Every Common Core math standard Brilliant teaches, grade by grade, with the lessons that develop each one.

Common Core math coverage: grade-by-grade Brilliant lesson mapping

The digital SAT math testing points, domain by domain, mapped to the Brilliant lessons that teach them.

Digital SAT math coverage: Brilliant lesson mapping by testing point

Every PSAT/NMSQT and PSAT 10 math testing point, mapped to the Brilliant lessons that teach it.

This page maps the math testing points of the digital PSAT/NMSQT and PSAT 10 — College Board publishes one set of content specifications for both — to the Brilliant lessons that teach them. Search by domain or skill to find the closest match. A testing point is listed only where Brilliant content fully or in part addresses the testing point directly. Algebra (≈35% / 13–15 questions) PSAT testing point What the testing point asks Brilliant targeted skill ALG.1 Create, solve, and interpret linear equations in one variable Linear Equations — Classifying equations by solutions, Combining fractional terms, Combining groups of expressions, Combining like terms to solve, Combining negatives to solve, Finding missing values with negatives, Finding unknown values, Modeling with linear equations, 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 two-step equations, Solving with reciprocals, Solving with subtracted variables, Solving with variables on both sides, Working with negative coefficients; Solving Equations — Combining terms in equations, Finding unknown values, Identifying equation results, Solving after combining, Solving grouped equations, Solving one-step equations, Transforming equations, Writing balanced equations, Writing equations from scales, Writing grouped equations ALG.2 Write and interpret linear equations in two variables Proportional Reasoning — Comparing proportional graphs, Graphing proportional relationships, Writing proportional equations; Linear Relationships — Computing slope, Finding perpendicular slopes, Graphing from point-slope form, Graphing lines from intercepts, Graphing lines from slope, Interpreting intercepts, Writing parallel line equations, Writing perpendicular line equations, Writing point-slope equations, Writing standard form equations; Coordinate Plane — Plotting horizontal and vertical lines; Solving Equations — Substituting known values; Linear Systems — Writing equations from constraints ALG.3 Model, evaluate, and interpret linear functions Visual Algebra — Building expressions from rate and start, Comparing pattern growth rates, Describing steady growth, Finding counts at faraway steps, Writing expressions for each shape, Writing rules for growing patterns, Writing separate even and odd rules; Linear Relationships — Calculating rates of change, Evaluating linear equations, Extending linear patterns, Finding constant change, Finding starting values, Graphing real-world relationships, Reading linear patterns, Writing slope-intercept equations; Introduction to Functions — Following function rules, Identifying function rules, Matching input-output pairs, Plotting numeric functions, Writing numeric function rules; Regression — Predicting from a model equation ALG.4 Create and solve systems of two linear equations 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; Linear Systems — Counting solutions to a system, Eliminating by adding equations, Finding solutions by graphing, Scaling equations to eliminate, Solving systems by graphing, Testing points in equations ALG.5 Create, solve, and graph linear inequalities Linear Systems — Checking points in inequalities, Classifying inequality solutions, Graphing inequality constraints, Graphing inequality solutions, Identifying inequality solutions, Writing inequality systems; Coordinate Plane — Combining two inequalities, Identifying strip regions, Reading solid and dashed boundaries, Shading regions for inequalities; Linear Equations — Comparing deals with percentages, Dividing by negatives in inequalities, Graphing compound inequalities or or (union)'), Identifying inequality solutions, Solving compound inequalities, Solving multi-step inequalities, Solving multi-step negative inequalities, Solving one-step inequalities, Writing compound inequalities; Solving Equations — Distinguishing inequality types, Finding inequality solutions, Graphing inequalities, Solving for boundary values, Translating words to inequalities, Writing inequalities from scales; Linear Relationships — Graphing linear inequalities, Identifying inequality solutions, Writing linear inequalities Advanced Math (≈32.5% / 12–14 questions) PSAT testing point What the testing point asks Brilliant targeted skill ADV.1 Factor and rewrite polynomial expressions Polynomials — Adding polynomials, Factoring out monomials, Multiplying monomials, Multiplying polynomials, Subtracting polynomials, Working with multivariable polynomials; Solving Equations — Combining like terms, Distributing over a sum by distributing the factor to each term'), Distributing over groups, Factoring common factors, Factoring into groups; Quadratics — Combining like terms, Combining signed terms, Combining terms with coefficients, Completing factors with negatives, Completing partial factorizations, Determining signs in products, Expanding binomial products, Factoring signed quadratics fully, Factoring simple quadratics, Factoring with leading coefficients, Factoring with negative constants, Finding constant terms, Finding linear terms, Multiplying with negative numbers, Recognizing perfect square patterns; Visual Algebra — Combining pattern expressions, Identifying equivalent expressions, Writing equivalent expressions; Linear Equations — Combining terms with decimals, Finding the greatest common factor; Coordinate Geometry — Identifying equivalent area expressions ADV.2 Solve quadratic, absolute value, rational, and radical equations Equations and Curves — Building equations from intersections, Controlling the number of intersections, Finding intersection points; Negative Numbers — Calculating absolute value of sums, Finding numbers at a given distance, Solving absolute value conditions; Quadratics — Checking solutions by substitution, Classifying solution types, Completing squares with fractions, Completing the square, Determining number of solutions, Isolating squared variables, Reading solutions from graphs, Solving by completing the square, Solving equations by factoring, Solving shifted square equations^2 + k = c by undoing each operation step by step'), Solving with square roots, Using the discriminant, Using the quadratic formula ADV.3 Model and interpret quadratic and exponential functions Equations and Curves — Applying shifts and stretches, Combining multiple transformations, Completing hyperbola equations, Identifying power function graphs, Identifying transformed graphs, Matching equations to graphs, Matching equations to graphs, Matching rational functions to graphs, Shifting the square root graph, Stretching and reflecting root graphs, Transforming hyperbola graphs, Transforming the square root graph; Polynomials — Applying single transformations, Combining transformations, Evaluating polynomials, Evaluating power functions, Identifying transformed features, Matching equations to graphs, Matching graphs to factored form; Visual Algebra — Breaking patterns into parts, Describing exponential growth, Describing growth that speeds up, Finding counts when growth speeds up, Identifying types of growth, Seeing squares inside patterns, Writing exponential expressions, Writing expressions as length times width; 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, Compare exponential growth to linear growth, Compare exponential growth to quadratic growth, Compare two exponential functions, Deduce an exponential function from two points, Evaluate an exponential at negative x-values, Evaluate an exponential at non-integer x-values, Evaluate an exponential expression, Express decay with a negative exponent, Find the base of an exponential function, Graph and compare compound interest functions, Identify exponential decay from a dot pattern, Identify exponential growth from a dot pattern, Set the coefficient of an exponential function, Write a compound growth or decay expression; Introduction to Functions — Combining reflections and stretches, Identifying function intervals, Reading continuous function graphs, Reflecting functions across axes, Sliding Function Graphs, Stretching Function Graphs; Quadratics — Connecting intercepts to factors, Converting to vertex form, Evaluating quadratic equations, Finding maximum and minimum values, Finding the axis of symmetry, Finding the vertex, Finding vertices using symmetry, Graphing by factoring, Graphing parabolas from vertex form, Plotting points on parabolas, Writing equations from graphs, Writing vertex form equations; Logarithms — Find the exponent in an exponential equation Problem-Solving and Data Analysis (≈20% / 7–9 questions) PSAT testing point What the testing point asks Brilliant targeted skill PSDA.1 Solve problems with ratios, rates, proportions, and units Proportional Reasoning — Comparing ratios with unit rates, Comparing unit prices, Finding the scale factor, Finding totals from ratios, Finding unit rates, Identifying equivalent ratios, Relating totals, rates, and amounts, Scaling by a given factor, Scaling recipes to a target, Scaling with non-whole numbers, Simplifying ratios, Writing equivalent ratios; Exploring Data Visually — Create a new column from existing columns, Creating new data columns PSDA.2 Solve percent and percent-change problems Percents — Calculating a percentage of a number, Calculating compound percent changes, Comparing split and single changes, Computing repeated percent growth, Converting percentages to fractions, Finding the percentage from two numbers, Reversing a percentage calculation, Writing compound change expressions, Writing percent change expressions; Exploring Data Visually — Reading pie charts; Linear Equations — Writing percent change expressions PSDA.3 Interpret data distributions and measures of center and spread 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 the mean (the average) of a data set, Finding the mean of uneven data, Finding the median, Finding totals from the mean, Matching data to box plots, Predicting how new data shifts the mean, Reading box plots, Seeing how outliers affect 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, Find frequencies and percentiles from a histogram, Group a data table to summarize categories, Read and compare bars on a bar chart, Read median, quartiles, and extremes from a boxplot, Reading histograms; Regression — Detecting hidden groups in data PSDA.4 Interpret scatterplots and fit models to data Regression — Choosing a model for curved data, Predicting from a regression line, Spotting nonlinear relationships, Transforming variables to straighten data; Exploring Data Visually — Describe the relationship in a scatter plot, Describing how two things relate, Identify and extend a trend on a line graph, Read coordinates of points on a scatter plot, Reading line graphs, Reading scatter plots, Spotting trends over time PSDA.5 Find probabilities and conditional probabilities from data Probability and Chance — Calculating probability, Changing probability by removing options, Comparing the likelihood of outcomes, Finding probability given a condition, Finding the probability of both events, Finding the probability of either event; Probability in Data — Estimating probabilities from past data, Finding conditional probabilities from data, Judging how often a rule fails; Exploring Data Visually — Find percents of a whole from a pie chart Geometry and Trigonometry (≈12.5% / 4–6 questions) PSAT testing point What the testing point asks Brilliant targeted skill GEO.1 Solve area, surface area, and volume problems Coordinate Geometry — Calculating rectangle area, Calculating right triangle area, Finding compound shape area, Writing area expressions with variables; Geometry and Measurement — Compare volumes by slicing and rearranging, Find and compare perimeters of figures, Find circumference from radius or diameter, Find surface area by adding face areas, Find surface area from base area and perimeter, Find volume as area of the base times height, Relate areas of similar shapes using scale factor, Use the one-third relationship for pyramids and cones GEO.2 Apply angle, congruence, and similarity theorems Geometry and Measurement — Compare angle measures in a diagram, Find the scale factor and unknown lengths, Find unknown angles around a point or on a line, Find unknown angles made by lines and in triangles, Match corresponding angles in similar shapes, Write an equation relating labeled angles; Coordinate Transformations — Proving similarity GEO.3 Use the Pythagorean theorem and right triangle trigonometry Coordinate Geometry — Applying the Pythagorean theorem to areas, Calculating a circle's radius, Calculating distance from coordinates, Finding side lengths with the Pythagorean theorem; Trigonometric Functions — Finding special right triangle sides How this page is built Every skill in Brilliant's math skill hierarchy is mapped to the single testing point it aligns with most closely, using College Board's Assessment Framework for the Digital SAT Suite (version 3.01, August 2024) as the authority for what each testing point requires and where its boundaries fall. Skills that build toward a testing point without teaching its stated content are excluded, so a skill appears here only where it addresses the testing point 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.

PSAT math coverage: Brilliant lesson mapping by testing point

ACT math standards grouped by score band, mapped to the Brilliant lessons that teach each one.

ACT math coverage: Brilliant lesson mapping by score range

The standards assessed on New York's Algebra I, Geometry and Algebra II Regents exams, mapped to Brilliant lessons.

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

AP Precalculus topics, unit by unit, mapped to the Brilliant lessons that teach them.

AP Precalculus coverage: unit-by-unit Brilliant lesson mapping

NC Math 1 standards mapped to the Brilliant lessons that teach them, for North Carolina's integrated pathway.

This page maps the standards of NC Math 1 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. North Carolina teaches an integrated high school pathway rather than the Algebra 1 → Geometry → Algebra 2 sequence, so each of NC Math 1, 2, and 3 mixes algebra, functions, geometry, and statistics. This page covers NC Math 1 only; NC Math 2 and NC Math 3 have their own pages. Math 1 is broadly the linear and exponential half of algebra, plus coordinate geometry and two-variable statistics. North Carolina writes its own codes, and they are not interchangeable with Common Core's even where the trailing part matches — NCDPI narrowed some standards, widened others, and folded several together. The codes below use dots throughout, so NCDPI's NC.M1.A-CED.1 appears here as NC.M1.A.CED.1. Number and Quantity — The Real Number System (NC.M1.N-RN) NC standard What the standard asks Brilliant targeted skill NC.M1.N.RN.2 Rewrite algebraic expressions with integer exponents using the properties of 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, 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 Algebra — Seeing Structure in Expressions (NC.M1.A-SSE) NC standard What the standard asks Brilliant targeted skill NC.M1.A.SSE.1.a Identify and interpret parts of a linear, exponential, or quadratic expression, including terms, factors, coefficients, and exponents. Exponential Functions — Evaluate an exponential expression NC.M1.A.SSE.3 Write an equivalent form of a quadratic expression ax² + bx + c, where a is an integer, by factoring to reveal the solutions of the equation or the zeros of the function the expression defines. Quadratics — Completing factors with negatives, Completing partial factorizations, Factoring signed quadratics fully, Factoring simple quadratics, Factoring with leading coefficients, Factoring with negative constants, Recognizing perfect square patterns Algebra — Arithmetic with Polynomial Expressions (NC.M1.A-APR) NC standard What the standard asks Brilliant targeted skill NC.M1.A.APR.1 Build an understanding that operations with polynomials are comparable to operations with integers by adding and subtracting quadratic expressions and by adding, subtracting, and multiplying linear expressions. 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 — Identifying equivalent expressions, Writing equivalent expressions NC.M1.A.APR.3 Understand the relationships among the factors of a quadratic expression, the solutions of a quadratic equation, and the zeros of a quadratic function. Quadratics — Connecting intercepts to factors Algebra — Creating Equations (NC.M1.A-CED) NC standard What the standard asks Brilliant targeted skill NC.M1.A.CED.1 Create equations and inequalities in one variable that represent linear, exponential, and quadratic relationships and use them to solve problems. Linear Equations — Comparing deals with percentages, Modeling with linear equations NC.M1.A.CED.2 Create and graph equations in two variables to represent linear, exponential, and quadratic relationships between quantities. Linear Relationships — Graphing lines from intercepts, Graphing real-world relationships, Writing standard form equations NC.M1.A.CED.3 Create systems of linear equations and inequalities to model situations in context. Linear Systems — Writing equations from constraints, Writing inequality systems; Linear Relationships — Writing linear inequalities Algebra — Reasoning with Equations and Inequalities (NC.M1.A-REI) NC standard What the standard asks Brilliant targeted skill NC.M1.A.REI.3 Solve linear equations and inequalities in one variable. Linear Equations — Combining fractional terms, Combining like terms to solve, Combining negatives to solve, Dividing by negatives in inequalities, Solving compound inequalities, 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 with reciprocals, Solving with subtracted variables, Solving with variables on both sides NC.M1.A.REI.4 Solve for the real solutions of quadratic equations in one variable by taking square roots and factoring. Quadratics — Isolating squared variables, Solving equations by factoring, Solving shifted square equations^2 + k = c by undoing each operation step by step'), Solving with square roots NC.M1.A.REI.6 Use tables, graphs, or algebraic methods (substitution and elimination) to find approximate or exact solutions to systems of linear equations and interpret solutions in terms of a context. 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 NC.M1.A.REI.10 Understand that the graph of a two-variable equation represents the set of all solutions to the equation. 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; Linear Relationships — Graphing from point-slope form; Quadratics — Reading solutions from graphs; Linear Systems — Testing points in equations NC.M1.A.REI.11 Build an understanding of why the x-coordinates of the points where the graphs of two linear, exponential, and/or quadratic equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x), and approximate solutions using graphing technology or successive approximations with a table of values. Exponential Functions — Compare two exponential functions, Graph and compare compound interest functions NC.M1.A.REI.12 Represent the solutions of a linear inequality or a system of linear inequalities graphically as a region of the plane. 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, Shading regions for inequalities; Linear Relationships — Graphing linear inequalities, Identifying inequality solutions Functions — Interpreting Functions (NC.M1.F-IF) NC standard What the standard asks Brilliant targeted skill NC.M1.F.IF.1 Build an understanding that a function from one set (the domain) to another (the range) assigns to each element of the domain exactly one element of the range, recognizing that if f is a function and x is in its domain then f(x) denotes the output of f at x, and that the graph of f is the graph of y = f(x). Introduction to Functions — Applying the vertical line test, Recognizing non-functions NC.M1.F.IF.2 Use function notation to evaluate linear, quadratic, and exponential functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Exponential Functions — Evaluate an exponential at negative x-values, Evaluate an exponential at non-integer x-values; Linear Relationships — Evaluating linear equations, Reading linear patterns; Quadratics — Evaluating quadratic equations, Plotting points on parabolas; Introduction to Functions — Following function rules, Identifying function rules, Matching input-output pairs NC.M1.F.IF.4 Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities, including intercepts; intervals where the function is increasing, decreasing, positive, or negative; and maximums and minimums. Linear Relationships — Finding starting values, Interpreting intercepts; Introduction to Functions — Identifying function intervals, Reading continuous function graphs NC.M1.F.IF.5 Interpret a function in terms of the context by relating its domain and range to its graph and, where applicable, to the quantitative relationship it describes. Introduction to Functions — Finding function domains, Finding function ranges NC.M1.F.IF.6 Calculate and interpret the average rate of change over a specified interval for a function presented numerically, graphically, and/or symbolically. Linear Relationships — Calculating rates of change, Computing slope, Finding constant change NC.M1.F.IF.7 Analyze linear, exponential, and quadratic functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features including domain and range; rate of change; intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and end behavior. Linear Relationships — Graphing lines from slope; Introduction to Functions — Plotting numeric functions NC.M1.F.IF.8.a Rewrite a quadratic function to reveal and explain different key features of the function. Quadratics — Graphing by factoring NC.M1.F.IF.8.b Interpret and explain growth and decay rates for an exponential function. Exponential Functions — Identify exponential decay from a dot pattern, Identify exponential growth from a dot pattern, Write a compound growth or decay expression Functions — Building Functions (NC.M1.F-BF) NC standard What the standard asks Brilliant targeted skill NC.M1.F.BF.1.a Build linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two ordered pairs (including reading these from a table). 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, Find the base of an exponential function, Set the coefficient of an exponential function; Visual Algebra — Building expressions from rate and start, Building sequences from rules, Writing exponential expressions, Writing expressions for each shape, Writing rules for growing patterns, Writing separate even and odd rules; Introduction to Functions — Writing numeric function rules; Linear Relationships — Writing point-slope equations, Writing slope-intercept equations NC.M1.F.BF.1.b Build a function that models a relationship between two quantities by combining linear, exponential, or quadratic functions with addition and subtraction, or two linear functions with multiplication. Visual Algebra — Breaking patterns into parts, Combining pattern expressions, Seeing squares inside patterns, Writing expressions as length times width Functions — Linear, Quadratic, and Exponential Models (NC.M1.F-LE) NC standard What the standard asks Brilliant targeted skill NC.M1.F.LE.1 Identify situations that can be modeled with linear and exponential functions, and justify the most appropriate model for a situation based on the rate of change over equal intervals. Visual Algebra — Describing growth that speeds up, Identifying types of growth; Linear Relationships — Recognizing linear relationships NC.M1.F.LE.3 Compare the end behavior of linear, exponential, and quadratic functions using graphs and tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. Exponential Functions — Compare exponential growth to linear growth, Compare exponential growth to quadratic growth Geometry — Expressing Geometric Properties with Equations (NC.M1.G-GPE) NC standard What the standard asks Brilliant targeted skill NC.M1.G.GPE.4 Use coordinates to solve geometric problems involving polygons algebraically: compute perimeters of polygons and areas of triangles and rectangles, and verify algebraically that a given set of points produces a particular type of triangle or quadrilateral. Coordinate Geometry — Calculating distance from coordinates, Calculating rectangle area, Calculating right triangle area, Finding compound shape area, Identifying equivalent area expressions, Writing area expressions with variables, Writing distance expressions with variables; Coordinate Plane — Measuring gridline distance NC.M1.G.GPE.5 Use coordinates to prove the slope criteria for parallel and perpendicular lines and use them to solve problems: determine if two lines are parallel, perpendicular, or neither, and find the equation of a line parallel or perpendicular to a given line through a given point. Linear Relationships — Finding perpendicular slopes, Writing parallel line equations, Writing perpendicular line equations Statistics and Probability — Interpreting Categorical and Quantitative Data (NC.M1.S-ID) NC standard What the standard asks Brilliant targeted skill NC.M1.S.ID.1 Use technology to represent data with plots on the real number line (histograms and box plots). Exploring Data Visually — Reading histograms NC.M1.S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets, and interpret differences in shape, center, and spread in context. Exploring Data Visually — Compare boxplots across datasets; Everyday Statistics — Comparing data sets with box plots; Regression — Detecting hidden groups in data NC.M1.S.ID.3 Examine the effects of extreme data points (outliers) on shape, center, and/or spread. Everyday Statistics — Seeing how outliers affect the mean, Spotting outliers, Using the outlier rule NC.M1.S.ID.6.a Represent data on two quantitative variables on a scatter plot and describe how the variables are related; fit a least squares regression line to linear data using technology and use the fitted function to solve problems. 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 NC.M1.S.ID.6.b Assess the fit of a linear function by analyzing residuals. Regression — Measuring how well a model fits NC.M1.S.ID.6.c Fit a function to exponential data using technology and use the fitted function to solve problems. Regression — Transforming variables to straighten data NC.M1.S.ID.7 Interpret in context the rate of change and the intercept of a linear model; use the linear model to interpolate and extrapolate predicted values, and assess the validity of a predicted value. Regression — Predicting from a model equation, Predicting from a regression line NC.M1.S.ID.8 Analyze patterns and describe relationships between two variables in context; using technology, determine the correlation coefficient of bivariate data and interpret it as a measure of the strength and direction of a linear relationship; use a scatter plot, correlation coefficient, and residual plot to determine the appropriateness of a linear model. Regression — Checking the groups inside data, Choosing the best predictor, Interpreting correlations in context, Reading correlation from a scatter plot, Spotting nonlinear relationships; Exploring Data Visually — Judging how strongly things relate How this page is built Every skill in the Brilliant math courses that reach North Carolina's high school mathematics is mapped to the single standard it aligns with most closely, using the North Carolina Standard Course of Study for Mathematics, adopted by the State Board of Education in June 2016, together with NCDPI's unpacking documents 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.

NC Math 1 coverage: standard-by-standard Brilliant lesson mapping

NC Math 2 standards mapped to the Brilliant lessons that teach them, covering quadratics through probability.

This page maps the standards of NC Math 2 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. North Carolina teaches an integrated high school pathway rather than the Algebra 1 → Geometry → Algebra 2 sequence, so each of NC Math 1, 2, and 3 mixes algebra, functions, geometry, and statistics. This page covers NC Math 2 only; NC Math 1 and NC Math 3 have their own pages. Math 2 adds quadratics, congruence and similarity, right triangle trigonometry, and probability. North Carolina writes its own codes, and they are not interchangeable with Common Core's even where the trailing part matches — NCDPI narrowed some standards, widened others, and folded several together. The codes below use dots throughout, so NCDPI's NC.M2.A-CED.1 appears here as NC.M2.A.CED.1. Number and Quantity — The Real Number System (NC.M2.N-RN) NC standard What the standard asks Brilliant targeted skill NC.M2.N.RN.1 Explain how expressions with rational exponents can be rewritten as radical expressions. Exponents and Radicals — Connecting fractional exponents to radicals NC.M2.N.RN.2 Rewrite expressions with radicals and rational exponents into equivalent expressions using the properties of exponents. Exponents and Radicals — Adding and subtracting like square roots, Evaluating general fractional exponents by applying the root and the power in either order'), Evaluating unit fraction exponents, Multiplying square root expressions, Simplifying and combining unlike radicals; Equations and Curves — Evaluating roots and inverse compositions, Simplifying fractional exponents Number and Quantity — The Complex Number System (NC.M2.N-CN) NC standard What the standard asks Brilliant targeted skill NC.M2.N.CN.1 Know there is a complex number i such that i² = -1, and that every complex number has the form a + bi where a and b are real numbers. Complex Numbers — Evaluating expressions with i, Evaluating real and imaginary parts, Simplifying powers of i Algebra — Seeing Structure in Expressions (NC.M2.A-SSE) NC standard What the standard asks Brilliant targeted skill NC.M2.A.SSE.3 Write an equivalent form of a quadratic expression by completing the square, where a is an integer of a quadratic expression ax² + bx + c, to reveal the maximum or minimum value of the function the expression defines. Quadratics — Completing the square, Converting to vertex form Algebra — Arithmetic with Polynomial and Rational Expressions (NC.M2.A-APR) NC standard What the standard asks Brilliant targeted skill NC.M2.A.APR.1 Extend the understanding that operations with polynomials are comparable to operations with integers by adding, subtracting, and multiplying polynomials. Polynomials — Adding polynomials, Multiplying monomials, Multiplying polynomials, Subtracting polynomials, Working with multivariable polynomials Algebra — Reasoning with Equations and Inequalities (NC.M2.A-REI) NC standard What the standard asks Brilliant targeted skill NC.M2.A.REI.4.a Solve for all solutions of quadratic equations in one variable, understanding that the quadratic formula is the generalization of solving ax² + bx + c by using the process of completing the square. Quadratics — Completing squares with fractions, Solving by completing the square, Using the quadratic formula NC.M2.A.REI.4.b Explain when quadratic equations will have non-real solutions and express complex solutions as a ± bi for real numbers a and b. Quadratics — Classifying solution types, Determining number of solutions, Solving with imaginary numbers, Using the discriminant; Complex Numbers — Solving equations with complex solutions Functions — Interpreting Functions (NC.M2.F-IF) NC standard What the standard asks Brilliant targeted skill NC.M2.F.IF.2 Extend the use of function notation to express the image of a geometric figure in the plane resulting from a translation, rotation by multiples of 90 degrees about the origin, reflection across an axis, or dilation as a function of its pre-image. Coordinate Transformations — Computing 180-degree rotations, Computing axis reflections, Computing quarter-turn rotations, Translating with coordinates NC.M2.F.IF.7 Analyze quadratic, square root, and inverse variation functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features including domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; maximums and minimums; symmetries; and end behavior. Equations and Curves — Connecting transformations to domain and range, Finding domain and range after transformations; Quadratics — Finding maximum and minimum values, Finding the axis of symmetry, Finding vertices using symmetry NC.M2.F.IF.8 Use equivalent expressions to reveal and explain different properties of a function by developing and using the process of completing the square to identify the zeros, extreme values, and symmetry in graphs and tables representing quadratic functions, and interpret these in terms of a context. Quadratics — Finding the vertex Functions — Building Functions (NC.M2.F-BF) NC standard What the standard asks Brilliant targeted skill NC.M2.F.BF.1 Write a function that describes a relationship between two quantities by building quadratic functions with real solution(s) and inverse variation functions given a graph, a description of a relationship, or ordered pairs (including reading these from a table). Quadratics — Writing equations from graphs, Writing vertex form equations NC.M2.F.BF.3 Understand the effects on the graphical and tabular representations of a linear, quadratic, square root, or inverse variation function f of k · f(x), f(x) + k, and f(x + k) for specific values of k (both positive and negative). Quadratics — Graphing parabolas from vertex form; Equations and Curves — Shifting the square root graph Geometry — Congruence (NC.M2.G-CO) NC standard What the standard asks Brilliant targeted skill NC.M2.G.CO.2 Experiment with transformations in the plane: represent transformations in the plane; compare rigid motions that preserve distance and angle measure (translations, reflections, rotations) to transformations that do not preserve both (e.g. stretches, dilations); understand that rigid motions produce congruent figures while dilations produce similar figures. Polar Coordinate Plane — Applying rotations and dilations; Coordinate Transformations — Combining stretches with transformations, Stretching along an axis NC.M2.G.CO.3 Given a triangle, quadrilateral, or regular polygon, describe any reflection or rotation symmetry — actions that carry the figure onto itself — identifying the center and angle(s) of rotation symmetry and the line(s) of reflection symmetry. Coordinate Transformations — Finding lines of symmetry, Finding rotational symmetry, Identifying types of symmetry NC.M2.G.CO.5 Given a geometric figure and a rigid motion, find the image of the figure; given a geometric figure and its image, specify a rigid motion or sequence of rigid motions that will transform the pre-image to its image. Coordinate Transformations — Combining rotations, Combining rotations and translations, Combining translations, Computing diagonal reflections, 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 NC.M2.G.CO.6 Determine whether two figures are congruent by specifying a rigid motion or sequence of rigid motions that will transform one figure onto the other. Coordinate Transformations — Proving congruence Geometry — Similarity, Right Triangles, and Trigonometry (NC.M2.G-SRT) NC standard What the standard asks Brilliant targeted skill NC.M2.G.SRT.1 Verify experimentally the properties of dilations with a given center and scale factor: (a) a line segment through the center of dilation and its image lie on the same line, and a segment not through the center is parallel to its image; (b) the length of the image of a segment equals the length of the segment times the scale factor; (c) the distance from the center of dilation to a point on the image equals the scale factor times the distance to the corresponding pre-image point; (d) dilations preserve angle measure. Geometry and Measurement — Find the scale factor and unknown lengths, Match corresponding angles in similar shapes; Coordinate Transformations — Scaling around any point, Scaling from the origin NC.M2.G.SRT.2 Understand similarity in terms of transformations: (a) determine whether two figures are similar by specifying a sequence of transformations that will transform one figure into the other; (b) use the properties of dilations to show that two triangles are similar when all corresponding pairs of sides are proportional and all corresponding pairs of angles are congruent. Polar Coordinate Plane — Choosing polar transformations, Combining transformations; Coordinate Transformations — Combining scaling and sliding, Proving similarity, Translating by scaling twice NC.M2.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve problems involving right triangles in terms of a context. Coordinate Geometry — Applying the Pythagorean theorem to areas, Finding side lengths with the Pythagorean theorem NC.M2.G.SRT.12 Develop properties of special right triangles (45-45-90 and 30-60-90) and use them to solve problems. Trigonometric Functions — Evaluating trig values at key angles, Finding special right triangle sides Statistics and Probability — Conditional Probability and the Rules of Probability (NC.M2.S-CP) NC standard What the standard asks Brilliant targeted skill NC.M2.S.CP.1 Describe events as subsets of the outcomes in a sample space using characteristics of the outcomes, or as unions, intersections, and complements of other events. Probability and Chance — Calculating probability, Comparing the likelihood of outcomes, Counting outcomes across overlapping events, Counting possible outcomes, Finding the probability something won't happen, Using Venn diagrams NC.M2.S.CP.3.b Understand that event A is independent from event B if the probability of A does not change in response to the occurrence of B — that is, P(A\ B) = P(A). Probability in Data — Identifying when events affect each other NC.M2.S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. Probability in Data — Estimating chances without data NC.M2.S.CP.6 Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in context. Probability in Data — Finding conditional probabilities from data, Judging how often a rule fails; Probability and Chance — Finding probability given a condition NC.M2.S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in context. Probability in Data — Adding probabilities of separate outcomes, Combining probabilities with a formula; Predicting with Probability — Combining cases into one probability; Probability and Chance — Finding the probability of either event NC.M2.S.CP.8 Apply the general Multiplication Rule P(A and B) = P(A)P(B\ A) = P(B)P(A\ B) and interpret the answer in context, including the case where A and B are independent: P(A and B) = P(A)P(B). Predicting with Probability — Applying Bayes' theorem; Probability in Data — Combining probabilities across cases, Finding probabilities of multi-step outcomes, Finding probability of two related events; Probability and Chance — Finding probability of two unrelated events, Finding the probability of both events How this page is built Every skill in the Brilliant math courses that reach North Carolina's high school mathematics is mapped to the single standard it aligns with most closely, using the North Carolina Standard Course of Study for Mathematics, adopted by the State Board of Education in June 2016, together with NCDPI's unpacking documents 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.

NC Math 2 coverage: standard-by-standard Brilliant lesson mapping

NC Math 3 standards mapped to the Brilliant lessons that teach them, from polynomials to statistical inference.

This page maps the standards of NC Math 3 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. North Carolina teaches an integrated high school pathway rather than the Algebra 1 → Geometry → Algebra 2 sequence, so each of NC Math 1, 2, and 3 mixes algebra, functions, geometry, and statistics. This page covers NC Math 3 only; NC Math 1 and NC Math 2 have their own pages. Math 3 adds polynomial, rational, exponential, and logarithmic functions, circles, trigonometric functions, and statistical inference. North Carolina writes its own codes, and they are not interchangeable with Common Core's even where the trailing part matches — NCDPI narrowed some standards, widened others, and folded several together. The codes below use dots throughout, so NCDPI's NC.M3.A-CED.1 appears here as NC.M3.A.CED.1. Number and Quantity — The Complex Number System (NC.M3.N-CN) NC standard What the standard asks Brilliant targeted skill NC.M3.N.CN.9 Use the Fundamental Theorem of Algebra to determine the number and potential types of solutions for polynomial functions. Polynomials — Relating roots and degree Algebra — Seeing Structure in Expressions (NC.M3.A-SSE) NC standard What the standard asks Brilliant targeted skill NC.M3.A.SSE.2 Use the structure of an expression to identify ways to write equivalent expressions. Logarithms — Change the base of a logarithm, Rewrite logarithms with the power rule, Rewrite logarithms with the product and quotient rules; Polynomials — Factoring out monomials, Factoring power differences, Solving by factoring; Equations and Curves — Rewriting equivalent equations, Simplifying by factoring, Simplifying rational expressions Algebra — Arithmetic with Polynomial and Rational Expressions (NC.M3.A-APR) NC standard What the standard asks Brilliant targeted skill NC.M3.A.APR.3 Understand the relationship among factors of a polynomial expression, the solutions of a polynomial equation, and the zeros of a polynomial function. Polynomials — Connecting roots and factors NC.M3.A.APR.7.a Understand the similarities between arithmetic with rational expressions and arithmetic with rational numbers: add and subtract two rational expressions a(x) and b(x) where the denominators of both are linear expressions. Equations and Curves — Adding rational expressions Algebra — Creating Equations (NC.M3.A-CED) NC standard What the standard asks Brilliant targeted skill NC.M3.A.CED.2 Create and graph equations in two variables to represent absolute value, polynomial, exponential, and rational relationships between quantities. Equations and Curves — Completing hyperbola equations, Finding equation parameters NC.M3.A.CED.3 Create systems of equations and/or inequalities to model situations in context. Equations and Curves — Building equations from intersections Algebra — Reasoning with Equations and Inequalities (NC.M3.A-REI) NC standard What the standard asks Brilliant targeted skill NC.M3.A.REI.1 Justify a solution method for equations and explain each step of the solving process using mathematical reasoning. Logarithms — Check solutions of logarithmic equations NC.M3.A.REI.11 Extend an understanding that the x-coordinates of the points where the graphs of two equations y = f(x) and y = g(x) intersect are the solutions of f(x) = g(x), and approximate solutions using graphing technology or successive approximations with a table of values. Equations and Curves — Controlling the number of intersections, Finding intersection points, Solving systems and unions of curves Functions — Interpreting Functions (NC.M3.F-IF) NC standard What the standard asks Brilliant targeted skill NC.M3.F.IF.2 Use function notation to evaluate piecewise-defined functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Introduction to Functions — Following conditional rules, Identifying conditional rules NC.M3.F.IF.4 Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities, to include periodicity and discontinuities. Trigonometric Functions — Identifying periodic function features, Predicting periodic values; Introduction to Functions — Reading discontinuous function graphs, Reading periodic function graphs NC.M3.F.IF.7 Analyze piecewise, absolute value, polynomial, exponential, rational, and trigonometric (sine and cosine) functions using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases, including domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; relative maximums and minimums; symmetries; end behavior; period; and discontinuities. Polynomials — Applying parity properties for a power function using the even or odd property'), Classifying even and odd powers, Deducing roots from symmetry, Determining sign between roots, Finding roots from graphs, Finding the y-intercept, Identifying dominant terms, Identifying sign regions, Identifying transformed features, Reading polynomial graphs, Recognizing polynomial symmetry, Using power function symmetry; Trigonometric Functions — Applying symmetry and periodicity rules; Equations and Curves — Determining domain and range, Finding asymptotes and holes, Finding hyperbola asymptotes, Finding hyperbola domain and range, Finding intercepts and sign regions, Finding vertical asymptotes, Identifying discontinuities and sign regions, Identifying power function graphs, Identifying symmetric points, Locating asymptotes, Matching rational functions to graphs, Reading intervals from hyperbolas, Reading values from graphs, Using hyperbola symmetry; Introduction to Functions — Evaluating floor and ceiling functions, Plotting conditional functions NC.M3.F.IF.9 Compare key features of two functions using different representations, by comparing properties of two different functions each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions). Polynomials — Comparing power functions Functions — Building Functions (NC.M3.F-BF) NC standard What the standard asks Brilliant targeted skill NC.M3.F.BF.1.a Build polynomial and exponential functions with real solution(s) given a graph, a description of a relationship, or ordered pairs (including reading these from a table). Polynomials — Matching equations to graphs, Matching graphs to factored form NC.M3.F.BF.1.b Build a new function, in terms of a context, by combining standard function types using arithmetic operations. Introduction to Functions — Combining functions with operations NC.M3.F.BF.3 Extend an understanding of the effects on the graphical and tabular representations of a function when replacing f(x) with k · f(x), f(x) + k, f(x + k), to include f(k · x) for specific values of k (both positive and negative). Equations and Curves — Applying reflections and equivalent stretches, Applying shifts and stretches, Combining multiple transformations, Identifying transformed graphs, Stretching and reflecting root graphs, Transforming hyperbola graphs, Transforming the square root graph, Writing transformations from constraints; Polynomials — Applying single transformations, Combining transformations; Introduction to Functions — Combining reflections and stretches, Reflecting functions across axes, Sliding Function Graphs, Stretching Function Graphs; Logarithms — Convert between log bases graphically, Transform a log graph using identities NC.M3.F.BF.4.a Understand the inverse relationship between exponential and logarithmic, quadratic and square root, and linear to linear functions, and use this relationship to solve problems using tables, graphs, and equations. Logarithms — Convert between exponential and logarithmic form, Estimate a logarithm, Evaluate a logarithm exactly, Solve logarithmic equations; Equations and Curves — Evaluating square roots of squares, Evaluating squaring and square roots, Graphing the square root function NC.M3.F.BF.4.b Determine if an inverse function exists by analyzing tables, graphs, and equations. Introduction to Functions — Determining invertibility NC.M3.F.BF.4.c If an inverse function exists for a linear, quadratic, and/or exponential function f, represent the inverse function f⁻¹ with a table, graph, or equation and use it to solve problems in terms of a context. Introduction to Functions — Finding inverse functions Functions — Linear, Quadratic, and Exponential Models (NC.M3.F-LE) NC standard What the standard asks Brilliant targeted skill NC.M3.F.LE.4 Use logarithms to express the solution to ab^(ct) = d, where a, b, c, and d are numbers, and evaluate the logarithm using technology. Logarithms — Find the exponent in an exponential equation, Solve exponential equations with logarithms Functions — Trigonometric Functions (NC.M3.F-TF) NC standard What the standard asks Brilliant targeted skill NC.M3.F.TF.1 Understand radian measure of an angle as: the ratio of the length of an arc on a circle subtended by the angle to its radius; a dimensionless measure of length defined by the quotient of arc length and radius that is a real number; and the domain for trigonometric functions. Trigonometric Functions — Constructing angles in radians, Converting degrees and radians NC.M3.F.TF.2.a Build an understanding of trigonometric functions by using tables, graphs and technology to represent the cosine and sine functions: interpret the sine function as the relationship between the radian measure of an angle formed by the horizontal axis and a terminal ray on the unit circle and its y-coordinate. Polar Coordinate Plane — Computing x and y from polar; Trigonometric Functions — Evaluating sine and cosine, Evaluating trig functions in radians, Reading sine from circular motion NC.M3.F.TF.2.b Build an understanding of trigonometric functions by using tables, graphs and technology to represent the cosine and sine functions: interpret the cosine function as the relationship between the radian measure of an angle formed by the horizontal axis and a terminal ray on the unit circle and its x-coordinate. Trigonometric Functions — Reading cosine from circular motion NC.M3.F.TF.5 Use technology to investigate the parameters a, b, and h of a sine function f(x) = a · sin(b · x) + h to represent periodic phenomena and interpret key features in terms of a context. Trigonometric Functions — Computing period from rotation speed, Finding transformed function periods, Identifying amplitude and midline, Matching functions with transformations, Transforming periodic functions Geometry — Circles (NC.M3.G-C) NC standard What the standard asks Brilliant targeted skill NC.M3.G.C.5 Using similarity, demonstrate that the length of an arc s for a given central angle is proportional to the radius r of the circle; define radian measure of the central angle as the ratio of the length of the arc to the radius, s/r; find arc lengths and areas of sectors of circles. Trigonometric Functions — Computing arc length, Constructing unit circle arcs; Polar Coordinate Plane — Computing arc lengths from angles, Computing arc lengths from fractions, Finding angles from arc lengths Geometry — Expressing Geometric Properties with Equations (NC.M3.G-GPE) NC standard What the standard asks Brilliant targeted skill NC.M3.G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem, and complete the square to find the center and radius of a circle given by an equation. Coordinate Geometry — Using the circle equation at the origin, Using the general circle equation; Equations and Curves — Writing circle and ellipse equations Geometry — Geometric Measurement and Dimension (NC.M3.G-GMD) NC standard What the standard asks Brilliant targeted skill NC.M3.G.GMD.3 Use the volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems. Geometry and Measurement — Find volume as area of the base times height, Use the one-third relationship for pyramids and cones How this page is built Every skill in the Brilliant math courses that reach North Carolina's high school mathematics is mapped to the single standard it aligns with most closely, using the North Carolina Standard Course of Study for Mathematics, adopted by the State Board of Education in June 2016, together with NCDPI's unpacking documents 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.

NC Math 3 coverage: standard-by-standard Brilliant lesson mapping

GCSE maths content statements across all six subject areas, mapped to the Brilliant lessons that teach them.

GCSE maths coverage: topic-by-topic Brilliant lesson mapping

A Level maths content, section by section across Pure and Statistics, mapped to the Brilliant lessons that teach it.

A Level maths coverage: topic-by-topic Brilliant lesson mapping

IB Math Analysis and Approaches SL syllabus items mapped to the Brilliant lessons that teach them.

IB Math AA SL coverage: syllabus-by-syllabus Brilliant lesson mapping

IB Math Analysis and Approaches HL syllabus items, core and higher level, mapped to Brilliant lessons.

IB Math AA HL coverage: syllabus-by-syllabus Brilliant lesson mapping

GRE Quantitative Reasoning topics across all four content areas, mapped to the Brilliant lessons that teach them.

GRE Quant coverage: topic-by-topic Brilliant lesson mapping

GMAT Focus Edition quantitative topics mapped to the Brilliant lessons that teach them, Quant and Data Insights.

This page maps the quantitative content of the GMAT Focus Edition to the Brilliant lessons that teach it. Search by topic or skill to find the closest match. A topic is listed only where Brilliant content fully or in part addresses it directly. The Focus Edition narrowed what the Quantitative Reasoning section asks: geometry was removed outright, and Data Sufficiency moved to the Data Insights section, which also carries table analysis, graphics interpretation, and multi-source reasoning. The rows below are grouped accordingly — the Quantitative Reasoning topics first, then the quantitative content that Data Insights assesses instead. GMAC does not publish reference codes for these topics, so the codes shown here (QR.ARI.1, DI.2, and so on) are Brilliant's own shorthand: the section's abbreviation followed by the topic's position in GMAC's ordering. Quantitative Reasoning — Arithmetic GMAT topic What the topic asks Brilliant targeted skill QR.ARI.1 Elementary operations. The four operations on integers, fractions, and decimals; signed numbers; order of operations; powers and roots applied to numbers; estimation and approximation as a route to an answer choice. Fractions — Adding fractions with different denominators, Adding fractions with shapes, Adding related fractions, Adding same-denominator fractions, Adding unrelated fractions, Multiplying fractions, Multiplying whole numbers by fractions, Shading fraction products on shapes, Showing fraction multiples on shapes, Showing fraction sums on shapes, Showing fractions of fractions, Solving fraction multiplication equations, Writing fraction multiples; Negative Numbers — Adding on the number line, Adding positive and negative numbers, Adding with signed tiles, Calculating absolute value of sums, Counting signed tile values, Evaluating expressions step by step, Rewriting subtraction as addition, Subtracting on the number line, Subtracting positive and negative numbers, Subtracting with signed tiles; Exponents and Radicals — Applying order of operations with exponents, Distinguishing negation from negative bases, Estimating with scientific notation, Evaluating cube roots and higher roots, Evaluating cubes, Evaluating expressions inside radicals, Evaluating fraction bar expressions, Evaluating general fractional exponents by applying the root and the power in either order'), Evaluating multi-operation expressions, Evaluating negative-base powers, Evaluating nested grouping expressions, Evaluating perfect squares, Evaluating powers and roots with arithmetic, Evaluating powers of negative one, Evaluating square roots, Evaluating unit fraction exponents, Evaluating whole-number powers, Evaluating zero-exponent expressions, Multiplying and dividing in scientific notation; Logarithms — Find the exponent in an exponential equation QR.ARI.2 Value, order, and factors. Comparing and ordering values; the number line and absolute value as distance; place value; factors, multiples, divisibility rules and remainders; prime numbers; greatest common divisor and least common multiple; even/odd and other integer properties; perfect squares. Negative Numbers — Calculating distance with subtraction, Comparing positive and negative numbers, Finding distance on the number line, Finding numbers at a given distance, Solving absolute value conditions; Fractions — Comparing any two fractions, Comparing fractions using shapes, Comparing fractions with matching parts, Comparing fractions with unlike denominators, Comparing same-denominator fractions, Comparing same-numerator fractions; Exponents and Radicals — Dividing with prime factorizations, Estimating magnitude with powers of ten, Estimating non-perfect square roots, Expressing numbers in scientific notation, Finding prime factorizations, Locating consecutive powers on number lines, Locating cubes on number lines, Locating multiples of powers, Locating negative powers on number lines, Multiplying with prime factorizations; Visual Algebra — Using mod notation for patterns, Using remainders to predict repeating patterns QR.ARI.3 Rates, ratios, and percents. Ratio and proportion; unit rate; speed, distance, and work rates; mixtures; percent of a quantity, percent increase and decrease; interest; profit, cost, markup, and discount. Proportional Reasoning — Adjusting ratios in mixtures, Comparing ratios with unit rates, Comparing unit prices, Finding the scale factor, Finding totals from ratios, Finding unit rates, Identifying equivalent ratios, Relating totals, rates, and amounts, Scaling by a given factor, Scaling recipes to a target, Scaling with non-whole numbers, Simplifying ratios, Writing equivalent ratios; Percents — Calculating a percentage of a number, Calculating compound percent changes, Comparing split and single changes, Computing repeated percent growth, Converting percentages to fractions, Finding the percentage from two numbers, Reversing a percentage calculation, Showing percent increases and decreases, Visualizing compound percent changes, Visualizing percentages on bars, Writing compound change expressions, Writing percent change expressions; Linear Relationships — Calculating rates of change, Finding constant change; Exponential Functions — Graph and compare compound interest functions, Write a compound growth or decay expression QR.ARI.4 Basic descriptive statistics. Mean, median, mode, range, and standard deviation (GMAC's own enumeration), including weighted averages and reasoning about how a data set's summary statistics respond to changes in the data. Everyday Statistics — Combining groups to find the mean, Comparing mean, median, and mode, 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, Seeing how outliers affect the mean, Updating the mean with new data, Updating the median with new data QR.ARI.5 Counting methods. The fundamental counting principle; permutations and combinations; systematic enumeration of possibilities. Probability and Chance — Counting outcomes across overlapping events, Counting possible outcomes Quantitative Reasoning — Algebra GMAT topic What the topic asks Brilliant targeted skill QR.ALG.1 Algebraic expressions and manipulations. Writing and simplifying algebraic expressions; combining like terms; expanding and factoring; operating on polynomial and rational expressions; applying exponent and radical rules to variable expressions; substituting into and evaluating an expression or a function. Exponents and Radicals — Adding and subtracting like square roots, Applying the power rule for exponents, Applying the product rule for exponents, Applying the quotient rule for exponents, Combining exponent rules to simplify, Connecting fractional exponents to radicals, Multiplying square root expressions, Rewriting with negative exponents, Simplifying and combining unlike radicals, Simplifying multi-base quotients, Simplifying negative exponents in denominators, Simplifying products with exponent zero, Simplifying with negative exponents; Polynomials — Adding polynomials, Applying parity properties for a power function using the even or odd property'), Evaluating polynomials, Evaluating power functions, Factoring out monomials, Factoring power differences, Finding the y-intercept, Multiplying monomials, Multiplying polynomials, Subtracting polynomials, Working with multivariable polynomials; Visual Algebra — Breaking patterns into parts, Combining pattern expressions, Identifying equivalent expressions, Seeing squares inside patterns, Writing equivalent expressions, Writing expressions as length times width; 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, Compare exponential growth to linear growth, Compare exponential growth to quadratic growth, Compare two exponential functions, Deduce an exponential function from two points, Evaluate an exponential at negative x-values, Evaluate an exponential at non-integer x-values, Evaluate an exponential expression, Express decay with a negative exponent, Find the base of an exponential function, Set the coefficient of an exponential function; Solving Equations — Combining like terms, Combining terms in equations, Distributing over a sum by distributing the factor to each term'), Distributing over groups, Factoring common factors, Factoring into groups, Reasoning with grouped expressions; Quadratics — Combining like terms, Combining signed terms, Combining terms with coefficients, Completing factors with negatives, Completing partial factorizations, Completing the square, Converting to vertex form, Determining signs in products, Evaluating quadratic equations, Expanding binomial products, Factoring signed quadratics fully, Factoring simple quadratics, Factoring with leading coefficients, Factoring with negative constants, Finding constant terms, Finding linear terms, Multiplying with area models, Multiplying with negative numbers, Plotting points on parabolas, Recognizing perfect square patterns; Linear Equations — Combining terms with decimals, Evaluating linear expressions, Finding the greatest common factor, Substituting negative values, Writing and simplifying expressions, Writing percent change expressions; Introduction to Functions — Evaluating composite functions, Following conditional rules, Following function rules, Identifying conditional rules, Identifying function rules, Matching input-output pairs, Writing composite function expressions, Writing numeric function rules; Coordinate Geometry — Writing area expressions with variables QR.ALG.2 Solving equations and inequalities. Solving linear equations; quadratic equations, including by factoring and the quadratic formula; systems of simultaneous equations; absolute-value equations; linear and simple nonlinear inequalities; reasoning about how many solutions an equation admits. Solving Equations — Chaining reasoning across equations, Checking value constraints, Choosing what to substitute, Deriving new equations, Distinguishing inequality types, Finding inequality solutions, Finding unknown values, Finding value ranges, Identifying equation results, Multiplying to eliminate, Setting up elimination, Solving after combining, Solving by subtracting equations, Solving for boundary values, Solving grouped equations, Solving one-step equations, Solving systems by combining, Solving systems by substitution, Solving with substitution, Substituting known values, Transforming equations; Quadratics — Checking solutions by substitution, Classifying solution types, Completing squares with fractions, Determining number of solutions, Isolating squared variables, Solving by completing the square, Solving equations by factoring, Solving shifted square equations^2 + k = c by undoing each operation step by step'), Solving with square roots, Using the discriminant, Using the quadratic formula; Linear Equations — Classifying equations by solutions, Combining fractional terms, Combining groups of expressions, 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 compound inequalities, 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; Polynomials — Connecting roots and factors, Solving by factoring; Linear Systems — Counting solutions to a system, Eliminating by adding equations, Scaling equations to eliminate; Linear Relationships — Identifying inequality solutions QR.ALG.3 Modeling and solving word problems with algebra. Translating a described situation into algebraic form — defining variables, writing the equation or system the situation implies — and solving it to answer the question asked; interpreting the result back in context. Linear Equations — Comparing deals with percentages, Modeling with linear equations; Linear Relationships — Evaluating linear equations, Writing linear inequalities, Writing slope-intercept equations, Writing standard form equations; Solving Equations — Translating words to inequalities, Writing balanced equations, Writing equations from scales, Writing grouped equations, Writing inequalities from scales; Linear Systems — Writing equations from constraints, Writing inequality systems; Proportional Reasoning — Writing proportional equations QR.ALG.4 Elementary probability, sequences, and partial sums. Elementary probability of single and compound events, including complements and simple independent/mutually exclusive combinations; arithmetic and geometric sequences; sums of the first n terms. Probability in Data — Adding probabilities of separate outcomes, Combining probabilities with a formula, Finding probabilities of multi-step outcomes; Visual Algebra — Building expressions from rate and start, Building sequences from rules, Describing exponential growth, Describing steady growth, Finding counts at faraway steps, Writing exponential expressions, Writing expressions for each shape, Writing rules for growing patterns, Writing separate even and odd rules; Probability and Chance — Calculating probability, Changing probability by removing options, Comparing the likelihood of outcomes, Finding probability of two unrelated events, Finding the probability of both events, Finding the probability of either event, Finding the probability something won't happen; Exponential Functions — Identify exponential decay from a dot pattern, Identify exponential growth from a dot pattern Data Insights — quantitative content outside the Quantitative Reasoning section GMAT topic What the topic asks Brilliant targeted skill DI.1 Data Sufficiency. Given a question and two statements labeled (1) and (2), decide whether the data given are sufficient to answer the question — analyzing a quantitative problem, recognizing which data are relevant, and determining at what point there is enough data to solve it, without solving it. Probability in Data — Choosing inputs for a simulation; Solving Equations — Evaluating mathematical statements DI.2 Multi-Source Reasoning. Examining data spread across two or three sources — text passages, tables, graphics, or a combination — and analyzing each source to answer several questions: recognizing discrepancies between sources, drawing inferences, and judging whether a source is relevant. Exploring Data Visually — Making a data-backed recommendation DI.3 Table Analysis. Sorting and analyzing a spreadsheet-like table of data to determine what information is relevant or meets a stated condition, and judging each of several statements true/false (or yes/no) against that condition. Exploring Data Visually — Creating new data columns, Filter a data table with conditions, Group a data table to summarize categories; Probability in Data — Estimating probabilities from past data DI.4 Graphics Interpretation. Interpreting information presented in a graph or graphical image — scatter plot, x/y graph, bar chart, pie chart, statistical curve distribution (GMAC's own list) — to discern relationships and make inferences, completing statements from drop-down choices. Linear Systems — Checking points in inequalities, Identifying inequality solutions, Reading points on a graph; Exploring Data Visually — Compare boxplots across datasets, Describe the relationship in a scatter plot, Describing how two things relate, Find frequencies and percentiles from a histogram, Find percents of a whole from a pie chart, Identify and extend a trend on a line graph, Judging how strongly things relate, Read and compare bars on a bar chart, Read coordinates of points on a scatter plot, Read median, quartiles, and extremes from a boxplot, Reading and comparing bar charts, Reading histograms, Reading line graphs, Reading pie charts, Reading scatter plots, Spotting trends over time; Everyday Statistics — Comparing data sets with box plots, Matching data to box plots, Reading box plots; Proportional Reasoning — Comparing proportional graphs, Graphing proportional relationships; Regression — Detecting hidden groups in data, Reading correlation from a scatter plot; Polynomials — Finding roots from graphs, Identifying sign regions, Reading polynomial graphs; Introduction to Functions — Identifying function intervals, Reading continuous function graphs, Reading discontinuous function graphs, Reading periodic function graphs; Linear Relationships — Interpreting intercepts, Recognizing linear relationships; Quadratics — Reading solutions from graphs How this page is built Every skill in the Brilliant math courses that reach the level the GMAT tests is mapped to the single topic it aligns with most closely, using GMAC's published content specification for the GMAT Focus Edition as the authority for what each topic requires and where its boundaries fall. Skills that build toward a topic without teaching its stated content are excluded, so a skill appears here only where it addresses the topic 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.

Alignment Mappings