NC EOG/EOC NC Math 1 Geometry Practice

NC EOG/EOC NC Math 1 Geometry. Practice it free.

EOC NC Math 1 domain (8-12% of the test, Table 1). Use coordinates to prove simple geometric theorems algebraically and to solve problems involving slope, parallel and perpendicular lines, distance, and partitioning of segments (G-GPE). This NC Math 1 reporting domain maps to 4 practice skills and 8 representative questions from the playable bank.

NC Math 1G4 mapped skills

Geometry skills

Use coordinates to prove simple geometric theorems algebraically (NC.M1.G-GPE.4)

Use slope criteria for parallel and perpendicular lines to solve geometric problems (NC.M1.G-GPE.5)

Find the point on a directed line segment that partitions it in a given ratio (NC.M1.G-GPE.6)

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

The graph of the equation $(x - 7)^2 + (y - 3)^2 = 25$ is a circle in the coordinate plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a\textsf{?}$

The center is $(7, 3)$ and the radius is $5\textsf{.}$ A point on the circle must satisfy $7 - 5 \le a \le 7 + 5\textsf{,}$ so $2 \le a \le 12\textsf{.}$ The value $9$ is in this interval.

Practice playeasy

Find the midpoint of $(2, 8)$ and $(6, 4)$ . What is the $x$ -coordinate?

$x$ -coordinate $= \dfrac{2 + 6}{2} = \dfrac{8}{2} = 4$ .

Practice playmedium

The equation of a line is $y = 2x + 1$ . Which equation represents the line that is perpendicular to this line and passes through the point $(4, 3)$ ?

Perpendicular lines have slopes that are negative reciprocals, so $m = -\dfrac{1}{2}$ . Substitute $(4, 3)$ into $y = -\dfrac{1}{2}x + b$ : $3 = -\dfrac{1}{2}(4) + b = -2 + b$ , so $b = 5$ . The equation is $y = -\dfrac{1}{2}x + 5\textsf{.}$

Practice playeasy

Line $j$ is defined by $y = -4x + 10$ . Line $o$ is perpendicular to line $j$ in the coordinate plane. What is the slope of line $o$ ?

Perpendicular lines have slopes that are negative reciprocals. The slope of line $j$ is $-4$ , so the slope of line $o$ is $\dfrac{1}{4}\textsf{.}$

Practice playeasy

The graph of the equation $(x - 4)^2 + (y + 5)^2 = 36$ is a circle in the coordinate plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a\textsf{?}$

The center is $(4, -5)$ and the radius is $6\textsf{.}$ A point on the circle must satisfy $4 - 6 \le a \le 4 + 6\textsf{,}$ so $-2 \le a \le 10\textsf{.}$ The value $3$ is in this interval.

Practice playeasy

Find the midpoint of $(2, 8)$ and $(6, 4)$ . What is the $y$ -coordinate?

$y$ -coordinate $= \dfrac{8 + 4}{2} = \dfrac{12}{2} = 6$ .

Practice playmedium

The equation of a line is $y = -3x + 2$ . Which equation represents the line that is perpendicular to this line and passes through the point $(3, 1)$ ?

Perpendicular lines have slopes that are negative reciprocals, so $m = \dfrac{1}{3}$ . Substitute $(3, 1)$ into $y = \dfrac{1}{3}x + b$ : $1 = \dfrac{1}{3}(3) + b = 1 + b$ , so $b = 0$ . The equation is $y = \dfrac{1}{3}x\textsf{.}$

Practice playeasy

Line $u$ is defined by $y = \dfrac{2}{5}x - 3$ . Line $v$ is perpendicular to line $u$ in the coordinate plane. What is the slope of line $v$ ?

Perpendicular lines have slopes that are negative reciprocals. The slope of line $u$ is $\dfrac{2}{5}$ , so the slope of line $v$ is $-\dfrac{5}{2}\textsf{.}$