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

This page maps the content of GRE Quantitative Reasoning to the Brilliant lessons that teach it. ETS organizes the measure into four content areas — arithmetic, algebra, geometry, and data analysis — and the topics within those areas are the rows below. 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 GRE tests no trigonometry, no calculus, and no formal proof. What it does test, it tests at a level most test-takers last studied years earlier, which is why the arithmetic topics below matter as much as the algebra ones.

ETS does not publish reference codes for these topics, so the codes shown here (ARI.1, ALG.4, and so on) are Brilliant's own shorthand: the content area's abbreviation followed by the topic's position in ETS's ordering of that area.

Part 1 — Arithmetic

GRE topic	What the topic asks	Brilliant targeted skill
ARI.1	Integers. Properties and types of integers: positive, negative, and zero; factors, divisors, multiples, and divisibility; least common multiple and greatest common divisor; division with quotient and remainder; even and odd integers and the parity of sums and products; prime numbers, composite numbers, and prime factorization.	Exponents and Radicals — Dividing with prime factorizations, Finding prime factorizations, Multiplying with prime factorizations; Visual Algebra — Using remainders to predict repeating patterns
ARI.2	Fractions. Numerator and denominator; equivalent fractions and reduction to lowest terms; adding, subtracting, multiplying, and dividing fractions, including common denominators and reciprocals; mixed numbers; and fractional expressions of the same forms.	Fractions — Adding fractions with different denominators, Adding related fractions, Adding same-denominator fractions, Adding unrelated fractions, Comparing any two fractions, Comparing fractions with unlike denominators, Multiplying fractions, Multiplying whole numbers by fractions, Reading equivalent fractions from shapes, Reading fractions from shapes, Recognizing equivalent fractions visually, Solving fraction multiplication equations, Writing equivalent fractions, Writing fraction multiples
ARI.3	Exponents and Roots. Exponent, base, and repeated multiplication; squaring; the sign of a negative base raised to even and odd powers; the exponent zero and negative exponents; square roots (both roots of a positive number, and the radical symbol denoting the nonnegative one); higher-order roots; and the arithmetic of radical expressions.	Exponents and Radicals — Adding and subtracting like square roots, Applying order of operations with exponents, Distinguishing negation from negative bases, Estimating magnitude with powers of ten, Estimating non-perfect square roots, Evaluating cube roots and higher roots, Evaluating cubes, Evaluating expressions inside radicals, Evaluating fraction bar expressions, 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 whole-number powers, Identifying exponential bases, Locating consecutive powers on number lines, Locating cubes on number lines, Locating multiples of powers, Locating negative powers on number lines, Multiplying square root expressions, Simplifying and combining unlike radicals, Writing expressions from patterns; Exponential Functions — Evaluate an exponential at negative x-values, Evaluate an exponential at non-integer x-values, Evaluate an exponential expression
ARI.5	Real Numbers. The real numbers as the rationals together with the irrationals; the real number line and the correspondence between points and numbers; the ordering relations `<`, `>`, `≤`, `≥` and their reading off the line; intervals and their four endpoint-inclusion types; absolute value as distance from 0 on the number line; and the twelve general properties of real numbers (commutativity, associativity, distributivity, identities and inverses, the zero-product property, division by zero being undefined, and the sign rules for sums and products).	Negative Numbers — Adding on the number line, Adding positive and negative numbers, Adding with signed tiles, Building numbers with tiles, Calculating absolute value of sums, Calculating distance with subtraction, Comparing positive and negative numbers, Counting signed tile values, Finding distance on the number line, Finding numbers at a given distance, Locating numbers on the number line, Rewriting subtraction as addition, Solving absolute value conditions, Subtracting on the number line, Subtracting positive and negative numbers, Subtracting with signed tiles; Linear Equations — Graphing compound inequalities, Writing compound inequalities
ARI.6	Ratio. Expressing the relative size of two positive quantities as a fraction, as "s to t", or as "s : t"; reducing a ratio to lowest terms; three-or-more-term ratios; and proportion as an equation relating two ratios, solved by cross multiplication.	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
ARI.7	Percent. Percent as "per hundred"; converting among percents, fractions, and decimals; computing a percent given the part and the whole; finding the part or the whole given a percent; percents greater than 100 and less than 1; and percent increase, percent decrease, and percent change.	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, Writing compound change expressions, Writing percent change expressions

Part 2 — Algebra

GRE topic	What the topic asks	Brilliant targeted skill
ALG.1	Algebraic Expressions. Variables, terms, like terms, constant terms, and coefficients; polynomials, the degree of a term and of a polynomial, and quadratic and cubic polynomials; adding, subtracting, and multiplying expressions; factoring out a common factor; factoring by pattern (difference of squares, perfect squares, and the standard quadratic factorizations); and simplifying rational algebraic expressions by factoring numerator and denominator.	Polynomials — Adding polynomials, Factoring out monomials, Factoring power differences, Multiplying monomials, Multiplying polynomials, Subtracting polynomials, Working with multivariable polynomials; Visual Algebra — Breaking patterns into parts, Building expressions from rate and start, Combining pattern expressions, Identifying equivalent expressions, Seeing squares inside patterns, Writing equivalent expressions, Writing expressions as length times width, Writing expressions for each shape, Writing rules for growing patterns, Writing separate even and odd rules; Solving Equations — Combining like terms, Distributing over a sum, Distributing over groups, Factoring common factors, Factoring into groups, Reasoning with grouped expressions, Writing grouped equations; Quadratics — Combining like terms, Combining signed terms, Combining terms with coefficients, Completing factors with negatives, Completing partial factorizations, Completing the square, 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 area models, Multiplying with negative numbers, 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; Coordinate Geometry — Identifying equivalent area expressions
ALG.2	Rules of Exponents. The seven rules of exponents on a variable base — negative exponents as reciprocals, the product and quotient rules, a power of a power, distributing an exponent over a product or quotient, the zero exponent — together with the equal-base principle (if `x^a = x^b` with `x` positive and `x ≠ 1`, then `a = b`) and the treatment of fractional exponents as roots.	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, Connecting fractional exponents to radicals, Evaluating general fractional exponents, Evaluating unit fraction exponents, Evaluating zero-exponent expressions, Multiplying and dividing in scientific notation, 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; Logarithms — Find the exponent in an exponential equation
ALG.3	Solving Linear Equations. Equations, solutions, and equivalent equations; the three rules for producing equivalent equations; solving a linear equation in one variable by combining like terms and isolating the variable; linear equations in two variables; and solving systems of two linear equations in two variables by substitution and by elimination, including recognizing when a system has no solution or infinitely many.	Solving Equations — Chaining reasoning across equations, Choosing what to substitute, Combining terms in equations, Deriving new equations, Finding unknown values, Identifying equation results, Multiplying to eliminate, Setting up elimination, Solving after combining, Solving by subtracting equations, Solving grouped equations, Solving one-step equations, Solving systems by combining, Solving systems by substitution, Solving with substitution, Substituting known values, Transforming equations; 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, 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; Linear Systems — Counting solutions to a system, Eliminating by adding equations, Scaling equations to eliminate, Testing points in equations
ALG.4	Solving Quadratic Equations. The standard form `ax² + bx + c = 0` with `a ≠ 0`; the fact that a quadratic has zero, one, or two real solutions; solving with the quadratic formula, including reading the expression under the radical; and solving by factoring and applying the zero-product property.	Quadratics — 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, Solving with square roots, Using the discriminant, Using the quadratic formula; Polynomials — Connecting roots and factors, Factoring biquadratic polynomials, Solving by factoring
ALG.5	Solving Linear Inequalities. The four inequality signs; inequality as a statement about a solution set; equivalent inequalities; and the two rules for solving — adding or subtracting a constant preserves direction, and multiplying or dividing by a negative constant reverses it.	Solving Equations — Distinguishing inequality types, Finding inequality solutions, Graphing inequalities, Solving for boundary values, Translating words to inequalities, Writing inequalities from scales; Linear Equations — Dividing by negatives in inequalities, Identifying inequality solutions, Solving compound inequalities, Solving multi-step inequalities, Solving multi-step negative inequalities, Solving one-step inequalities
ALG.6	Functions. Function notation `f(x)`; a function as a rule taking each input to exactly one output, while different inputs may share an output; evaluating a function at a value; and the domain of a function, both when stated explicitly and when it is the set of inputs for which the output is a real number (excluding division by zero and even roots of negatives).	Introduction to Functions — Applying the vertical line test, Finding function domains, Following conditional rules, Following function rules, Identifying conditional rules, Identifying function rules, Matching input-output pairs, Recognizing non-functions, Writing numeric function rules; Polynomials — Evaluating polynomials, Evaluating power functions
ALG.7	Applications. Translating verbal descriptions into algebraic expressions and equations, then solving them: average (arithmetic mean) problems, mixture problems, rate problems, work problems, and interest problems — both simple annual interest and compound interest, where interest is added to the principal at regular intervals.	Linear Equations — Comparing deals with percentages, Modeling with linear equations, Writing percent change expressions; Linear Relationships — Evaluating linear equations, Reading linear patterns; Exponential Functions — Graph and compare compound interest functions, Write a compound growth or decay expression; Linear Systems — Writing equations from constraints, Writing inequality systems
ALG.8	Coordinate Geometry. The rectangular (xy-) coordinate system: axes, origin, quadrants, ordered pairs, and locating points; reflections of a point about the axes and the origin; the distance between two points; the slope of a line through two points as rise over run, including horizontal and vertical lines; slope-intercept form `y = mx + b`, x- and y-intercepts, and the parallel and perpendicular slope conditions; graphing linear equations and linear inequalities, including shaded solution regions and systems of inequalities; graphing quadratic equations as parabolas; and graphing circles in the plane.	Coordinate Geometry — Calculating a circle's radius, Calculating distance from coordinates, Estimating distance between points, Plotting shifted circles, Using the circle equation at the origin, Using the general circle equation, Writing distance expressions with variables; Linear Relationships — Calculating rates of change, Computing slope, Extending linear patterns, Finding constant change, Finding perpendicular slopes, Finding starting values, Graphing from point-slope form, Graphing linear inequalities, Graphing lines from intercepts, Graphing lines from slope, Graphing real-world relationships, Identifying inequality solutions, Interpreting intercepts, Writing linear inequalities, Writing parallel line equations, Writing perpendicular line equations, Writing point-slope equations, Writing slope-intercept equations, Writing standard form equations; Linear Systems — Checking points in inequalities, Classifying inequality solutions, Finding solutions by graphing, Graphing inequality constraints, Graphing inequality solutions, Identifying inequality solutions, Reading points on a graph, Solving systems by graphing; Coordinate Plane — Combining two inequalities, Distinguishing x and y coordinates, Drawing lines through points, Identifying strip regions, Identifying the origin, Identifying the x-axis and y-axis, Measuring gridline distance, Plotting horizontal and vertical lines, Reading and plotting coordinate pairs, Reading solid and dashed boundaries, Shading regions for inequalities, Working with negative coordinates; Proportional Reasoning — Comparing proportional graphs, Graphing proportional relationships, Writing proportional equations; Quadratics — Connecting intercepts to factors, Evaluating quadratic equations, Graphing by factoring, Writing equations from graphs
ALG.9	Graphs of Functions. Graphing a function in the xy-plane by plotting `(x, f(x))`; the graphs of the elementary functions ETS presents — linear, quadratic (the parabola), absolute value (V-shaped, expressed piecewise), and square root (half a parabola on its side); reading intercepts, the vertex, the domain and range, and points of intersection off a graph, and finding intersections algebraically; reflections about the x-axis and about the line `y = x`; and the general transformation rules — `h(x) + c` and `h(x) − c` shift the graph up and down, `h(x + c)` and `h(x − c)` shift it left and right, and `c·h(x)` stretches or shrinks it vertically according to whether `c` is greater or less than 1.	Polynomials — Applying single transformations, Combining transformations, Finding roots from graphs, Finding the y-intercept, Identifying transformed features, Reading polynomial graphs; Introduction to Functions — Combining reflections and stretches, Finding function ranges, Plotting conditional functions, Plotting numeric functions, Reading continuous function graphs, Reading discontinuous function graphs, Reflecting functions across axes, Sliding Function Graphs, Stretching Function Graphs; Quadratics — Converting to vertex form, Finding maximum and minimum values, Finding the axis of symmetry, Finding the vertex, Finding vertices using symmetry, Graphing parabolas from vertex form, Plotting points on parabolas, Reading solutions from graphs, Writing vertex form equations

Part 3 — Geometry

GRE topic	What the topic asks	Brilliant targeted skill
GEO.1	Lines and Angles. Lines, line segments, endpoints, congruent segments, and midpoints; the four angles formed by two intersecting lines and the equality of opposite (vertical) angles; angle notation and measurement in degrees; right, acute, obtuse, and straight angles and perpendicular lines; parallel lines; and the angle relationships formed when a transversal crosses two parallel lines.	Geometry and Measurement — Compare angle measures in a diagram, Find unknown angles around a point or on a line, Find unknown angles made by lines and in triangles, Write an equation relating labeled angles
GEO.2	Polygons. Polygon, sides, and vertices, with "polygon" meaning convex polygon throughout; dividing an n-sided polygon into n − 2 triangles and the resulting interior-angle sum `(n − 2)(180°)`; regular polygons and the measure of each of their angles; and the perimeter and the area of a polygon.	Geometry and Measurement — Find a regular polygon's exterior and interior angles, Find and compare perimeters of figures, Find the interior angle sum of a polygon; Coordinate Geometry — Finding compound shape area, Writing area expressions with variables
GEO.3	Triangles. Three sides and three interior angles summing to 180°; the triangle inequality; the three special triangles ETS names — equilateral, isosceles (with the equal-angles-opposite-equal-sides relation and its converse), and right, with hypotenuse and legs; the Pythagorean theorem and its use to find a missing side; the 45°-45°-90° and 30°-60°-90° triangles and their side ratios; the area formula `A = ½bh` with base and height; and congruent and similar triangles, including corresponding parts and the proportionality of corresponding sides.	Coordinate Geometry — Applying the Pythagorean theorem to areas, Calculating right triangle area, Finding side lengths with the Pythagorean theorem; Geometry and Measurement — Find the scale factor and unknown lengths, Match corresponding angles in similar shapes, Relate areas of similar shapes using scale factor
GEO.4	Quadrilaterals. Four sides and four interior angles summing to 360°; the four special types ETS names — rectangle (four right angles, opposite sides parallel and congruent, congruent diagonals), square (a rectangle with four congruent sides), parallelogram (both pairs of opposite sides parallel, with opposite sides and opposite angles congruent), and trapezoid (at least one pair of parallel sides, called the bases) — and the area formulas for each, including the trapezoid's `A = ½(b₁ + b₂)h`.	Coordinate Geometry — Calculating rectangle area
GEO.5	Circles. Center, radius, diameter, chord, and congruent circles; circumference, π as the constant ratio of circumference to diameter, and `C = 2πr`; arcs, including the length of an arc as the corresponding fraction of the circumference; the area `A = πr²`; sectors, whose area is the same fraction of the circle's area as the arc's degree measure is of 360°; tangent lines and their perpendicularity to the radius at the point of tangency; central angles and inscribed angles; and polygons inscribed in and circumscribed about circles.	Geometry and Measurement — Find circumference from radius or diameter
GEO.6	Three-Dimensional Figures. The basic solids ETS names — rectangular solids, cubes, cylinders, spheres, pyramids, and cones — with detailed treatment of the rectangular solid (six rectangular faces, 12 edges, 8 vertices; length, width, height; volume `V = ℓwh`; surface area as the sum of the six faces) and the right circular cylinder (two congruent parallel circular bases, the axis, the height, the volume `V = πr²h`, and the surface area as the two bases plus the lateral surface).	Geometry and Measurement — Compare volumes by slicing and rearranging, Find surface area by adding face areas, Find surface area from base area and perimeter, Find volume as area of the base times height, Use the one-third relationship for pyramids and cones

Part 4 — Data Analysis

GRE topic	What the topic asks	Brilliant targeted skill
DAT.1	Methods for Presenting Data. Quantitative and categorical variables and the distribution of a variable; frequency, frequency distributions, relative frequency, and relative frequency distributions; tables as a presentation method; and the graphical methods ETS reviews — bar graphs, segmented bar graphs, histograms, circle (pie) graphs, scatterplots, and line graphs — including reading values and trends off each.	Regression — Choosing the best predictor, Detecting hidden groups in data, Predicting from a regression line, Reading correlation from a scatter plot, Spotting nonlinear relationships; Exploring Data Visually — Choosing the right chart, 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, Group a data table to summarize categories, 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, Reading and comparing bar charts, Reading histograms, Reading line graphs, Reading pie charts, Reading scatter plots, Spotting trends over time
DAT.2	Numerical Methods for Describing Data. Statistics grouped as measures of central tendency, position, and dispersion: the arithmetic mean (including weighted means), median, and mode; quartiles (Q₁, Q₂ = the median, Q₃) and percentiles, and the boxplot that displays them; and the range, the interquartile range `Q₃ − Q₁`, and the standard deviation, computed from each value's deviation from the mean, together with outliers and the standardization of a data value in standard-deviation units.	Everyday Statistics — Combining groups to find 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, 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, Spotting outliers, Updating the mean with new data, Updating the median with new data, Using the outlier rule; Exploring Data Visually — Compare boxplots across datasets, Read median, quartiles, and extremes from a boxplot
DAT.3	Counting Methods. Sets and lists, members and elements, finite and infinite sets, subsets, the empty set, and set size notation; intersection, union, disjoint (mutually exclusive) sets, the inclusion-exclusion principle, and Venn diagrams for two or three sets; the multiplication principle for independent successive choices; permutations and factorial notation, including permutations of k objects from n; and combinations, with the number of k-element subsets of an n-element set.	Probability and Chance — Counting outcomes across overlapping events, Counting possible outcomes, Using Venn diagrams
DAT.4	Probability. Probability experiments, outcomes, sample spaces, and events; probability as a number from 0 to 1 with the probabilities of all outcomes summing to 1; the probability of an event under equally likely outcomes as a ratio of counts; the events "E and F" and "E or F"; mutually exclusive events; and the three rules — inclusion-exclusion for `P(E or F)`, its simplification when E and F are mutually exclusive, and `P(E and F) = P(E)P(F)` when E and F are independent, together with the fact that two events of positive probability cannot be both mutually exclusive and independent.	Probability in Data — Adding probabilities of separate outcomes, Combining probabilities across cases, Combining probabilities with a formula, Estimating probabilities from past data, Finding conditional probabilities from data, Finding probabilities of multi-step outcomes, Finding probability of two related events, Identifying when events affect each other, Judging how often a rule fails; Probability and Chance — Calculating probability, Changing probability by removing options, Comparing the likelihood of outcomes, Finding probability given a condition, 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; Predicting with Probability — Combining cases into one probability
DAT.5	Distributions of Data, Random Variables, and Probability Distributions. Distributions of data shown as relative frequency histograms, with the mean, median, and standard deviation located on the picture; random variables as variables whose values depend on chance; the link that a random variable's probability distribution is the same as the relative frequency distribution of the data; the mean of a random variable, also called its expected value, computed as a probability-weighted sum; continuous probability distributions and density curves; and the normal distribution — bell-shaped, with mean, median, and mode nearly equal, symmetric grouping about the mean, about two-thirds of the data within one standard deviation and almost all within two.	Predicting with Probability — Adding up probabilities to a threshold, Reading a probability plot; Probability and Chance — Calculating expected value, Calculating expected value for multiple events, Comparing expected values
DAT.6	Data Interpretation. Answering multi-part questions against a single data presentation: reading exact and approximate values out of a table or graph, combining them with percent, ratio, and descriptive-statistics reasoning, computing changes and percent changes across categories or years, and evaluating whether given statements about the presentation are true.	Exploring Data Visually — Create a new column from existing columns, Creating new data columns, Filter a data table with conditions

How this page is built

Every skill in the Brilliant math courses that reach the level the GRE tests is mapped to the single topic it aligns with most closely, using ETS's published content specification for the Quantitative Reasoning measure of the GRE General Test, together with its Math Review 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.