New York Regents math coverage: exam-by-exam Brilliant lesson mapping

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)

NY Standard	What the standard asks	Brilliant targeted skill
AI.N.RN.3.a	Operate with rational numbers and square roots	Exponents and Radicals — Adding and subtracting like square roots, Multiplying square root expressions, Simplifying and combining unlike radicals; Equations and Curves — Evaluating square roots of squares

Quantities (AI-N.Q)

NY Standard	What the standard asks	Brilliant targeted skill
AI.N.Q.1	Use units to guide multi-step problem solving	Exploring Data Visually — Comparing on a log scale, Creating new data columns

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
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; Polynomials — Factoring out monomials; Linear Equations — Finding the greatest common factor, Writing percent change expressions; Visual Algebra — Identifying equivalent expressions, Writing equivalent expressions
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; Equations and Curves — Simplifying with exponent rules, Simplifying with exponent rules

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; 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	Linear Systems — Writing equations from constraints; Linear Relationships — Writing linear inequalities, Writing standard form equations
AI.A.CED.3	Represent constraints with equations and inequalities	Linear Systems — Writing inequality systems
AI.A.CED.4	Rearrange formulas to isolate a quantity	Equations and Curves — Rewriting equivalent equations

Reasoning with Equations and Inequalities (AI-A.REI)

NY Standard	What the standard asks	Brilliant targeted skill
AI.A.REI.1.a	Justify each step in solving linear and quadratic equations	Solving Equations — Identifying equation results, Transforming equations
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, Identifying inequality solutions, 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; Solving Equations — Distinguishing inequality types, Finding inequality solutions, Finding unknown values, Graphing inequalities, 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 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, Isolating squared variables, Reading solutions from graphs, 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	Solving Equations — Choosing what to substitute, Multiplying to eliminate, Setting up elimination, Solving by subtracting equations, Solving systems by combining, Solving systems by substitution, Solving with substitution, Substituting known values; Linear Systems — Counting solutions to a system, Eliminating by adding equations, Finding solutions by graphing, Scaling equations to eliminate, Solving systems by graphing; Vectors and Matrices — Solving systems graphically
AI.A.REI.10	Graphs as solution sets of equations	Equations and Curves — Analyzing implicit equations, Evaluating equations at points, Finding points on a curve, Matching equations to graphs, Matching equations to graphs, Verifying points on curves; Quadratics — Evaluating quadratic equations, Plotting points on parabolas; Linear Relationships — Graphing from point-slope form; Coordinate Plane — Plotting horizontal and vertical lines; Introduction to Functions — Plotting numeric functions; Linear Systems — Reading points on a graph, 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
AI.A.REI.12	Graph solutions of linear inequalities and systems	Linear Systems — Checking points in inequalities, Classifying inequality solutions, Graphing inequality constraints, Graphing inequality solutions, Identifying inequality solutions; Coordinate Plane — Combining two inequalities, Identifying strip regions, Reading solid and dashed boundaries, Shading regions for inequalities; Linear Relationships — Graphing linear inequalities, Identifying inequality solutions

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, Evaluate an exponential expression; Linear Relationships — Evaluating linear equations, Reading linear patterns; Polynomials — Evaluating power functions; Introduction to Functions — Following conditional rules, Following function rules, Identifying conditional rules, Identifying function rules, Matching input-output pairs
AI.F.IF.4	Interpret key features of graphs in context	Linear Relationships — Finding starting values, Graphing real-world relationships, Interpreting intercepts; Introduction to Functions — Identifying function intervals, Reading continuous 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 lines from intercepts, Graphing lines from slope
AI.F.IF.7.b	Graph square root, piecewise, and absolute value functions	Introduction to Functions — Evaluating floor and ceiling functions, Plotting conditional functions, Reading discontinuous function graphs
AI.F.IF.8.a	Find zeros, extrema, and symmetry of quadratics	Quadratics — Converting to vertex form, 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)

NY Standard	What the standard asks	Brilliant targeted skill
AI.F.BF.1.a	Build a function or explicit sequence from context	Visual Algebra — Breaking patterns into parts, Building expressions from rate and start, Finding counts at faraway steps, Finding counts when growth speeds up, Seeing squares inside patterns, Writing exponential expressions, Writing expressions as length times width, Writing expressions for each shape, Writing rules for growing patterns, Writing separate even and odd rules; Introduction to Functions — Writing numeric function rules
AI.F.BF.3.a	Transform graphs with f(x)+k, k f(x), and f(x+k)	Equations and Curves — Shifting the square root graph, Transforming the square root graph; Introduction to Functions — Sliding Function Graphs; Quadratics — Writing equations from graphs, Writing vertex form equations

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	Visual Algebra — Describing growth that speeds up, Identifying types of growth; Linear Relationships — Recognizing linear relationships
AI.F.LE.1.b	Recognize situations with a constant rate of change	Visual Algebra — Describing steady growth
AI.F.LE.1.c	Recognize constant percent growth or decay	Visual Algebra — Describing exponential growth; Exponential Functions — Identify exponential decay from a dot pattern, Identify exponential growth from a dot pattern
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 plotted points, Build an exponential function over negative domain, Deduce an exponential function from two points, Find the base of an exponential function, Set the coefficient of an exponential function, Write a compound growth or decay expression; 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

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, Reading box plots; Exploring Data Visually — Reading histograms
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, Finding totals from the mean, Predicting how new data shifts the mean, Splitting data into quarters, Updating the mean with new data, Updating the median with new data; 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.5	Interpret two-way tables and relative frequencies	Probability in Data — Estimating probabilities from past data
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; Regression — Fitting a line to data, Modeling one subgroup at a time, Predicting from a model equation, Predicting from a regression line, Spotting nonlinear relationships, 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 — Checking the groups inside data, Choosing the best predictor, Interpreting correlations in context, Reading correlation from a scatter plot

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 — Computing 180-degree rotations, Computing axis reflections, Computing diagonal reflections, Computing quarter-turn rotations, 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	Polar Coordinate Plane — Applying rotations and dilations; Vectors and Matrices — Applying sequential transformations, Composing geometric transformations, Representing shifts as vectors; Coordinate Transformations — Combining rotations, Combining rotations and translations, Combining translations, Connecting reflections and rotations, Recognizing mirror images, 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
GEO.G.CO.9	Prove and apply theorems about lines and angles	Geometry and Measurement — Compare angle measures in a diagram, Write an equation relating labeled angles
GEO.G.CO.10	Prove and apply theorems about triangles	Geometry and Measurement — Find the interior angle sum of a polygon, Find unknown angles made by lines and in triangles

Similarity, Right Triangles, and Trigonometry (GEO-G.SRT)

NY Standard	What the standard asks	Brilliant targeted skill
GEO.G.SRT.1	Verify properties of dilations experimentally	Coordinate Transformations — Scaling around any point, Scaling from the origin, Translating by scaling twice
GEO.G.SRT.2	Decide if figures are similar using transformations	Coordinate Transformations — Combining scaling and sliding, Proving similarity; Geometry and Measurement — Find the scale factor and unknown lengths, Match corresponding angles in similar shapes
GEO.G.SRT.6	Define trigonometric ratios in right triangles	Complex Numbers — Interpreting angle sum diagrams
GEO.G.SRT.7	Sine and cosine of complementary angles	Trigonometric Functions — Applying complementary angle relationships
GEO.G.SRT.8	Solve right triangles in applied problems	Coordinate Geometry — Applying the Pythagorean theorem to areas, Finding side lengths with the Pythagorean theorem; Vectors and Matrices — Combining velocities from bearings, Computing vector magnitude, Decomposing vectors with trigonometry, Drawing vectors from polar form, Finding polar angles, Using non-polar angle decomposition; Polar Coordinate Plane — Converting to polar coordinates; Trigonometric Functions — Finding special right triangle sides

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	Polar Coordinate Plane — Computing arc lengths from angles, Computing arc lengths from fractions, Finding angles from arc lengths

Expressing Geometric Properties with Equations (GEO-G.GPE)

NY Standard	What the standard asks	Brilliant targeted skill
GEO.G.GPE.1.a	Derive a circle's equation and find center and radius	Coordinate Geometry — Using the circle equation at the origin, Using the general circle equation; Equations and Curves — Writing circle and ellipse equations
GEO.G.GPE.5	Slope criteria for parallel and perpendicular lines	Linear Relationships — Finding perpendicular slopes, Writing parallel line equations, Writing perpendicular line equations
GEO.G.GPE.7	Find perimeter and area using coordinates	Coordinate Geometry — Calculating distance from coordinates, Calculating rectangle area, Calculating right triangle area, Finding compound shape area, Writing area expressions with variables

Geometric Measurement and Dimension (GEO-G.GMD)

NY Standard	What the standard asks	Brilliant targeted skill
GEO.G.GMD.3	Volume formulas for cylinders, pyramids, cones, and spheres	Geometry and Measurement — Find volume as area of the base times height, Use the one-third relationship for pyramids and cones

Regents Algebra II

The Real Number System (AII-N.RN)

NY Standard	What the standard asks	Brilliant targeted skill
AII.N.RN.1	Explain the meaning of rational exponents	Exponential Functions — Evaluate an exponential at non-integer x-values; Exponents and Radicals — Evaluating general fractional exponents, Evaluating unit fraction exponents; Equations and Curves — Evaluating roots and inverse compositions
AII.N.RN.2	Convert between radicals and rational exponents	Exponents and Radicals — Connecting fractional exponents to radicals; Equations and Curves — Simplifying fractional exponents

The Complex Number System (AII-N.CN)

NY Standard	What the standard asks	Brilliant targeted skill
AII.N.CN.1	Understand imaginary and complex numbers	Complex Numbers — Evaluating real and imaginary parts
AII.N.CN.2	Add, subtract, and multiply complex numbers	Complex Numbers — Adding and subtracting complex numbers, Evaluating expressions with i, Multiplying complex numbers, Rotating by multiplying by i, Scaling complex numbers, Simplifying powers of i

Seeing Structure in Expressions (AII-A.SSE)

NY Standard	What the standard asks	Brilliant targeted skill
AII.A.SSE.2	Use structure to rewrite polynomial and rational expressions	Polynomials — Factoring biquadratic polynomials, Factoring power differences; Quadratics — Factoring signed quadratics fully, Factoring with leading coefficients; Equations and Curves — Simplifying by factoring, Simplifying rational expressions

Arithmetic with Polynomials and Rational Expressions (AII-A.APR)

NY Standard	What the standard asks	Brilliant targeted skill
AII.A.APR.3	Find zeros of polynomials, factoring them first	Polynomials — Connecting roots and factors, Solving by factoring

Reasoning with Equations and Inequalities (AII-A.REI)

NY Standard	What the standard asks	Brilliant targeted skill
AII.A.REI.4.b	Solve quadratics including complex solutions	Quadratics — Completing squares with fractions, Solving by completing the square, Solving with imaginary numbers; Complex Numbers — Solving equations with complex solutions
AII.A.REI.7.b	Solve systems with a line and a parabola or circle	Equations and Curves — Solving systems and unions of curves
AII.A.REI.11	Solve equations and inequalities from graph intersections	Equations and Curves — Controlling the number of intersections, Finding intersection points, Reading intervals from hyperbolas, Reading values from graphs; Trigonometric Functions — Solving equations from the tangent graph, Solving equations from trig graphs, Solving trig equations on an interval

Interpreting Functions (AII-F.IF)

NY Standard	What the standard asks	Brilliant targeted skill
AII.F.IF.4	Interpret key features including end behavior and periodicity	Polynomials — Finding roots from graphs, Finding the y-intercept, Identifying sign regions, Reading polynomial graphs; Equations and Curves — Identifying symmetric points, Using hyperbola symmetry; Trigonometric Functions — Predicting periodic values; Introduction to Functions — Reading periodic function graphs
AII.F.IF.7.c	Graph polynomial functions showing zeros and end behavior	Polynomials — Determining sign between roots, Identifying dominant terms, Identifying transformed features, Matching equations to graphs, Matching graphs to factored form; Equations and Curves — Identifying power function graphs
AII.F.IF.7.e	Graph cube root, exponential, log, and trig functions	Trigonometric Functions — Finding transformed function periods, Identifying amplitude and midline, Identifying periodic function features; Logarithms — Graph a logarithmic function
AII.F.IF.9	Compare polynomial, log, and trig functions across forms	Polynomials — Comparing power functions

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
AII.F.BF.3.b	Transform graphs including f(kx) and even-odd symmetry	Polynomials — Applying parity properties, Applying single transformations, Classifying even and odd powers, Combining transformations, Deducing roots from symmetry, Recognizing polynomial symmetry, Using power function symmetry; Equations and Curves — Applying reflections and equivalent stretches, Applying shifts and stretches, Combining multiple transformations, Completing hyperbola equations, Connecting transformations to domain and range, Finding equation parameters, Identifying transformed graphs, Stretching and reflecting root graphs, Transforming hyperbola graphs, Writing transformations from constraints; 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 — Identifying phase shift relationships, Transforming periodic functions
AII.F.BF.4.a	Find the inverse of a one-to-one function	Introduction to Functions — 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, Estimate a logarithm, Evaluate a logarithm exactly, Solve logarithmic equations

Linear, Quadratic, and Exponential Models (AII-F.LE)

NY Standard	What the standard asks	Brilliant targeted skill
AII.F.LE.2	Build linear or exponential functions in multi-step contexts	Exponential Functions — Build an exponential function from non-integer points
AII.F.LE.4	Solve exponential equations using logarithms	Logarithms — Solve exponential equations with logarithms

Trigonometric Functions (AII-F.TF)

NY Standard	What the standard asks	Brilliant targeted skill
AII.F.TF.1	Understand radian measure of angles	Trigonometric Functions — Computing arc length, Constructing angles in radians, Constructing unit circle arcs, 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, Finding angle pairs for trig values, 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
AII.F.TF.5	Model periodic phenomena with trigonometric functions	Trigonometric Functions — Computing period from rotation speed, Matching functions with transformations
AII.F.TF.8	Prove and use the Pythagorean identity	Trigonometric Functions — Using the Pythagorean identity

Interpreting Categorical and Quantitative Data (AII-S.ID)

NY Standard	What the standard asks	Brilliant targeted skill
AII.S.ID.6.a	Fit quadratic, exponential, or power models to data	Regression — Choosing a model for curved data, Transforming variables to straighten data

Making Inferences and Justifying Conclusions (AII-S.IC)

NY Standard	What the standard asks	Brilliant targeted skill
AII.S.IC.6.a	Draw conclusions from numerical summaries	Exploring Data Visually — Making a data-backed recommendation

Conditional Probability and the Rules of Probability (AII-S.CP)

NY Standard	What the standard asks	Brilliant targeted skill
AII.S.CP.1	Describe events as subsets of a sample space	Probability and Chance — Comparing the likelihood of outcomes, Counting outcomes across overlapping events, Counting possible outcomes, Using Venn diagrams
AII.S.CP.4	Two-way tables, independence, and conditional probability	Probability in Data — Finding conditional probabilities from data, Identifying when events affect each other, Judging how often a rule fails; Probability and Chance — Finding probability given a condition
AII.S.CP.7	Apply the addition rule	Probability in Data — Adding probabilities of separate outcomes, Combining probabilities with a formula; Probability and Chance — Finding the probability of either event

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 practised, 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.