Will this help with my child's Algebra II homework?

Yes. StudyPug covers every strand in New York Algebra II, from complex numbers and polynomial functions to trigonometry and probability, so your child can find help on the exact topic assigned that night.

How long are the video lessons?

Most video lessons run between five and fifteen minutes, focused on a single concept. Students can pause, rewind, and rewatch as many times as needed until the idea clicks.

Is there a state test for Algebra II in New York?

Yes. New York students typically take the Algebra II Regents exam, which assesses the full range of topics in this course. StudyPug practice aligns to those same New York Next Generation Mathematics Learning Standards.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, and desktop browsers, so your child can practice Algebra II at home, at school, or on the go without needing to install anything.

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NY High School Algebra II Curriculum

Give your high schooler the support they need to succeed in New York Algebra II, with lessons and practice problems covering every strand from polynomials to probability.

NY High School Algebra II Curriculum

IDMath Standard DescriptionStudyPug Topic

NY.AII-N.RN.1Explore how the meaning of rational exponents follows from extending the properties of integer exponents.
- Convert between radicals and rational exponents
- Exponents: Product rule (a^x)(a^y) = a^(x+y)
- Exponents: Division rule: a^x / a^y = a^(x-y)
- Exponents: Power rule: (a^x)^y = a^(xy)
- Exponents: Negative exponents
- Exponents: Zero exponent: a^0 = 1
- Exponents: Rational exponents
NY.AII-N.RN.2Convert between radical expressions and expressions with rational exponents using the properties of exponents.
- Solving for exponents
- Operations with radicals
- Conversion between entire radicals and mixed radicals
- Converting radicals to mixed radicals
- Converting radicals to entire radicals
- Adding and subtracting radicals
- Multiplying and dividing radicals
- Rationalize the denominator
- Evaluating and simplifying radicals
NY.AII-N.CN.1Know there is a complex number i such that i^2 = –1, and every complex number has the form a + bi with a and b real.
- Understanding the number systems
- Introduction to imaginary numbers
NY.AII-N.CN.2Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
- Combining the exponent rules
- Complex numbers and complex planes
- Adding and subtracting complex numbers
- Multiplying and dividing complex numbers
NY.AII-A.SSE.2Recognize and use the structure of an expression to identify ways to rewrite it.
- Polynomial components
- Simplifying rational expressions and restrictions
- Applications of polynomials
- Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
NY.AII-A.SSE.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- Common factors of polynomials
- Adding and subtracting rational expressions
- Evaluating polynomials
- Using algebra tiles to factor polynomials
- Solving polynomial equations
NY.AII-A.APR.2Apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
- Greatest common factors (GCF)
- Remainder theorem
- Polynomial long division
- Polynomial synthetic division
NY.AII-A.APR.3Identify zeros of polynomial functions when suitable factorizations are available.
- Factoring polynomials: x^2 + bx + c
- Characteristics of polynomial graphs
- Factor theorem
- Rational zero theorem
NY.AII-A.APR.6Rewrite rational expressions in different forms: Write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).
- Applications of polynomial functions
- Solving polynomial inequalities
- Fundamental theorem of algebra
NY.AII-A.CED.1Create equations and inequalities in one variable to represent a real-world context.
- Introduction to linear equations
- Solving rational equations
- Solving exponential equations using exponent rules
NY.AII-A.REI.1bExplain each step when solving rational or radical equations as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
- Combination of both parallel and perpendicular line equations
- Applications of inequalities
- What is linear programming?
NY.AII-A.REI.2Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.
- Evaluating and simplifying radicals
- Solving radical equations
- Square and square roots
- Cubic and cube roots
NY.AII-A.REI.4bSolve quadratic equations by: i) inspection, ii) taking square roots, iii) factoring, iv) completing the square, v) the quadratic formula, and vi) graphing. Write complex solutions in a + bi form.
- Solving quadratic equations by factoring
- Solving quadratic equations by completing the square
- Using quadratic formula to solve quadratic equations
- Multiplying and dividing radicals
- Rationalize the denominator
NY.AII-A.REI.7bSolve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
- System of linear-quadratic equations
- Nature of roots of quadratic equations: The discriminant
- Applications of quadratic equations
- Solving quadratic inequalities
NY.AII-A.REI.11Given the equations y = f(x) and y = g(x): i) recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x); ii) find the solutions approximately using technology to graph the functions or make tables of values; iii) find the solution of f(x) < g(x) or f(x) ≤ g(x) graphically; and iv) interpret the solution in context.
- Graphing linear functions using table of values
- Graphing exponential functions
- Graphing logarithmic functions
- The inverse of 3 x 3 matrices with matrix row operations
- The inverse of 3 x 3 matrix with determinants and adjugate
NY.AII-F.IF.3Recognize that a sequence is a function whose domain is a subset of the integers.
- Greatest common factors (GCF)
- Introduction to sequences
- Sigma notation
NY.AII-F.IF.4bFor a function that models a relationship between two quantities: i) interpret key features of graphs and tables in terms of the quantities; and ii) sketch graphs showing key features given a verbal description of the relationship.
- Word problems of graphing linear functions
- Characteristics of quadratic functions
- Relationship between two variables
- Understand relations between x- and y-intercepts
- Combining transformations of functions
- Reflection across the y-axis: y = f(-x)
- Reflection across the x-axis: y = -f(x)
- Transformations of functions: Horizontal stretches
- Transformations of functions: Vertical stretches
NY.AII-F.IF.6Calculate and interpret the average rate of change of a function over a specified interval.
- Rate of change
- Direct variation
NY.AII-F.IF.7Graph functions and show key features of the graph by hand and using technology when appropriate.
- Graphing linear functions using a single point and slope
- Graphing quadratic functions: General form VS. Vertex form
- Graphing exponential functions
- Graphing logarithmic functions
- Graphing from slope-intercept form y=mx+b
- Graphing transformations of exponential functions
- Graphing transformations of logarithmic functions
- Sine graph: y = sin x
- Cosine graph: y = cos x
- Tangent graph: y = tan x
- Cotangent graph: y = cot x
- Secant graph: y = sec x
- Cosecant graph: y = csc x
NY.AII-F.IF.8Write a function in different but equivalent forms to reveal and explain different properties of the function.
- Slope intercept form: y = mx + b
- General form: Ax + By + C = 0
- Point-slope form: y - y_1 = m(x - x_1)
- Converting from general to vertex form by completing the square
- Adding functions
- Subtracting functions
- Multiplying functions
- Dividing functions
- Operations with functions
NY.AII-F.IF.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- Parallel and perpendicular lines in linear functions
- Graphs of rational functions
- Inequalities of combined functions
NY.AII-F.BF.1aWrite a function that describes a relationship between two quantities.
- Applications of linear relations
- Finding an exponential function given its graph
- Finding a logarithmic function given its graph
NY.AII-F.BF.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
- Arithmetic sequences
- Geometric sequences
- Arithmetic series
- Geometric series
- Infinite geometric series
NY.AII-F.BF.3bUsing f(x) + k, k f(x), f(kx), and f(x + k): i) identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); ii) find the value of k given the graphs; iii) write a new function using the value of k; and iv) use technology to experiment with cases and explore the effects on the graph. Include recognizing even and odd functions from their graphs.
- Transformations of quadratic functions
- Transformations of functions: Horizontal translations
- Transformations of functions: Vertical translations
NY.AII-F.BF.4aFind the inverse of a one-to-one function both algebraically and graphically.
- Finding the quadratic functions for given parabolas
- Inverse functions
NY.AII-F.BF.5aUnderstand inverse relationships between exponents and logarithms algebraically and graphically.
- Product rule of logarithms
- Solving exponential equations with logarithms
- What is a logarithm?
- Converting from logarithmic form to exponential form
- Evaluating logarithms without a calculator
- Common logarithms
- Natural log: ln
- Evaluating logarithms using change-of-base formula
- Converting from exponential form to logarithmic form
NY.AII-F.BF.6Represent and evaluate the sum of a finite arithmetic or finite geometric series, using summation (sigma) notation.
- Sigma notation
NY.AII-F.BF.7Explore the derivation of the formulas for finite arithmetic and finite geometric series. Use the formulas to solve problems.
- Arithmetic series
- Geometric series
NY.AII-F.LE.2Construct a linear or exponential function symbolically given: i) a graph; ii) a description of the relationship; and iii) two input-output pairs (include reading these from a table).
- Graphing linear functions using table of values
NY.AII-F.LE.4Use logarithms to solve exponential equations, such as ab^ct = d (where a, b, c, and d are real numbers and b > 0) and evaluate the logarithm using technology.
- Quotient rule of logarithms
- Combining product rule and quotient rule in logarithms
- Power rule of logarithms
- Evaluating logarithms using logarithm rules
NY.AII-F.LE.5Interpret the parameters in a linear or exponential function in terms of a context.
- Exponential growth and decay by a factor
- Finance: Compound interest
- Continuous growth and decay
- Logarithmic scale: Richter scale (earthquake)
- Logarithmic scale: pH scale
- Logarithmic scale: dB scale
- Finance: Future value and present value
NY.AII-F.TF.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- Converting between degrees and radians
- Trigonometric ratios of angles in radians
- Radian measure and arc length
NY.AII-F.TF.2Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.
- Unit circle
NY.AII-F.TF.5Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift, and midline.
- Graphing transformations of trigonometric functions
- Determining trigonometric functions given their graphs
NY.AII-F.TF.8Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1. Find the value of any of the six trigonometric functions given any other trigonometric function value and when necessary find the quadrant of the angle.
- Pythagorean identities
NY.AII-S.ID.4aRecognize whether or not a normal curve is appropriate for a given data set.
- Introduction to normal distribution
- Normal distribution and continuous random variable
- Z-scores and random continuous variables
NY.AII-S.ID.4bIf appropriate, determine population percentages using a graphing calculator for an appropriate normal curve.
- Introduction to normal distribution
- Normal distribution and continuous random variable
- Z-scores and random continuous variables
NY.AII-S.ID.6aRepresent bivariate data on a scatter plot, and describe how the variables' values are related.
- Reading and drawing line graphs
- Bivariate, scatter plots and correlation
NY.AII-S.IC.2Determine if a value for a sample proportion or sample mean is likely to occur based on a given simulation.
- Sampling distributions
- Rare event rule
NY.AII-S.IC.3Recognize the purposes of and differences among surveys, experiments, and observational studies. Explain how randomization relates to each.
- Census and bias
NY.AII-S.IC.4Given a simulation model based on a sample proportion or mean, construct the 95% interval centered on the statistic (+/- two standard deviations) and determine if a suggested parameter is plausible.
- Margin of error
- Confidence intervals to estimate population mean
- Making a confidence interval
NY.AII-S.IC.6aUse the tools of statistics to draw conclusions from numerical summaries.
- Influencing factors in data collection
NY.AII-S.IC.6bUse the language of statistics to critique claims from informational texts. For example, causation vs correlation, bias, measures of center and spread.
- Influencing factors in data collection
NY.AII-S.CP.1Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
- Introduction to probability
- Organizing outcomes
- Introduction to probability
- Set notation
- Set builder notation
- Intersection and union of 2 sets
- Intersection and union of 3 sets
NY.AII-S.CP.7Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
- Addition rule for "OR"

Algebra II

About High School New York Algebra II

New York Algebra II follows the New York Next Generation Mathematics Learning Standards. This course covers rational exponents and complex numbers, polynomial and rational expressions, quadratic and radical equations, function transformations and inverses, exponential and logarithmic relationships, trigonometric functions, sequences and series, and statistics and probability. StudyPug provides step-by-step video lessons and practice problems aligned to every strand so students can get help exactly when they need it.

Strands: rational exponents, complex numbers, polynomials, rational expressions, equations and inequalities, functions and inverses, exponential and logarithmic functions, trigonometry, sequences and series, and statistics and probability
Step-by-step video lessons for every Algebra II topic
Practice problems with instant feedback for each strand
Content aligned to the New York Next Generation Mathematics Learning Standards

Curriculum topics by strand

Find lessons and practice for every New York Algebra II strand, aligned to the New York Next Generation Mathematics Learning Standards.

Topic includes:

Practice

Video

Quiz

Math Standard Description

StudyPug Topic

New York High School Algebra II Topics

Rational Exponents and Radicals: Extending integer exponent properties to rational exponents and converting between radical and exponential forms.
Complex Numbers: Understanding the imaginary unit, performing arithmetic with complex numbers in a + bi form, and writing complex solutions to quadratic equations.
Polynomial and Rational Expressions: Rewriting and factoring polynomials, applying the Remainder Theorem, identifying zeros, and working with rational expressions including polynomial long division.
Equations and Inequalities: Creating and solving rational and radical equations, identifying extraneous solutions, solving quadratic equations by multiple methods, and solving linear-quadratic systems algebraically and graphically.
Functions: Interpreting key features of graphs and tables, analyzing average rate of change, graphing transformations, writing arithmetic and geometric sequences explicitly and recursively, and finding inverse functions.
Exponential and Logarithmic Functions: Constructing exponential functions, using logarithms to solve exponential equations, understanding inverse relationships between exponents and logarithms, and representing finite series with sigma notation.
Trigonometric Functions: Radian measure, the unit circle, the six trigonometric functions, periodicity, modeling periodic phenomena, and proving the Pythagorean identity.
Statistics and Probability: Normal distributions, scatter plots, sample proportions and means, survey and experiment design, conditional probability, two-way frequency tables, and the Addition Rule.

How StudyPug Helps New York High School Algebra II Students

When a student gets stuck on a problem - whether it involves completing the square, finding the inverse of a function, or interpreting a confidence interval - StudyPug provides step-by-step video solutions that walk through the reasoning behind each move, not just the final answer.

Every lesson is mapped to the New York Next Generation Mathematics Learning Standards, so students practice exactly what their Algebra II class is covering, and parents can see progress across each strand without guesswork.

Aligned to New York High School Algebra II Curriculum

StudyPug content for Algebra II is built around the New York Next Generation Mathematics Learning Standards, the same framework that shapes classroom instruction and the Algebra II Regents exam. Each strand - from polynomial functions and complex numbers through trigonometry and statistics - is covered so that what a student practices on StudyPug matches what their teacher is assigning in class.

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Last updated June 5, 2026

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