NY State Math Algebra I Algebra Practice

NY State Math Algebra I Algebra. Practice it free.

Per the NYSED Algebra I Educator Guide blueprint, the Algebra conceptual category is 48%–61% of credit and includes the domains Seeing Structure in Expressions (A-SSE), Arithmetic with Polynomials and Rational Expressions (A-APR), Creating Equations (A-CED), and Reasoning with Equations and Inequalities (A-REI). This Algebra I reporting domain maps to 46 practice skills and 8 representative questions from the playable bank.

Algebra IA-SSE, A-APR, A-CED, A-REI46 mapped skills

Algebra skills

Interpret the structure of expressions

Write expressions in equivalent forms to reveal their characteristics

Perform arithmetic operations on polynomials

Understand the relationship between zeros and factors of polynomials

Create equations that describe numbers or relationships

Understand solving equations as a process of reasoning and explain the reasoning

Solve equations and inequalities in one variable

Solve systems of equations

Represent and solve equations and inequalities graphically

Standards basis

New York State Learning Standards / New York State Next Generation Learning Standards (NGLS) — New York

How the NY State Math reports it

New York’s Grades 3–8 math tests and Regents math exams are state-developed assessments rather than a shared national framework. The grades 3–8 exams are aligned to New York State learning standards, and the Regents math sequence includes Algebra I, Geometry, and Algebra II, with the June 2026 Algebra II exam explicitly based on the New York State Next Generation Learning Standards.

Blueprint & weighting

Grades 3–8: the official page and the retrieved administration guide describe item/credit structure and timing, but no published domain-by-domain blueprint weighting was located in the primary sources used here. Regents (high school): NYSED publishes a per-conceptual-category 'percent of test by credit' blueprint for each course in its Educator Guides. Algebra I — Number & Quantity 4%–10%, Algebra 48%–61%, Functions 24%–32%, Statistics & Probability 7%–15%. Geometry (single conceptual category, by domain) — Congruence (G-CO) 27%–34%, Similarity, Right Triangles, & Trigonometry (G-SRT) 29%–37%, Circles (G-C) 2%–8%, Expressing Geometric Properties with Equations (G-GPE) 12%–18%, Geometric Measurement & Dimensions (G-GMD) 2%–8%, Modeling with Geometry (G-MG) 8%–15%. Algebra II — Number & Quantity 4%–8%, Algebra 30%–39%, Functions 38%–45%, Statistics & Probability 14%–22%.

Official sources

NYSED Grades 3–8 ELA and Math Test Manuals
NYSED Directions for Administering Regents Examinations
NYSED High School Regents Examinations

8 free questions · 0/0 correct

Practice playeasy

Which expression is equivalent to $x^2 - 6x + 8$ ?

Find two numbers with product $8$ and sum $-6$ : $-2$ and $-4$ . So $x^2 - 6x + 8 = (x-2)(x-4)$ .

Practice playmedium

What are all and only the zeros of the polynomial defined by $p(x)=x^3+4x^2+4x$ ?

Factor out $x$ : $p(x)=x(x^2+4x+4)=x(x+2)^2$ . Set each factor equal to zero: $x=0 \Rightarrow x=0$ ; $(x+2)^2=0$ , so $(x+2)=0 \Rightarrow x=-2$ . The zero $-2$ has multiplicity $2$ , so the zeros are $0$ , $-2$ , and $-2$ .

Practice playhard

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

Cross-multiply to clear the fraction: $5(4x - 3y) = 2(x + y)$ , so $20x - 15y = 2x + 2y$ . Collect like terms to get $18x = 17y$ . Divide both sides by $y$ , then by $18$ , to obtain $\dfrac{x}{y} = \dfrac{17}{18}\textsf{.}$

Practice playmedium

If $\dfrac{x^{2} + 6x + 9}{x + 3} = 4$ and $x \neq -3\textsf{,}$ what is the value of $x\textsf{?}$

Factor the numerator as a perfect square: $x^{2} + 6x + 9 = (x+3)^{2}$ . For $x \neq -3$ , one factor of $x+3$ cancels, giving $x+3 = 4$ , so $x = 1\textsf{.}$

Practice playeasy

$\begin{cases} y \le -x + 10 \\ y > x - 1 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $x = 4$ , which of the following could be a value of $y$ ?

Substitute $x = 4$ . From $y \le -x + 10$ , $y \le 6$ . From $y > x - 1$ , $y > 3$ . The value $y = 5$ satisfies $3 < 5 \le 6$ .

Practice playmedium

Which is the completely factored form of $16x^{3} + 24x^{2} - 8x$ ?

The greatest common factor of $16x^{3}$ , $24x^{2}$ , and $8x$ is $8x\textsf{.}$ Factoring gives $8x(2x^{2} + 3x - 1)$ .

Practice playeasy

Which expression is equivalent to $25x^{2} - 36$ ?

$25x^{2} - 36 = (5x)^{2} - 6^{2} = (5x - 6)(5x + 6)$ .

Practice playmedium

Which expression is equivalent to $\dfrac{35v}{k} + 70v$ , where $k > 0$ ?

Write $70v$ with denominator $k$ : $\dfrac{35v}{k} + \dfrac{70vk}{k} = \dfrac{35v + 70vk}{k} = \dfrac{35v(1 + 2k)}{k}$ .

NY State Math Algebra I Algebra. Practice it free.

Algebra skills

Interpret the structure of expressions

Write expressions in equivalent forms to reveal their characteristics

Perform arithmetic operations on polynomials

Understand the relationship between zeros and factors of polynomials

Create equations that describe numbers or relationships

Understand solving equations as a process of reasoning and explain the reasoning

Solve equations and inequalities in one variable

Solve systems of equations

Represent and solve equations and inequalities graphically

Topics mapped to this domain

Factoring quadratic expressions (ACT)

Factorable polynomial zeros (ACT)

Rational equations — find a ratio (ACT)

Rational equation solving (SAT)

Linear inequality system solutions

Common factor factoring (SAT)

Difference of squares factoring

Equivalent rational expressions (SAT)

Factoring patterns

Factoring quadratics

Quadratic expression values from equations

Monomial expression multiplication (SAT)

8 free questions · 0/0 correct

Turn algebra into game time.

More Algebra I domains