NC EOG/EOC NC Math 3 Functions Practice

NC EOG/EOC NC Math 3 Functions. Practice it free.

EOC NC Math 3 domain (32-36% of the test, Table 1). Interpret and analyze functions including polynomial, rational, exponential, logarithmic, and trigonometric functions (F-IF); build new functions and find inverses (F-BF); use logarithms to solve exponential models (F-LE); and extend trigonometry to radian measure and the unit circle (F-TF). This NC Math 3 reporting domain maps to 19 practice skills and 8 representative questions from the playable bank.

NC Math 3F19 mapped skills

Functions skills

Understand the concept of a function and use function notation (NC.M3.F-IF.1, NC.M3.F-IF.2)

Interpret and analyze key features of functions, including polynomial, rational, and trigonometric functions, from multiple representations (NC.M3.F-IF.4, NC.M3.F-IF.7, NC.M3.F-IF.9)

Build functions by combining functions and find inverse functions (NC.M3.F-BF.1, NC.M3.F-BF.3, NC.M3.F-BF.4)

Construct and compare exponential and logarithmic models and use logarithms to solve for an exponent (NC.M3.F-LE.3, NC.M3.F-LE.4)

Extend the domain of trigonometric functions using radian measure of angles and the unit circle (NC.M3.F-TF.1, NC.M3.F-TF.2, NC.M3.F-TF.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 playmedium

The real solution of $2e^{3x}=10$ is

Divide by $2$ to get $e^{3x}=5$ . Take $\ln$ : $3x=\ln 5$ . Divide by $3$ to get $x=\dfrac{\ln 5}{3}\textsf{.}$

Practice playmedium

At what $x$ -value does the graph of $y = 3(x - 5)^2(x + 8)$ intercept the $x$ -axis?

Set $y = 0$ : $3(x - 5)^2(x + 8) = 0$ . The constant $3 \neq 0$ , so the zeros are $x = 5$ (from the repeated factor) and $x = -8$ . Among the choices, only $5$ is an x-coordinate of an x-intercept.

Practice playeasy

$f(x) = (x - 2)^2 + 10$

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 $a = 1 > 0$ , so the graph opens upward and the minimum occurs at the vertex. Here $h = 2$ , so the vertex is at $x = 2$ . Therefore, $f(x)$ reaches its minimum when $x = 2$ .

Practice playeasy

The equation $y = x^2 + 8x + 7$ relates $x$ and $y$ . What value of $x$ gives the least value of $y$ ?

The parabola opens upward, so the smallest $y$ is at the vertex. For $y = ax^2 + bx + c$ , the $x$ -value at the vertex is $x = -\dfrac{b}{2a}$ . Here $a = 1$ and $b = 8$ , so $x = -\dfrac{8}{2(1)} = -\dfrac{8}{2} = -4$ . Therefore, $y$ is smallest when $x = -4$ .

Practice playmedium

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

Work from the outside in. Since $j(4) = 5$ , we need $k(l(x)) = 4$ . Since $k(1) = 4$ , we need $l(x) = 1$ . From the table, $l(5) = 1$ , so $x = 5$ .

Practice playhard

Using these definitions of $f$ and $g$ ,
$f(x)=\begin{cases} x+2 & \text{for } x < 0 \\ 1-2x & \text{for } x \geq 0 \end{cases}$
$g(x)=\begin{cases} 3x & \text{for } x \leq 1 \\ x^{2} & \text{for } x > 1 \end{cases}$
what is $g(f(4))\textsf{?}$

Start with the inner function: $4 \geq 0$ , so $f(4)=1-2(4)=-7$ . Then $-7 \leq 1$ , so $g(-7)=3(-7)=-21\textsf{.}$

Practice playeasy

The $x$ -intercept of the graph of $y = 5x - 15$ in the coordinate plane is $(x, 0)$ . What is the value of $x$ ?

At the $x$ -intercept, $y = 0$ , so $0 = 5x - 15$ , $5x = 15$ , and $x = 3\textsf{.}$

Practice playeasy

Convert $\dfrac{\pi}{2}$ to degrees.

$\dfrac{\pi}{2} \times \dfrac{180°}{\pi} = 90°$ .

NC EOG/EOC NC Math 3 Functions. Practice it free.

Functions skills

Understand the concept of a function and use function notation (NC.M3.F-IF.1, NC.M3.F-IF.2)

Interpret and analyze key features of functions, including polynomial, rational, and trigonometric functions, from multiple representations (NC.M3.F-IF.4, NC.M3.F-IF.7, NC.M3.F-IF.9)

Build functions by combining functions and find inverse functions (NC.M3.F-BF.1, NC.M3.F-BF.3, NC.M3.F-BF.4)

Construct and compare exponential and logarithmic models and use logarithms to solve for an exponent (NC.M3.F-LE.3, NC.M3.F-LE.4)

Extend the domain of trigonometric functions using radian measure of angles and the unit circle (NC.M3.F-TF.1, NC.M3.F-TF.2, NC.M3.F-TF.5)

Topics mapped to this domain

Solving exponential equations with logarithms (ACT)

Factored polynomial x-intercepts (SAT)

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)

Degree-radian conversion

Unit circle trig values (SAT)

Evaluating functions

Evaluating functions at a value

Evaluating functions from percent change

8 free questions · 0/0 correct

Turn functions into game time.

More NC Math 3 domains