NC EOG/EOC NC Math 3 Number and Quantity and Algebra Practice

NC EOG/EOC NC Math 3 Number and Quantity and Algebra. Practice it free.

EOC NC Math 3 domain (32-36% of the test, Table 1). Use the Fundamental Theorem of Algebra (N-CN.9); interpret and rewrite polynomial, rational, and exponential expressions (A-SSE); perform arithmetic on polynomials and rational expressions including the Remainder Theorem and zeros (A-APR); and create and solve equations, including logarithmic and rational equations (A-CED, A-REI). This NC Math 3 reporting domain maps to 22 practice skills and 8 representative questions from the playable bank.

NC Math 3N,A22 mapped skills

Number and Quantity and Algebra skills

Use the Fundamental Theorem of Algebra to determine the number of solutions of a polynomial equation (NC.M3.N-CN.9)

Interpret the structure of and rewrite polynomial, rational, and exponential expressions (NC.M3.A-SSE.1, NC.M3.A-SSE.2, NC.M3.A-SSE.3)

Understand the relationship between zeros and factors of polynomials and rewrite simple rational expressions (NC.M3.A-APR.2, NC.M3.A-APR.3, NC.M3.A-APR.6, NC.M3.A-APR.7)

Create equations and inequalities in one and two variables to solve and model problems (NC.M3.A-CED.1, NC.M3.A-CED.2, NC.M3.A-CED.3)

Understand solving equations as a reasoning process and solve rational equations (NC.M3.A-REI.1, NC.M3.A-REI.2)

Solve equations approximately by finding intersections of graphs, including exponential and logarithmic equations (NC.M3.A-REI.11)

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

Which is a factored form of $x^2 - x - 20$ ?

Find two numbers with product $-20$ and sum $-1$ : $4$ and $-5$ . So $x^2 - x - 20 = (x+4)(x-5)$ .

Practice playmedium

If $4x^{2} - 16x + 8 = 0$ , what is $x^{2} - 4x\textsf{?}$

Factoring out the GCF $4$ gives $4(x^{2} - 4x + 2) = 0$ . Since $4(0) = 0$ , $x^{2} - 4x + 2 = 0$ . Isolate the desired expression by subtracting $2$ from both sides: $x^{2} - 4x = -2$ .

Practice playmedium

What are all and only the zeros of the polynomial defined by $p(x)=x^3+3x^2-x-3$ ?

Group: $p(x)=(x^3+3x^2)+(-x-3)=x^2(x+3)-(x+3)=(x+3)(x^2-1)=(x+3)(x+1)(x-1)$ . After factoring, set each linear factor equal to zero: $(x+3)=0 \Rightarrow x=-3$ ; $(x+1)=0 \Rightarrow x=-1$ ; $(x-1)=0 \Rightarrow x=1$ . The zeros are $-3$ , $-1$ , and $1$ .

Practice playmedium

If $\dfrac{x + 4y}{2x + y} = \dfrac{3}{5}$ , then $\dfrac{x}{y}=$

Cross-multiply to clear the fraction: $5(x + 4y) = 3(2x + y)$ , so $5x + 20y = 6x + 3y$ . Collect like terms to get $x = 17y$ . Divide both sides by $y$ to obtain $\dfrac{x}{y} = 17\textsf{.}$

Practice playmedium

If $\dfrac{x^{2} - 16}{x - 4} = 9$ and $x \neq 4\textsf{,}$ what is the value of $x\textsf{?}$

Factor the numerator: $x^{2} - 16 = (x-4)(x+4)$ . For $x \neq 4$ , the factor $x-4$ cancels, giving $x+4 = 9$ , so $x = 5\textsf{.}$

Practice playeasy

Which expression is equivalent to $\dfrac{x^{2}-5x+6}{x^{2}-4}$ when $x \neq 2$ and $x \neq -2\textsf{?}$

Factor: $\dfrac{(x-2)(x-3)}{(x-2)(x+2)}=\dfrac{x-3}{x+2}$ for $x \neq \pm 2\textsf{.}$

Practice playeasy

During exercise, a target heart rate $h$ , in beats per minute, is greater than $60$ and less than $100$ . Which inequality represents the possible values of $h$ ?

Greater than $60$ and less than $100$ are both strict, so $60 < h < 100$ .

Practice playeasy

When $4x + 2y = 10$ is rewritten as $y = mx + b$ , what is the slope $m$ ?

Solve for $y$ : $2y = -4x + 10$ , so $y = -2x + 5$ and $m = -2$ .

NC EOG/EOC NC Math 3 Number and Quantity and Algebra. Practice it free.

Number and Quantity and Algebra skills

Use the Fundamental Theorem of Algebra to determine the number of solutions of a polynomial equation (NC.M3.N-CN.9)

Interpret the structure of and rewrite polynomial, rational, and exponential expressions (NC.M3.A-SSE.1, NC.M3.A-SSE.2, NC.M3.A-SSE.3)

Understand the relationship between zeros and factors of polynomials and rewrite simple rational expressions (NC.M3.A-APR.2, NC.M3.A-APR.3, NC.M3.A-APR.6, NC.M3.A-APR.7)

Create equations and inequalities in one and two variables to solve and model problems (NC.M3.A-CED.1, NC.M3.A-CED.2, NC.M3.A-CED.3)

Understand solving equations as a reasoning process and solve rational equations (NC.M3.A-REI.1, NC.M3.A-REI.2)

Solve equations approximately by finding intersections of graphs, including exponential and logarithmic equations (NC.M3.A-REI.11)

Topics mapped to this domain

Factoring quadratic expressions (ACT)

Quadratic expression values from equations

Factorable polynomial zeros (ACT)

Rational equations — find a ratio (ACT)

Rational equation solving (SAT)

Simplifying rational expressions (ACT)

Compound inequality situations

Linear equation forms

Linear equation from two points (SAT)

Linear inequality situations (ACT/SAT/PSAT 8/9/10)

Linear raise total earnings

Linear system word problems (ACT/SAT)

8 free questions · 0/0 correct

Turn number and quantity and algebra into game time.

More NC Math 3 domains