topics mapped to this domain

Y-intercept as a point

Exponent rules

Evaluating exponential functions

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

Linear Algebra Basics: Systems

Multi-step linear equations

Scientific notation

Operations with scientific notation (ACT)

Solve linear equation for x (ACT)

Square roots and cube roots

8 free questions · 0/0 correct

Turn expressions and equations into game time.

More Grade 8 domains