NC EOG/EOC Grade 8 The Number System, Expressions and Equations Practice

NC EOG/EOC Grade 8 The Number System, Expressions and Equations. Practice it free.

EOG grade 8 combined domain (24-28% of the test, Table 2). Know that there are numbers that are not rational and approximate them by rational numbers; work with radicals and integer exponents; understand the connections between proportional relationships, lines, and linear equations; and analyze and solve linear equations and pairs of simultaneous linear equations. This Grade 8 reporting domain maps to 11 practice skills and 8 representative questions from the playable bank.

Grade 8NS,EE11 mapped skills

The Number System, Expressions and Equations skills

Know that there are numbers that are not rational, and approximate irrational numbers by rational numbers

Work with radicals and integer exponents and use scientific notation

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

Analyze and solve linear equations and pairs of simultaneous linear equations

Standards basis

North Carolina Standard Course of Study (NCSCOS) — North Carolina

How the NC EOG/EOC reports it

North Carolina’s math assessments are state-developed EOG/EOC tests aligned to the North Carolina Standard Course of Study (NCSCOS) for Mathematics, adopted June 2016, rather than a shared multistate framework. The EOG Grades 3-8 Mathematics Test Specifications and the EOC NC Math 1 and NC Math 3 Test Specifications publish, in Table 1/Table 2, the range of total items by domain (the official domain weight distributions). The NCSCOS K-8 domains carry CCSS domain codes (NC.3.OA, NC.8.F, …) and are CCSS-derived; NC Math 1 and NC Math 3 are integrated high-school EOC courses whose standards carry NC.M1/NC.M3 conceptual-category codes (Number and Quantity, Algebra, Functions, Geometry, Statistics and Probability).

Blueprint & weighting

Published per-domain weight ranges come from the NC DPI EOG/EOC Mathematics Test Specifications (April 2026), Table 1/Table 2 (range of total items by domain). EOG grades 3-5 (Table 1): Operations and Algebraic Thinking 32-36% (g3) / 14-18% (g4) / 9-13% (g5); Number and Operations in Base Ten 9-13% / 25-29% / 25-29%; Number and Operations – Fractions 28-32% / 30-34% / 39-43%; Measurement and Data, Geometry 23-27% / 23-27% / 19-23%. EOG grades 6-8 (Table 2): Ratios and Proportional Relationships 24-28% (g6) / 24-28% (g7) / — (g8); The Number System 20-24% / 8-12% / —; Expressions and Equations 22-26% / 20-24% / —; The Number System, Expressions and Equations (combined) — / — / 24-28%; Functions — / — / 28-32%; Geometry 12-16% / 16-20% / 24-28%; Statistics and Probability 12-16% / 22-26% / 16-20%. EOC (Table 1): NC Math 1 — Number and Quantity and Algebra 36-40%, Functions 32-36%, Geometry 8-12%, Statistics and Probability 18-20%; NC Math 3 — Number and Quantity and Algebra 32-36%, Functions 32-36%, Geometry 20-24%, Statistics and Probability 8-12%.

Official sources

NC DPI End-of-Grade (EOG)
NC DPI 2025-26 EOC Assessment Brief
NC DPI EOG Mathematics Grades 3-8 Test Specifications (April 2026)

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

$\sqrt{27}$ lies between two consecutive integers. Enter the larger one.

$5^2 = 25 < 27 < 36 = 6^2$ , so $\sqrt{27}$ is between $5$ and $6$ ; the larger is $6$ .

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 $n = 5$ .

NC EOG/EOC Grade 8 The Number System, Expressions and Equations. Practice it free.

The Number System, Expressions and Equations skills

Know that there are numbers that are not rational, and approximate irrational numbers by rational numbers

Work with radicals and integer exponents and use scientific notation

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

Irrational number approximations

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 the number system, expressions and equations into game time.

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