NC EOG/EOC NC Math 1 Functions Practice

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

EOC NC Math 1 domain (32-36% of the test, Table 1). Understand the concept of a function and use function notation (F-IF.1, F-IF.2); build, interpret, and analyze linear, quadratic, and exponential functions (F-IF, F-BF); and construct and compare linear and exponential models (F-LE). This NC Math 1 reporting domain maps to 22 practice skills and 8 representative questions from the playable bank.

NC Math 1F22 mapped skills

Functions skills

Understand the concept of a function and use function notation, including sequences (NC.M1.F-IF.1, NC.M1.F-IF.2, NC.M1.F-IF.3)

Interpret key features of functions from graphs, tables, and symbolic forms in context (NC.M1.F-IF.4, NC.M1.F-IF.5, NC.M1.F-IF.6)

Analyze linear, quadratic, and exponential functions using different representations (NC.M1.F-IF.7, NC.M1.F-IF.8, NC.M1.F-IF.9)

Build a function that models a relationship between two quantities (NC.M1.F-BF.1, NC.M1.F-BF.2)

Construct and compare linear and exponential models and interpret their parameters (NC.M1.F-LE.1, NC.M1.F-LE.3, NC.M1.F-LE.5)

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

At what $x$ -value does the graph of $y = 4(x + 12)(x - 3)(x + 2)$ intercept the $x$ -axis?

Set $y = 0$ : $4(x + 12)(x - 3)(x + 2) = 0$ . The constant $4 \neq 0$ , so the zeros are $x = -12$ , $x = 3$ , and $x = -2$ . Among the choices, only $3$ is an x-coordinate of an x-intercept.

Practice playeasy

The equation of a line is $4x - 5y = -40\textsf{.}$ What is the $y$ -intercept of the line?

The $y$ -intercept is the value of $y$ when $x = 0\textsf{.}$ Substituting gives $-5y = -40\textsf{,}$ so $y = 8\textsf{.}$

Practice playeasy

$f(x) = 3(x - 1)^2 + 7$

The function $f$ is defined by the given equation. For what value of $x$ does $f(x)$ reach its minimum?

The equation is in vertex form $f(x) = a(x - h)^2 + k$ with $a = 3 > 0$ , so the graph opens upward and the minimum occurs at the vertex. Here $h = 1$ , so the vertex is at $x = 1$ . The leading coefficient $3$ does not change the $x$ -coordinate of the vertex. Therefore, $f(x)$ reaches its minimum when $x = 1$ .

Practice playeasy

The graph of $y = x^2 - 4x + 1$ is a parabola that opens upward. What is the $x$ -coordinate of its lowest point?

Because this parabola opens upward, its lowest point is the vertex. For $y = ax^2 + bx + c$ , the $x$ -value at the vertex is $x = -\dfrac{b}{2a}$ . Here $a = 1$ and $b = -4$ , so $x = -\dfrac{-4}{2(1)} = \dfrac{4}{2} = 2$ . Therefore, the lowest point has $x$ -coordinate $2$ .

Practice playmedium

The table defines functions for positive integers $x \leq 5$ .
$\begin{array}{c|c|c|c} x & p(x) & q(x) & r(x) \\ \hline 1 & 4 & 5 & 1 \\ 2 & 2 & 3 & 5 \\ 3 & 1 & 4 & 2 \\ 4 & 5 & 2 & 3 \\ 5 & 3 & 1 & 4 \end{array}$
If $p(q(r(x))) = 5$ , what is the value of $x$ ?

Work from the outside in. Since $p(4) = 5$ , we need $q(r(x)) = 4$ . Since $q(3) = 4$ , we need $r(x) = 3$ . From the table, $r(4) = 3$ , so $x = 4$ .

Practice playmedium

Piecewise functions $f$ and $g$ are shown.
$f(x)=\begin{cases} |x|+3 & \text{for } x \leq 4 \\ 2x-5 & \text{for } x > 4 \end{cases}$
$g(x)=\begin{cases} 6-x & \text{for } x \leq 0 \\ x+1 & \text{for } x > 0 \end{cases}$
Find the value of $f(g(0))\textsf{.}$

Start with the inner function: $0 \leq 0$ , so $g(0)=6-0=6$ . Then $6 > 4$ , so $f(6)=2(6)-5=7\textsf{.}$

Practice playmedium

The $x$ -intercept of the graph of $y = -4x - 20$ in the coordinate plane is $(x, 0)$ . What is the value of $x$ ?

At the $x$ -intercept, $y = 0$ , so $0 = -4x - 20$ , $-4x = 20$ , and $x = -5\textsf{.}$

Practice playeasy

The function $f$ is defined by $f(x) = 3x^{2} + 2$ . What is the value of $f(x)$ when $x = 2$ ?

Substitute $x = 2$ : $f(2) = 3(2)^{2} + 2 = 3(4) + 2 = 12 + 2 = 14$ .

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

Functions skills

Understand the concept of a function and use function notation, including sequences (NC.M1.F-IF.1, NC.M1.F-IF.2, NC.M1.F-IF.3)

Interpret key features of functions from graphs, tables, and symbolic forms in context (NC.M1.F-IF.4, NC.M1.F-IF.5, NC.M1.F-IF.6)

Analyze linear, quadratic, and exponential functions using different representations (NC.M1.F-IF.7, NC.M1.F-IF.8, NC.M1.F-IF.9)

Build a function that models a relationship between two quantities (NC.M1.F-BF.1, NC.M1.F-BF.2)

Construct and compare linear and exponential models and interpret their parameters (NC.M1.F-LE.1, NC.M1.F-LE.3, NC.M1.F-LE.5)

Topics mapped to this domain

Factored polynomial x-intercepts (SAT)

Intercepts from general form

Quadratic minimum from vertex form

Quadratic minimum x-value

Function table composition (ACT)

Piecewise function composition (ACT)

Slope-intercept intercepts (SAT/PSAT 8/9/10)

Evaluating functions

Evaluating functions at a value

Evaluating functions from percent change

Evaluating functions in context

Interpreting function values in context

8 free questions · 0/0 correct

Turn functions into game time.

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