North Carolina NC Math 1 End-of-Course (EOC) assessment (NCDPI): the conceptual categories and weightings, the calculator-inactive and calculator-active sections, the item types, the reference sheet question, the five achievement levels, and how to study for the End-of-Course test

The NC Math 1 End-of-Course (EOC) assessment is North Carolina's state test for the NC Math 1 course, administered by the North Carolina Department of Public Instruction (NCDPI). It is built directly from the North Carolina Standard Course of Study (NCSCOS) for Mathematics, whose Math 1 codes begin with NC.M1 (for example NC.M1.A-REI.3, solving linear equations and inequalities). This page is the index for the whole course: it explains the five conceptual categories and their weight ranges, the calculator-inactive and calculator-active sections, the item types, the reference sheet question, the achievement levels, and how to study each strand. The topic pages below carry the worked NC Math 1 EOC-style questions across the online item types. NC Math 3 also has its own EOC; this hub centers on NC Math 1 and notes Math 3 where it is in scope.

What the EOC is and why it matters

NC EOC assessments are course-level tests, not a single exit exam. NC Math 1 is the foundational high school math EOC, normally taken when a student completes the course in grade 8 or grade 9. State Board of Education policy (TEST-003, the requirement many districts still cite by its older code GCS-C-003) directs schools to use the EOC result as at least 20 percent of the student's final course grade, so the test is not separate from the class: it is part of the grade. NC Math 1 also feeds forward into NC Math 2 and NC Math 3, which makes its skills the base of the whole high school math sequence.

The EOC is delivered online, with windows tied to the end of the course: it is given near the close of the term in which the course finishes.

The five conceptual categories

The NCDPI test specifications organize the NCSCOS standards into five conceptual categories, and the official blueprint publishes a percent-of-items range for each. Algebra and Functions dominate the test.

Two consequences follow. First, Algebra and Functions together are the bulk of the test, so reading and building linear, quadratic, and exponential functions and solving fluently is the surest route to a strong score. Second, Statistics and Probability is a reliable middle block (about a fifth of the items) that is quick to bank with data displays and linear models. Geometry is the smallest category but still appears every form through coordinate reasoning. The categories are reported as ranges, so the exact count of items shifts a little from form to form; the topic pages note which standard each item targets as you go.

The two sections and the calculator policy

The NC Math 1 EOC is built from 60 items: 50 operational items that count toward the score plus 10 embedded field-test items that do not. The operational items are split across two sections, and the calculator rule changes between them.

• Calculator-inactive section: 15 operational items. This section tests fluency you must have without a calculator: solving linear equations, simplifying expressions, factoring, and reading a graph.
• Calculator-active section: 35 operational items. The larger section, where a graphing calculator or the on-screen NCTest calculator is allowed.

Students must be provided a graphing calculator for the calculator-active work, plus graph paper and blank paper, and the online test includes an on-screen calculator. The estimated time is about 180 minutes (3 hours) for most students, with a maximum of 240 minutes (4 hours) except where documented accommodations allow more.

The item types

The online test mixes traditional multiple choice with technology-enhanced items (TEIs). Both sections may use these:

• Multiple choice (MC). Four options, one correct, no partial credit. Still the largest single share of points.
• Gridded response or numeric entry. You type a number or grid in a numeric answer, for example entering a solution, a slope, or a coordinate. There are no options to work backward from.
• Technology-enhanced items. You interact with the screen: drag values into a table, select all correct statements, plot a point or a line, or complete a multi-part task.

Because gridded-response and many TEIs are scored by exact match, a sign slip that a multiple-choice distractor might have caught now simply costs the point. Show structure and check signs.

The reference sheet question

This is a point where North Carolina differs from many states, so it is worth stating clearly. The current NCDPI test specifications say that NC Math 3 students are provided a reference sheet, but NC Math 1 students are not. In other words, NC Math 1 gives you no formula sheet at all.

That means you must carry every formula in memory:

• Linear forms. Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$, slope-intercept $y = mx + b$, point-slope $y - y_1 = m(x - x_1)$, and standard form $Ax + By = C$.
• Quadratic tools. Standard form $y = ax^2 + bx + c$, the axis of symmetry $x = \frac{-b}{2a}$, and the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
• Distance. The distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ and the Pythagorean theorem $a^2 + b^2 = c^2$.
• Exponential and sequences. Growth and decay $y = a(1 \pm r)^t$, the arithmetic rule $a_n = a_1 + (n - 1)d$, and the geometric rule $a_n = a_1 r^{\,n-1}$.

Achievement levels

Raw points convert to a scale score, reported in five achievement levels:

• Level 1 - did not meet the course standards; limited command of the content.
• Level 2 - below the proficiency standard; partial command.
• Level 3 - the grade-level proficient (GLP) standard; met North Carolina's course-level expectations.
• Level 4 - college and career ready (CCR); on track for college and career expectations.
• Level 5 - the highest level; superior command, well beyond CCR.

NCDPI counts Levels 3, 4, and 5 together as proficient for reporting, while Levels 4 and 5 mark the college and career ready standard. The raw points needed for each level vary by form because NCDPI equates each administration. Aim past Level 3: securing Algebra and Functions reliably and adding the smaller categories is what moves a student toward Level 4 and Level 5.

How to study NC Math 1

1. Bank Algebra and Functions first. Together they are most of the points. Reading and building linear, quadratic, and exponential functions, plus fluent solving and systems, is the largest, most reliable block.
2. Drill the non-calculator skills. The calculator-inactive section bans the calculator on roughly 30 percent of your score. Solving, factoring, simplifying, and graph reading must be automatic.
3. Memorize every formula. NC Math 1 gives no reference sheet. The slope formula, line forms, axis of symmetry, quadratic formula, distance formula, and exponential models must all be in memory.
4. Train every item type. Practice gridded and numeric entry and technology-enhanced items, not just multiple choice. The test checks whether you can produce answers, not only recognize them.
5. Show structure even with a calculator. Exact-match and multi-part items reward the correct setup, so write the model or the steps before you compute.

The course, topic by topic

Each topic below has its own answer page with worked NC Math 1 EOC-style questions across the online item types, plus an overview guide and a quiz for each module.

Expressions and operations (Number and Quantity, Algebra).

• Interpreting expressions and their parts, rewriting expressions using structure, polynomial operations: add, subtract, multiply, factoring quadratic expressions, radicals and rational exponents, rational and irrational numbers.

Linear equations and functions (Algebra, Functions).

• Solving linear equations in one variable, solving linear inequalities in one variable, creating equations and inequalities from context, rearranging literal equations and formulas, slope and writing linear equations, graphing linear equations in two variables.

Systems of equations and inequalities (Algebra).

• Solving systems of linear equations algebraically, solving systems by graphing, why equivalent systems work, graphing linear inequalities in two variables, modeling with systems and constraints.

Functions and exponential models (Functions, Algebra).

• Function notation, domain, and range, interpreting key features of graphs, average rate of change, arithmetic and geometric sequences, exponential functions, growth, and decay, comparing linear, quadratic, and exponential models, solving quadratic equations.

Descriptive statistics (Statistics and Probability).

• Representing data: dot plots, histograms, and box plots, comparing center and spread, two-way frequency tables, scatter plots and linear models, correlation, causation, and the correlation coefficient.

Coordinate geometry and reasoning (Geometry).

• Slope criteria for parallel and perpendicular lines, proving geometric theorems with coordinates, the distance formula and the coordinate plane, partitioning a directed line segment, midpoint and the coordinate plane.

For the official materials

NCDPI publishes the EOC NC Math 1 and NC Math 3 test specifications, the released form, the calculator policy, and the testing time tables on its End-of-Course (EOC) pages, and the North Carolina Standard Course of Study for Mathematics lives on the NCDPI Mathematics standards site. Always study from the current released items and the official specifications, because the item types, the weightings, the reference-sheet policy, and the standards are specific to North Carolina.