This page maps the mathematics standards assessed on New York's Regents examinations — Algebra I, Geometry, and Algebra II — to the Brilliant lessons that teach them. Search by standard code or skill to find the closest match. A standard is listed only where Brilliant content fully or in part addresses the standard directly.
Regents Algebra I
The Real Number System (AI-N.RN)
Quantities (AI-N.Q)
Seeing Structure in Expressions (AI-A.SSE)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| AI.A.SSE.1.b | Interpret expression parts as single entities | Linear Equations — Combining groups of expressions
Solving Equations — Reasoning with grouped expressions |
| AI.A.SSE.2 | Use structure to factor quadratic expressions | Quadratics — Completing factors with negatives, Completing partial factorizations, Factoring simple quadratics, Factoring with negative constants, Recognizing perfect square patterns
Solving Equations — Factoring common factors, Factoring into groups
Linear Equations — Finding the greatest common factor |
| AI.A.SSE.3.c | Rewrite exponential expressions with integer exponents | Exponents and Radicals — Applying the power rule for exponents, Applying the product rule for exponents, Applying the quotient rule for exponents, Combining exponent rules to simplify, Dividing with prime factorizations, Evaluating zero-exponent expressions, Multiplying and dividing in scientific notation, Multiplying with prime factorizations, Rewriting with negative exponents, Simplifying multi-base quotients, Simplifying negative exponents in denominators, Simplifying products with exponent zero, Simplifying with negative exponents
Exponential Functions — Express decay with a negative exponent |
Arithmetic with Polynomials and Rational Expressions (AI-A.APR)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| AI.A.APR.1 | Add, subtract, and multiply polynomials | Polynomials — Adding polynomials, Multiplying monomials, Multiplying polynomials, Subtracting polynomials, Working with multivariable polynomials
Solving Equations — Combining like terms, Combining terms in equations, Distributing over a sum, Distributing over groups
Quadratics — Combining like terms, Combining signed terms, Combining terms with coefficients, Determining signs in products, Expanding binomial products, Finding constant terms, Finding linear terms, Multiplying with area models, Multiplying with negative numbers
Visual Algebra — Combining pattern expressions, Identifying equivalent expressions
Linear Equations — Combining terms with decimals, Writing and simplifying expressions |
| AI.A.APR.3 | Find zeros of factored quadratics and cubics | Quadratics — Connecting intercepts to factors |
Creating Equations (AI-A.CED)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| AI.A.CED.1 | Create linear, quadratic, or exponential models | Linear Equations — Comparing deals with percentages, Modeling with linear equations
Solving Equations — Translating words to inequalities, Writing balanced equations, Writing equations from scales, Writing grouped equations, Writing inequalities from scales |
| AI.A.CED.2 | Create two-variable equations and inequalities | Proportional Reasoning — Relating totals, rates, and amounts
Linear Systems — Set up a system from a scenario
Quadratics — Writing equations for motion, Writing equations for real situations
Real-World Algebra — Writing formulas with variables
Linear Relationships — Writing linear inequalities, Writing standard form equations
Percents — Writing percent change expressions |
| AI.A.CED.3 | Represent constraints with equations and inequalities | Solving Equations — Checking value constraints, Finding value ranges
Linear Systems — Identifying inequality solutions, Writing equations from constraints, Writing inequality systems
Linear Equations — Interpret a linear solution in context |
Reasoning with Equations and Inequalities (AI-A.REI)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| AI.A.REI.3 | Solve linear equations and inequalities in one variable | Linear Equations — Classifying equations by solutions, Combining fractional terms, Combining like terms to solve, Combining negatives to solve, Dividing by negatives in inequalities, Finding missing values with negatives, Finding unknown values, Recognizing equations with many solutions, Recognizing equations with no solution, Solving equations by distributing, Solving equations by factoring, Solving equations with fractions, Solving equations with parentheses, Solving for negative answers, Solving multi-step inequalities, Solving multi-step negative inequalities, Solving one-step inequalities, Solving two-step equations, Solving with reciprocals, Solving with subtracted variables, Solving with variables on both sides, Working with negative coefficients
Linear Relationships — Find the input that reaches a target value
Solving Equations — Finding unknown values, Solving after combining, Solving for boundary values, Solving grouped equations, Solving one-step equations |
| AI.A.REI.4.a | Complete the square to rewrite quadratic equations | Quadratics — Completing squares with fractions, Completing the square, Converting to vertex form, Solving by completing the square |
| AI.A.REI.4.b | Solve quadratic equations with real solutions | Quadratics — Checking solutions by substitution, Classifying solution types, Determining number of solutions, Finding when objects arrive, Isolating squared variables, Predicting whether a target is reached, Solving equations by factoring, Solving shifted square equations, Solving with square roots, Using the discriminant, Using the quadratic formula |
| AI.A.REI.6.a | Solve linear systems algebraically and graphically | Linear Systems — Counting solutions to a system, Eliminating by adding equations, Finding solutions by graphing, Scaling equations to eliminate, Solving systems by graphing
Solving Equations — Multiplying to eliminate, Solving by subtracting equations, Solving systems by combining, Solving systems by substitution, Solving with substitution, Substituting known values |
| AI.A.REI.10 | Graphs as solution sets of equations | Quadratics — Evaluating quadratic equations, Plotting points on parabolas
Linear Relationships — Extending linear patterns, Graphing lines from intercepts
Coordinate Plane — Plotting horizontal and vertical lines
Linear Systems — Testing points in equations |
| AI.A.REI.11 | Solve equations by finding graph intersections | Exponential Functions — Compare two exponential functions, Graph and compare compound interest functions
Linear Systems — Interpret the solution of a system in context
Quadratics — Reading solutions from graphs |
| AI.A.REI.12 | Graph solutions of linear inequalities and systems | Coordinate Plane — Combining two inequalities, Identifying strip regions, Shading regions for inequalities
Linear Systems — Graphing inequality constraints, Graphing inequality solutions
Linear Relationships — Graphing linear inequalities |
Interpreting Functions (AI-F.IF)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| AI.F.IF.1 | Understand the definition of a function | Introduction to Functions — Applying the vertical line test, Finding function ranges, Recognizing non-functions |
| AI.F.IF.2 | Use and interpret function notation | Exponential Functions — Evaluate an exponential at negative x-values
Introduction to Functions — Evaluating composite functions, Following conditional rules, Following function rules, Identifying conditional rules, Identifying function rules, Matching input-output pairs
Linear Relationships — Evaluating linear equations, Reading linear patterns |
| AI.F.IF.4 | Interpret key features of graphs in context | Linear Relationships — Finding starting values, Graphing real-world relationships, Interpreting intercepts
Quadratics — Finding the best possible value, Interpreting results in context
Introduction to Functions — Identifying function intervals, Reading continuous function graphs, Reading discontinuous function graphs |
| AI.F.IF.5 | Find a function's domain from its graph or context | Introduction to Functions — Finding function domains |
| AI.F.IF.6 | Average rate of change for quadratic and exponential models | Linear Relationships — Calculating rates of change, Computing slope, Finding constant change |
| AI.F.IF.7.a | Graph linear, quadratic, and exponential functions | Quadratics — Finding maximum and minimum values, Graphing by factoring, Graphing parabolas from vertex form
Linear Relationships — Graphing from point-slope form, Graphing lines from slope
Introduction to Functions — Plotting numeric functions |
| AI.F.IF.7.b | Graph square root, piecewise, and absolute value functions | Introduction to Functions — Evaluating floor and ceiling functions, Plotting conditional functions |
| AI.F.IF.8.a | Find zeros, extrema, and symmetry of quadratics | Quadratics — Finding the axis of symmetry, Finding the vertex, Finding vertices using symmetry |
| AI.F.IF.9 | Compare quadratic and exponential functions across forms | Visual Algebra — Comparing pattern growth rates |
Building Functions (AI-F.BF)
Linear, Quadratic, and Exponential Models (AI-F.LE)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| AI.F.LE.1.a | Justify growth by equal differences or equal factors | Exponential Functions — Classify a relationship as linear or exponential, Identify exponential decay from a dot pattern, Identify exponential growth from a dot pattern
Visual Algebra — Describing exponential growth, Describing growth that speeds up, Identifying types of growth |
| AI.F.LE.1.b | Recognize situations with a constant rate of change | Linear Relationships — Classify a relationship as linear and proportional, Recognizing linear relationships
Visual Algebra — Describing steady growth, Identifying what each step adds |
| AI.F.LE.2 | Build linear or exponential functions in simple contexts | Exponential Functions — Build a decay function with a fractional base, Build an exponential function from non-integer points, Build an exponential function from plotted points, Build an exponential function over negative domain, Deduce an exponential function from two points, Evaluate an exponential expression, Find the base of an exponential function, Set the coefficient of an exponential function, Write a compound growth or decay expression, Write a function for a growth or decay scenario
Visual Algebra — Building expressions from rate and start, Writing exponential expressions, Writing expressions for each shape, Writing rules for growing patterns
Introduction to Functions — Writing numeric function rules
Linear Relationships — Writing point-slope equations, Writing slope-intercept equations |
| AI.F.LE.3 | Exponential growth eventually exceeds polynomial growth | Exponential Functions — Compare exponential growth to linear growth, Compare exponential growth to quadratic growth |
| AI.F.LE.5 | Interpret parameters of linear and exponential models | Quadratics — Understanding motion equations |
Interpreting Categorical and Quantitative Data (AI-S.ID)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| AI.S.ID.1 | Display data in dot plots, histograms, and box plots | Everyday Statistics — Matching data to box plots |
| AI.S.ID.2 | Compare center and spread of two data sets | Everyday Statistics — Combining groups to find the mean, Comparing data above and below the mean, Comparing data sets with box plots, Comparing mean, median, and mode, Finding quartiles, Finding the mean (the average) of a data set, Finding the mean of uneven data, Finding the median, Predicting how new data shifts the mean, Reading box plots, Splitting data into quarters, Updating the mean with new data, Updating the median with new data, Using the outlier rule
Exploring Data Visually — Compare boxplots across datasets |
| AI.S.ID.3 | Interpret shape, center, and spread with outliers | Regression — Detecting hidden groups in data
Everyday Statistics — Seeing how outliers affect the mean |
| AI.S.ID.6.a | Fit a linear model to data and use it in context | Exploring Data Visually — Describe the relationship in a scatter plot, Describing how two things relate, Identify and extend a trend on a line graph, Spotting trends over time
Linear Relationships — Fit a line to data and predict
Regression — Fitting a line to data, Modeling one subgroup at a time, Predicting from a model equation, Predicting from a regression line, Tuning a model to fit better, Using categories in a model |
| AI.S.ID.7 | Interpret slope and intercept of a linear model | Regression — Interpreting model coefficients, Reading a model with several variables, Rescaling for a change of units |
| AI.S.ID.8 | Compute and interpret the correlation coefficient | Regression — Choosing the best predictor, Interpreting correlations in context, Measuring how well a model fits, Reading correlation from a scatter plot, Spotting nonlinear relationships
Exploring Data Visually — Judging how strongly things relate |
Regents Geometry
Congruence (GEO-G.CO)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| GEO.G.CO.2 | Represent transformations as functions in the plane | Coordinate Transformations — Combining stretches with transformations, Computing 180-degree rotations, Computing axis reflections, Computing diagonal reflections, Computing quarter-turn rotations, Stretching along an axis, Translating with coordinates |
| GEO.G.CO.3 | Rotations and reflections that carry a polygon onto itself | Coordinate Transformations — Finding lines of symmetry, Finding rotational symmetry, Identifying types of symmetry |
| GEO.G.CO.5 | Draw transformed figures and transformation sequences | Coordinate Transformations — Combining rotations, Combining rotations and translations, Combining translations, Connecting reflections and rotations, Reflecting across any line, Reflecting across axes, Reversing reflections, Reversing rotations, Reversing translations, Rotating around any point, Rotating around the origin, Rotating by reflecting twice, Rotating clockwise, Sliding points and shapes, Translating by reflecting twice, Translating by rotating twice |
| GEO.G.CO.6 | Use rigid motions to determine congruence | Coordinate Transformations — Proving congruence, Recognizing mirror images |
| GEO.G.CO.9 | Prove and apply theorems about lines and angles | Geometry and Measurement — Compare angle measures in a diagram, Find unknown angles around a point or on a line, Write an equation relating labeled angles |
| GEO.G.CO.10 | Prove and apply theorems about triangles | Geometry and Measurement — Find unknown angles made by lines and in triangles |
Similarity, Right Triangles, and Trigonometry (GEO-G.SRT)
Circles (GEO-G.C)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| GEO.G.C.5 | Relate central angle, arc length, and sector area | Trigonometric Functions — Computing arc length |
Expressing Geometric Properties with Equations (GEO-G.GPE)
Geometric Measurement and Dimension (GEO-G.GMD)
Regents Algebra II
The Real Number System (AII-N.RN)
The Complex Number System (AII-N.CN)
Seeing Structure in Expressions (AII-A.SSE)
Arithmetic with Polynomials and Rational Expressions (AII-A.APR)
Reasoning with Equations and Inequalities (AII-A.REI)
Interpreting Functions (AII-F.IF)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| AII.F.IF.3 | Recognize sequences as functions, explicit or recursive | Limits — Finding and plotting sequence terms |
| AII.F.IF.4 | Interpret key features including end behavior and periodicity | Trigonometric Functions — Describing how oscillations change, Identifying periodic function features, Predicting periodic values
Polynomials — Finding the y-intercept, Identifying sign regions, Reading polynomial graphs
Introduction to Functions — Reading periodic function graphs
Derivatives — Sorting intervals by direction of change |
| AII.F.IF.6 | Average rate of change for polynomial, log, and trig models | Derivatives — Comparing rates of change, Finding average rate of change, Finding average velocity |
| AII.F.IF.7.c | Graph polynomial functions showing zeros and end behavior | Polynomials — Deducing roots from symmetry, Determining sign between roots, Finding roots from graphs, Identifying dominant terms, Matching equations to graphs, Matching graphs to factored form, Relating roots and degree |
| AII.F.IF.7.e | Graph cube root, exponential, log, and trig functions | Logarithms — Graph a logarithmic function
Equations and Curves — Identifying power function graphs |
Building Functions (AII-F.BF)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| AII.F.BF.1.b | Combine functions using arithmetic operations | Introduction to Functions — Combining functions with operations
Trigonometric Functions — Interpreting changing oscillation models, Modeling changing oscillations |
| AII.F.BF.2 | Write sequences recursively and explicitly | Limits — Converting recursive formulas to explicit formulas, Finding a formula from a graph, Writing recursive formulas for sequences |
| AII.F.BF.3.b | Transform graphs including f(kx) and even-odd symmetry | Equations and Curves — Applying reflections and equivalent stretches, Combining multiple transformations, Connecting transformations to domain and range, Finding domain and range after transformations, Identifying transformed graphs, Shifting the square root graph, Stretching and reflecting root graphs, Transforming the square root graph, Writing transformations from constraints
Polynomials — Applying single transformations, Classifying even and odd powers, Combining transformations, Identifying transformed features, Recognizing polynomial symmetry
Introduction to Functions — Combining reflections and stretches, Reflecting functions across axes, Stretching Function Graphs
Logarithms — Convert between log bases graphically, Transform a log graph using identities
Trigonometric Functions — Finding transformed function periods, Identifying amplitude and midline, Identifying phase shift relationships, Matching functions with transformations, Transforming periodic functions |
| AII.F.BF.4.a | Find the inverse of a one-to-one function | Introduction to Functions — Determining invertibility, Finding inverse functions
Equations and Curves — Graphing the square root function |
| AII.F.BF.5.a | Inverse relationship between exponents and logarithms | Logarithms — Convert between exponential and logarithmic form, Evaluate a logarithm exactly, Undo a logarithm or an exponential with its inverse |
| AII.F.BF.6 | Evaluate finite series with sigma notation | Integrals — Reading and writing sigma notation |
Linear, Quadratic, and Exponential Models (AII-F.LE)
Trigonometric Functions (AII-F.TF)
| NY Standard | What the standard asks | Brilliant targeted skill |
|---|
| AII.F.TF.1 | Understand radian measure of angles | Polar Coordinate Plane — Computing arc lengths from angles, Finding angles from arc lengths
Trigonometric Functions — Computing period from rotation speed, Constructing angles in radians, Constructing unit circle arcs, Converting degrees and radians, Identifying angles from geometry |
| AII.F.TF.2 | Find trig values from the unit circle in radians | Polar Coordinate Plane — Computing x and y from polar
Trigonometric Functions — Evaluating sine and cosine, Evaluating tangent at an angle, Evaluating trig functions in radians, Evaluating trig values at key angles, Reading cosine from circular motion, Reading sine from circular motion |
| AII.F.TF.4 | Symmetry and periodicity of trigonometric functions | Trigonometric Functions — Applying symmetry and periodicity rules, Describing all solutions with periodicity, Determining tangent sign by quadrant, Finding angle pairs for trig values |
| AII.F.TF.5 | Model periodic phenomena with trigonometric functions | Trigonometric Functions — Interpreting trig models, Modeling situations with trig functions |
| AII.F.TF.8 | Prove and use the Pythagorean identity | Trigonometric Functions — Using the Pythagorean identity |
Interpreting Categorical and Quantitative Data (AII-S.ID)
Making Inferences and Justifying Conclusions (AII-S.IC)
Conditional Probability and the Rules of Probability (AII-S.CP)
How this page is built
Every skill in Brilliant's math skill hierarchy is mapped to the single standard it aligns with most closely, using the New York State Next Generation Mathematics Learning Standards, as scoped by NYSED's Educator Guide blueprint for each Regents examination as the authority for what each standard requires and where its boundaries fall. Skills that build toward a standard without teaching its stated content are excluded, so a skill appears here only where it addresses the standard directly.
Each skill links to a lesson where it is practiced, and hovering a skill shows the description learners see for it. This page is regenerated from the mapping, so it reflects the current state rather than a fixed snapshot.
