NY State Math Algebra II Functions Practice

NY State Math Algebra II Functions. Practice it free.

Per the NYSED Algebra II Educator Guide blueprint, the Functions conceptual category is 38%–45% of credit and includes the domains Interpreting Functions (F-IF), Building Functions (F-BF), Linear, Quadratic, and Exponential Models (F-LE), and Trigonometric Functions (F-TF). This Algebra II reporting domain maps to 35 practice skills and 8 representative questions from the playable bank.

Algebra IIF-IF, F-BF, F-LE, F-TF35 mapped skills

Functions skills

Understand the concept of a function and use function notation

Interpret functions that arise in applications in terms of the context

Analyze functions using different representations

Build a function that models a relationship between two quantities

Build new functions from existing functions

Construct and compare linear, quadratic, and exponential models and solve problems

Interpret expressions for functions in terms of the situation they model

Extend the domain of trigonometric functions using the unit circle

Model periodic phenomena with trigonometric functions

Prove and apply trigonometric identities

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 is the Pythagorean identity?

The fundamental Pythagorean identity is $\sin^{2}\theta + \cos^{2}\theta = 1\textsf{.}$

Practice playeasy

For which value of $x$ does the graph of $y = (x - 15)(x + 7)$ intercept the $x$ -axis?

Set $y = 0$ : $(x - 15)(x + 7) = 0$ . The zeros are $x = 15$ and $x = -7$ . Of the choices, $15$ is an x-coordinate of an x-intercept.

Practice playeasy

$f(x) = (x - 9)^2 - 2$

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 $h = 9$ , so the vertex is at $x = 9$ . Therefore, $f(x)$ reaches its minimum when $x = 9$ .

Practice playeasy

The equation $y = x^2 + 4x + 3$ models a quantity $y$ in terms of $x$ . For what value of $x$ is $y$ as small as possible?

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 $b = 4$ , so $x = -\dfrac{4}{2(1)} = -\dfrac{4}{2} = -2$ . Therefore, $y$ is as small as possible when $x = -2$ .

Practice playeasy

Convert $\dfrac{2\pi}{3}$ to degrees.

$\dfrac{2\pi}{3} \times \dfrac{180°}{\pi} = 120°$ .

Practice playeasy

What is the domain of $\arcsin(x)$ ?

The domain of $\arcsin(x)$ is $[-1,\, 1]$ .

Practice playeasy

What is $\tan\left(\dfrac{7\pi}{4}\right)$ ?

The reference angle for $\dfrac{7\pi}{4}$ is $\dfrac{\pi}{4}$ . Tangent is negative in Quadrant IV, so $\tan\left(\dfrac{7\pi}{4}\right) = -\tan\left(\dfrac{\pi}{4}\right) = -1$ .

Practice playmedium

A forest preserve had $4{,}000$ acres of woodland in $2010$ . Each year from $2010$ through $2020$ , a model estimates that the woodland area decreased by $5\%$ of the area the previous year. Which equation defines this model, where $a(t)$ is the estimated woodland area, in acres, $t$ years after $2010$ ?

The starting area is $4{,}000$ acres, and a $5\%$ yearly decrease means multiplying by $0.95$ each year, so $a(t) = 4{,}000(0.95)^t$ .

NY State Math Algebra II Functions. Practice it free.

Functions skills

Understand the concept of a function and use function notation

Interpret functions that arise in applications in terms of the context

Analyze functions using different representations

Build a function that models a relationship between two quantities

Build new functions from existing functions

Construct and compare linear, quadratic, and exponential models and solve problems

Interpret expressions for functions in terms of the situation they model

Extend the domain of trigonometric functions using the unit circle

Model periodic phenomena with trigonometric functions

Prove and apply trigonometric identities

Topics mapped to this domain

Trig identities

Factored polynomial x-intercepts (SAT)

Quadratic minimum from vertex form

Quadratic minimum x-value

Degree-radian conversion

Inverse trig domain and range

Unit circle trig values (SAT)

Writing exponential equations from context (SAT)

Interpreting exponential parameters

Interpreting linear parameters

Linear coefficient interpretations (SAT/PSAT 8/9/10)

Arithmetic sequence nth term

8 free questions · 0/0 correct

Turn functions into game time.

More Algebra II domains