ACT math coverage: Brilliant lesson mapping by score range

This page maps the mathematics standards of the ACT to the Brilliant lessons that teach them. ACT publishes its College and Career Readiness Standards in six strands — Number and Quantity, Algebra, Functions, a shared Algebra/Functions strand, Geometry, and Statistics and Probability — and groups the standards within each strand by the ACT score range at which students typically demonstrate them. Those standards are the rows below. 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.

A score range is a difficulty band, not a grade level: it describes what a student scoring in that range is likely to know and be able to do, so content taught early in school can still sit at a high range because the ACT asks harder questions about it. Each code combines the two — G.501 is a Geometry standard in the 24–27 band, and S.201 is a Statistics and Probability standard in the 13–15 band. ACT sets its College Readiness Benchmark for mathematics at a score of 22.

Number and Quantity

Score range 13–15 (N 2xx)

ACT standard	What the standard asks	Brilliant targeted skill
N.202	Recognize equivalent fractions and fractions in lowest terms	Proportional Reasoning — Identifying equivalent ratios, Simplifying ratios, Writing equivalent ratios; Fractions — Reading equivalent fractions from shapes, Recognizing equivalent fractions visually, Selecting correct fraction shapes, Shading fractions with unequal parts, Spotting incorrect fraction shapes, Writing equivalent fractions

Score range 16–19 (N 3xx)

ACT standard	What the standard asks	Brilliant targeted skill
N.303	Locate rational numbers on the number line	Negative Numbers — Locating numbers on the number line

Score range 20–23 (N 4xx)

ACT standard	What the standard asks	Brilliant targeted skill
N.401	Exhibit knowledge of elementary number concepts such as rounding, the ordering of decimals, pattern identification, primes, and greatest common factor	Visual Algebra — Describing growth that speeds up, Identifying types of growth
N.402	Write positive powers of 10 by using exponents	Exponents and Radicals — Estimating magnitude with powers of ten
N.403	Comprehend the concept of length on the number line, and find the distance between two points	Negative Numbers — Calculating distance with subtraction, Finding distance on the number line
N.404	Understand absolute value in terms of distance	Negative Numbers — Calculating absolute value of sums
N.405	Find the distance in the coordinate plane between two points with the same x-coordinate or y-coordinate	Coordinate Plane — Measuring gridline distance; Coordinate Geometry — Writing distance expressions with variables

Score range 24–27 (N 5xx)

ACT standard	What the standard asks	Brilliant targeted skill
N.501	Order fractions	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
N.503	Work with numerical factors	Exponents and Radicals — Finding prime factorizations
N.504	Exhibit some knowledge of the complex numbers	Complex Numbers — Adding and subtracting complex numbers, Evaluating expressions with i, Plotting complex numbers, Simplifying powers of i, Solving equations with complex solutions
N.505	Add and subtract matrices that have integer entries	Vectors and Matrices — Adding and subtracting matrices

Score range 28–32 (N 6xx)

ACT standard	What the standard asks	Brilliant targeted skill
N.601	Apply number properties involving prime factorization	Exponents and Radicals — Dividing with prime factorizations, Multiplying with prime factorizations
N.602	Apply number properties involving even/odd numbers and factors/multiples	Visual Algebra — Using mod notation for patterns, Using remainders to predict repeating patterns
N.603	Apply number properties involving positive/negative numbers	Negative Numbers — Adding on the number line, Adding positive and negative numbers, Adding with signed tiles, Building numbers with tiles, Comparing positive and negative numbers, Counting signed tile values, Subtracting on the number line, Subtracting positive and negative numbers, Subtracting with signed tiles
N.605	Apply properties of rational exponents	Exponents and Radicals — Connecting fractional exponents to radicals, Evaluating general fractional exponents, Evaluating unit fraction exponents; Exponential Functions — Evaluate an exponential at non-integer x-values; Equations and Curves — Evaluating roots and inverse compositions, Simplifying fractional exponents
N.606	Multiply two complex numbers	Complex Numbers — Multiplying complex numbers, Multiplying conjugate pairs, Scaling complex numbers
N.607	Use relations involving addition, subtraction, and scalar multiplication of vectors and of matrices	Vectors and Matrices — Adding vectors by components, Adding vectors from angles, Adding velocity vectors, Combining velocities from bearings, Computing relative velocity, Decomposing into linear combinations, Drawing linear combinations, Drawing vector differences, Drawing vector sums, Evaluating linear combinations, Finding opposite vectors, Identifying scalar multiples, Scaling matrices, Scaling to a target magnitude, Scaling vectors, Subtracting vectors by components, Transforming vectors with matrices, Using standard basis vectors

Score range 33–36 (N 7xx)

ACT standard	What the standard asks	Brilliant targeted skill
N.704	Apply properties of complex numbers and the complex number system	Complex Numbers — Dividing complex numbers, Evaluating real and imaginary parts, Finding complex conjugates
N.705	Multiply matrices	Vectors and Matrices — Applying matrix transformations, Composing transformations by multiplying, Multiplying matrices, Multiplying matrices by vectors, Repeating matrix transformations
N.706	Apply properties of matrices and properties of matrices as a number system	Vectors and Matrices — Determining matrix product dimensions

Algebra

Score range 13–15 (A 2xx)

ACT standard	What the standard asks	Brilliant targeted skill
A.201	Exhibit knowledge of basic expressions (e.g., identify an expression for a total as b + g)	Solving Equations — Writing balanced equations, Writing equations from scales, Writing grouped equations

Score range 16–19 (A 3xx)

ACT standard	What the standard asks	Brilliant targeted skill
A.301	Substitute whole numbers for unknown quantities to evaluate expressions	Linear Equations — Evaluating linear expressions
A.302	Solve one-step equations to get integer or decimal answers	Linear Equations — Finding missing values with negatives, Finding unknown values; Solving Equations — Finding unknown values, Solving one-step equations
A.303	Combine like terms (e.g., 2x + 5x)	Solving Equations — Combining like terms, Combining terms in equations; Linear Equations — Combining terms with decimals

Score range 20–23 (A 4xx)

ACT standard	What the standard asks	Brilliant targeted skill
A.401	Evaluate algebraic expressions by substituting integers for unknown quantities	Equations and Curves — Evaluating equations at points, Finding points on a curve, Verifying points on curves; Quadratics — Evaluating quadratic equations, Plotting points on parabolas; Linear Equations — Substituting negative values, Working with negative coefficients
A.402	Add and subtract simple algebraic expressions	Visual Algebra — Combining pattern expressions
A.403	Solve routine first-degree equations	Linear Equations — Combining fractional terms, Combining like terms to solve, Combining negatives to solve, Solving equations by distributing, 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; Solving Equations — Solving after combining, Solving grouped equations
A.404	Multiply two binomials	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
A.405	Match simple inequalities with their graphs on the number line (e.g., x ≥ –3/5)	Solving Equations — Distinguishing inequality types, Graphing inequalities; Linear Equations — Identifying inequality solutions
A.406	Exhibit knowledge of slope	Visual Algebra — Describing steady growth; Linear Relationships — Finding constant change, Graphing lines from slope

Score range 24–27 (A 5xx)

ACT standard	What the standard asks	Brilliant targeted skill
A.502	Solve real-world problems by using first-degree equations	Linear Relationships — Evaluating linear equations
A.503	Solve first-degree inequalities when the method does not involve reversing the inequality sign	Solving Equations — Finding inequality solutions, Solving for boundary values; Linear Equations — Solving multi-step inequalities, Solving one-step inequalities
A.504	Match compound inequalities with their graphs on the number line (e.g., –10.5 < x ≤ 20.3)	Linear Equations — Graphing compound inequalities, Solving compound inequalities, Writing compound inequalities
A.505	Add, subtract, and multiply polynomials	Polynomials — Adding polynomials, Multiplying monomials, Multiplying polynomials, Subtracting polynomials, Working with multivariable polynomials; Solving Equations — Distributing over a sum, Distributing over groups
A.506	Identify solutions to simple quadratic equations	Quadratics — Checking solutions by substitution, Reading solutions from graphs
A.507	Solve quadratic equations in the form (x + a)(x + b) = 0, where a and b are numbers or variables	Quadratics — Connecting intercepts to factors; Polynomials — Connecting roots and factors
A.508	Factor simple quadratics (e.g., the difference of squares and perfect square trinomials)	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; Polynomials — Factoring power differences
A.509	Work with squares and square roots of numbers	Exponents and Radicals — Adding and subtracting like square roots, Estimating non-perfect square roots, Evaluating expressions inside radicals, Evaluating perfect squares, Evaluating square roots, Multiplying square root expressions, Simplifying and combining unlike radicals; Equations and Curves — Evaluating square roots of squares, Evaluating squaring and square roots
A.510	Work with cubes and cube roots of numbers	Exponents and Radicals — Evaluating cube roots and higher roots, Evaluating cubes, Locating cubes on number lines
A.511	Work with scientific notation	Exponents and Radicals — Estimating with scientific notation, Expressing numbers in scientific notation, Multiplying and dividing in scientific notation
A.512	Work problems involving positive integer exponents	Exponents and Radicals — Applying order of operations with exponents, Applying the power rule for exponents, Applying the product rule for exponents, Applying the quotient rule for exponents, Combining exponent rules to simplify, Distinguishing negation from negative bases, Evaluating fraction bar expressions, Evaluating multi-operation expressions, Evaluating negative-base powers, Evaluating nested grouping expressions, Evaluating powers and roots with arithmetic, Evaluating powers of negative one, Evaluating whole-number powers, Identifying exponential bases, Locating consecutive powers on number lines, Locating multiples of powers, Simplifying multi-base quotients, Simplifying products with exponent zero, Simplifying with negative exponents, Writing expressions from patterns; Exponential Functions — Evaluate an exponential at negative x-values, Evaluate an exponential expression; Equations and Curves — Simplifying with exponent rules, Simplifying with exponent rules
A.513	Determine when an expression is undefined	Exponents and Radicals — Identifying zero-to-the-zero forms

Score range 28–32 (A 6xx)

ACT standard	What the standard asks	Brilliant targeted skill
A.601	Manipulate expressions and equations	Equations and Curves — Adding rational expressions, Analyzing implicit equations, Rewriting equivalent equations, Simplifying by factoring, Simplifying rational expressions; Linear Equations — Combining groups of expressions, Finding the greatest common factor, Solving equations by factoring; Quadratics — Completing the square, Converting to vertex form; Solving Equations — Constructing balanced equations, Factoring common factors, Factoring into groups, Identifying equation results, Transforming equations; Polynomials — Factoring out monomials; Coordinate Geometry — Identifying equivalent area expressions; Visual Algebra — Identifying equivalent expressions; Negative Numbers — Rewriting subtraction as addition
A.602	Solve linear inequalities when the method involves reversing the inequality sign	Linear Equations — Dividing by negatives in inequalities, Solving multi-step negative inequalities
A.604	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, Substituting known values; Linear Systems — Counting solutions to a system, Eliminating by adding equations, Finding solutions by graphing, Scaling equations to eliminate, Solving systems by graphing, Testing points in equations; Vectors and Matrices — Solving systems graphically, Solving systems with inverses
A.605	Solve quadratic equations	Quadratics — Completing squares with fractions, Isolating squared variables, Solving by completing the square, Solving equations by factoring, Solving shifted square equations, Solving with imaginary numbers, Solving with square roots, Using the quadratic formula; Polynomials — Factoring biquadratic polynomials, Solving by factoring
A.606	Solve absolute value equations	Negative Numbers — Finding numbers at a given distance

Score range 33–36 (A 7xx)

ACT standard	What the standard asks	Brilliant targeted skill
A.701	Solve simple absolute value inequalities	Negative Numbers — Solving absolute value conditions

Functions

Score range 13–15 (F 2xx)

ACT standard	What the standard asks	Brilliant targeted skill
F.201	Extend a given pattern by a few terms for patterns that have a constant increase or decrease between terms	Visual Algebra — Continuing a visual pattern; Linear Relationships — Extending linear patterns

Score range 16–19 (F 3xx)

ACT standard	What the standard asks	Brilliant targeted skill
F.301	Extend a given pattern by a few terms for patterns that have a constant factor between terms	Visual Algebra — Building sequences from rules; Exponential Functions — Identify exponential decay from a dot pattern, Identify exponential growth from a dot pattern

Score range 20–23 (F 4xx)

ACT standard	What the standard asks	Brilliant targeted skill
F.401	Evaluate linear and quadratic functions, expressed in function notation, at integer values	Introduction to Functions — Following conditional rules, Following function rules, Identifying conditional rules, Identifying function rules, Matching input-output pairs

Score range 24–27 (F 5xx)

ACT standard	What the standard asks	Brilliant targeted skill
F.501	Evaluate polynomial functions, expressed in function notation, at integer values	Polynomials — Evaluating polynomials, Evaluating power functions
F.503	Build functions and use quantitative information to identify graphs for relations that are proportional or linear	Proportional Reasoning — Comparing proportional graphs, Graphing proportional relationships, Writing proportional equations; Introduction to Functions — Plotting numeric functions; Linear Relationships — Recognizing linear relationships, Writing point-slope equations, Writing slope-intercept equations
F.505	Understand the concept of a function as having a well-defined output value at each valid input value	Introduction to Functions — Applying the vertical line test, Recognizing non-functions
F.506	Understand the concept of domain and range in terms of valid input and output, and in terms of function graphs	Logarithms — Check solutions of logarithmic equations, Find the domain of a logarithmic function; Equations and Curves — Connecting transformations to domain and range, Finding domain and range after transformations, Writing transformations from constraints; Introduction to Functions — Finding function domains, Finding function ranges
F.508	Find the domain of polynomial functions and rational functions	Equations and Curves — Determining domain and range, Finding hyperbola domain and range
F.510	Find where a rational function’s graph has a vertical asymptote	Equations and Curves — Finding asymptotes and holes, Finding hyperbola asymptotes, Finding vertical asymptotes, Locating asymptotes

Score range 28–32 (F 6xx)

ACT standard	What the standard asks	Brilliant targeted skill
F.601	Relate a graph to a situation described qualitatively in terms of faster change or slower change	Clustering & Classification — Choosing the number of clusters
F.604	Evaluate composite functions at integer values	Introduction to Functions — Evaluating composite functions

Score range 33–36 (F 7xx)

ACT standard	What the standard asks	Brilliant targeted skill
F.701	Compare actual values and the values of a modeling function to judge model fit and compare models	Regression — Measuring how well a model fits
F.702	Build functions for relations that are exponential	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, Express decay with a negative exponent, Find the base of an exponential function, Set the coefficient of an exponential function, Write a compound growth or decay expression; Visual Algebra — Writing exponential expressions
F.703	Exhibit knowledge of geometric sequences	Visual Algebra — Describing exponential growth
F.704	Exhibit knowledge of unit circle trigonometry	Polar Coordinate Plane — Computing x and y from polar, Finding quadrants from angles; Trigonometric Functions — Constructing angles in radians, Constructing unit circle angles, Converting degrees and radians, Determining tangent sign by quadrant, Evaluating sine and cosine, Evaluating tangent at an angle, Evaluating trig functions in radians, Evaluating trig values at key angles, Finding angles beyond one revolution, Finding coterminal angles, Identifying angles from geometry, Reading cosine from circular motion, Reading sine from circular motion
F.705	Match graphs of basic trigonometric functions with their equations	Trigonometric Functions — Finding transformed function periods, Identifying amplitude and midline, Matching functions with transformations
F.706	Use trigonometric concepts and basic identities to solve problems	Trigonometric Functions — Applying complementary angle relationships, Applying symmetry and periodicity rules, Computing period from rotation speed, Describing all solutions with periodicity, Factoring non-linear trig equations, Finding angle pairs for trig values, Identifying phase shift relationships, Solving equations from the tangent graph, Solving equations from trig graphs, Solving equations with inverse cosine, Solving equations with inverse sine, Solving trig equations on an interval, Using the Pythagorean identity
F.707	Exhibit knowledge of logarithms	Logarithms — Convert between exponential and logarithmic form, Estimate a logarithm, Evaluate a logarithm exactly, Find the exponent in an exponential equation, Graph a logarithmic function, Solve exponential equations with logarithms, Solve logarithmic equations
F.708	Write an expression for the composite of two simple functions	Introduction to Functions — Writing composite function expressions

Algebra and Functions

Score range 16–19 (AF 3xx)

ACT standard	What the standard asks	Brilliant targeted skill
AF.301	Solve routine one-step arithmetic problems using positive rational numbers, such as single-step percent	Fractions — Adding fractions with shapes, Adding same-denominator fractions, Multiplying fractions, Multiplying whole numbers by fractions, Shading fraction products on shapes, Showing fraction multiples on shapes, Showing fractions of fractions, Solving fraction multiplication equations, Writing fraction multiples; Percents — Calculating a percentage of a number, Finding the percentage from two numbers; Proportional Reasoning — Finding the scale factor, Finding unit rates, Scaling by a given factor
AF.302	Solve some routine two-step arithmetic problems	Fractions — Adding fractions with different denominators, Adding related fractions, Adding unrelated fractions; Negative Numbers — Evaluating expressions step by step; Visual Algebra — Finding counts when growth speeds up
AF.303	Relate a graph to a situation described qualitatively in terms of familiar properties such as before and after, increasing and decreasing, higher and lower	Exploring Data Visually — Describe the relationship in a scatter plot, Identify and extend a trend on a line graph

Score range 20–23 (AF 4xx)

ACT standard	What the standard asks	Brilliant targeted skill
AF.401	Solve routine two-step or three-step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and estimating by using a given average value in place of actual values	Proportional Reasoning — Comparing unit prices, Finding totals from ratios, Relating totals, rates, and amounts, Scaling recipes to a target, Scaling with non-whole numbers; Visual Algebra — Finding counts at faraway steps; Percents — Reversing a percentage calculation
AF.402	Perform straightforward word-to-symbol translations	Percents — Converting percentages to fractions, Writing percent change expressions; Solving Equations — Translating words to inequalities; Geometry and Measurement — Write an equation relating labeled angles; Linear Equations — Writing and simplifying expressions; Introduction to Functions — Writing numeric function rules
AF.403	Relate a graph to a situation described in terms of a starting value and an additional amount per unit (e.g., unit cost, weekly growth)	Linear Relationships — Finding starting values, Graphing real-world relationships, Reading linear patterns

Score range 24–27 (AF 5xx)

ACT standard	What the standard asks	Brilliant targeted skill
AF.501	Solve multistep arithmetic problems that involve planning or converting common derived units of measure (e.g., feet per second to miles per hour)	Regression — Rescaling for a change of units
AF.502	Build functions and write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions)	Visual Algebra — Building expressions from rate and start, Writing expressions for each shape, Writing rules for growing patterns; Linear Equations — Comparing deals with percentages, Modeling with linear equations, Writing percent change expressions; Solving Equations — Writing inequalities from scales
AF.503	Match linear equations with their graphs in the coordinate plane	Linear Relationships — Graphing from point-slope form, Graphing lines from intercepts; Coordinate Plane — Plotting horizontal and vertical lines

Score range 28–32 (AF 6xx)

ACT standard	What the standard asks	Brilliant targeted skill
AF.601	Solve word problems containing several rates, proportions, or percentages	Proportional Reasoning — Comparing ratios with unit rates
AF.602	Build functions and write expressions, equations, and inequalities for common algebra settings (e.g., distance to a point on a curve and profit for variable cost and demand)	Coordinate Geometry — Writing area expressions with variables; Linear Systems — Writing equations from constraints, Writing inequality systems; Visual Algebra — Writing expressions as length times width; Linear Relationships — Writing linear inequalities, Writing standard form equations
AF.603	Interpret and use information from graphs in the coordinate plane	Linear Systems — Checking points in inequalities, Identifying inequality solutions, Reading points on a graph; Introduction to Functions — Combining functions with operations, Identifying function intervals, Reading continuous function graphs, Reading discontinuous function graphs, Reading periodic function graphs; Equations and Curves — Finding intersection points, Reading intervals from hyperbolas, Reading values from graphs, Solving systems and unions of curves, Testing points against inequalities; Polynomials — Finding roots from graphs, Identifying sign regions, Reading polynomial graphs; Linear Relationships — Identifying inequality solutions, Interpreting intercepts; Trigonometric Functions — Identifying periodic function features, Predicting periodic values; Regression — Predicting from a regression line; Exploring Data Visually — Read coordinates of points on a scatter plot
AF.604	Given an equation or function, find an equation or function whose graph is a translation by a specified amount up or down	Logarithms — Transform a log graph using identities

Score range 33–36 (AF 7xx)

ACT standard	What the standard asks	Brilliant targeted skill
AF.701	Solve complex arithmetic problems involving percent of increase or decrease or requiring integration of several concepts (e.g., using several ratios, comparing percentages, or comparing averages)	Percents — Calculating compound percent changes, Comparing split and single changes, Computing repeated percent growth, Writing compound change expressions
AF.702	Build functions and write expressions, equations, and inequalities when the process requires planning and/or strategic manipulation	Visual Algebra — Breaking patterns into parts, Seeing squares inside patterns, Writing equivalent expressions, Writing separate even and odd rules
AF.703	Analyze and draw conclusions based on properties of algebra and/or functions	Polynomials — Applying parity properties, Comparing power functions, Determining sign between roots; Solving Equations — Chaining reasoning across equations, Checking value constraints, Deriving new equations, Deriving variable inequalities, Determining inequality direction, Evaluating mathematical statements, Finding value ranges, Reasoning with grouped expressions; Linear Equations — Classifying equations by solutions, Recognizing equations with many solutions, Recognizing equations with no solution; Quadratics — Classifying solution types, Determining number of solutions, Using the discriminant; Exponential Functions — Compare exponential growth to linear growth, Compare exponential growth to quadratic growth, Compare two exponential functions, Graph and compare compound interest functions; Visual Algebra — Comparing pattern growth rates
AF.704	Analyze and draw conclusions based on information from graphs in the coordinate plane	Polynomials — Classifying even and odd powers, Deducing roots from symmetry, Recognizing polynomial symmetry, Relating roots and degree, Using power function symmetry; Linear Systems — Classifying inequality solutions; Equations and Curves — Controlling the number of intersections; Regression — Spotting nonlinear relationships
AF.705	Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c	Equations and Curves — Building equations from intersections, Completing hyperbola equations, Finding equation parameters, Finding intercepts and sign regions, Identifying discontinuities and sign regions, Identifying power function graphs, Identifying transformed graphs, Matching equations to graphs, Matching equations to graphs, Matching rational functions to graphs; Polynomials — Finding the y-intercept, Identifying transformed features, Matching equations to graphs, Matching graphs to factored form; Quadratics — Graphing by factoring, Graphing parabolas from vertex form, Writing equations from graphs, Writing vertex form equations
AF.706	Given an equation or function, find an equation or function whose graph is a translation by specified amounts in the horizontal and vertical directions	Equations and Curves — Applying shifts and stretches, Combining multiple transformations, Shifting the square root graph, Transforming hyperbola graphs, Transforming the square root graph; Polynomials — Applying single transformations, Combining transformations; Introduction to Functions — Sliding Function Graphs; Trigonometric Functions — Transforming periodic functions

Geometry

Score range 13–15 (G 2xx)

ACT standard	What the standard asks	Brilliant targeted skill
G.201	Estimate the length of a line segment based on other lengths in a geometric figure	Coordinate Geometry — Comparing diagonal and single-direction distance, Comparing direct and gridline distance, Estimating distance between points, Placing bounds on distance, Ranking points by distance

Score range 16–19 (G 3xx)

ACT standard	What the standard asks	Brilliant targeted skill
G.301	Exhibit some knowledge of the angles associated with parallel lines	Geometry and Measurement — Compare angle measures in a diagram
G.303	Compute the area of rectangles when whole number dimensions are given	Coordinate Geometry — Calculating rectangle area

Score range 20–23 (G 4xx)

ACT standard	What the standard asks	Brilliant targeted skill
G.402	Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°)	Geometry and Measurement — Find unknown angles around a point or on a line
G.403	Compute the area and perimeter of triangles and rectangles in simple problems	Coordinate Geometry — Calculating right triangle area
G.406	Locate points in the coordinate plane	Coordinate Plane — Drawing lines through points, Reading and plotting coordinate pairs, Working with negative coordinates; Polar Coordinate Plane — Locating points from coordinates
G.407	Translate points up, down, left, and right in the coordinate plane	Coordinate Transformations — Combining translations, Reversing translations, Sliding points and shapes, Translating with coordinates; Vectors and Matrices — Representing shifts as vectors

Score range 24–27 (G 5xx)

ACT standard	What the standard asks	Brilliant targeted skill
G.501	Use several angle properties to find an unknown angle measure	Geometry and Measurement — Find a regular polygon's exterior and interior angles, Find the interior angle sum of a polygon, Find unknown angles made by lines and in triangles
G.502	Count the number of lines of symmetry of a geometric figure	Coordinate Transformations — Finding lines of symmetry, Identifying types of symmetry
G.505	Compute the perimeter of simple composite geometric figures with unknown side lengths	Geometry and Measurement — Find and compare perimeters of figures
G.507	Compute the area and circumference of circles after identifying necessary information	Geometry and Measurement — Find circumference from radius or diameter
G.509	Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths	Complex Numbers — Interpreting angle sum diagrams
G.510	Determine the slope of a line from points or a graph	Linear Relationships — Calculating rates of change, Computing slope, Finding perpendicular slopes
G.512	Find the coordinates of a point rotated 180° around a given center point	Coordinate Transformations — Computing 180-degree rotations, Rotating around any point, Translating by rotating twice

Score range 28–32 (G 6xx)

ACT standard	What the standard asks	Brilliant targeted skill
G.601	Use relationships involving area, perimeter, and volume of geometric figures to compute another measure (e.g., surface area for a cube of a given volume and simple geometric probability)	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
G.602	Use the Pythagorean theorem	Coordinate Geometry — Applying the Pythagorean theorem to areas, Finding side lengths with the Pythagorean theorem
G.603	Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent triangles	Geometry and Measurement — Match corresponding angles in similar shapes
G.604	Apply basic trigonometric ratios to solve right-triangle problems	Vectors and Matrices — Decomposing vectors with trigonometry, Drawing vectors from polar form, Using non-polar angle decomposition; Trigonometric Functions — Finding special right triangle sides
G.605	Use the distance formula	Coordinate Geometry — Calculating a circle's radius, Calculating distance from coordinates; Vectors and Matrices — Computing vector magnitude; Polar Coordinate Plane — Converting to polar coordinates; Complex Numbers — Finding absolute value, Finding complex number distance; Clustering & Classification — Finding distance with several variables
G.606	Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point	Linear Relationships — Writing parallel line equations, Writing perpendicular line equations
G.607	Find the coordinates of a point reflected across a vertical or horizontal line or across y = x	Coordinate Transformations — Computing axis reflections, Computing diagonal reflections, Reflecting across any line, Reflecting across axes, Reversing reflections, Rotating by reflecting twice, Translating by reflecting twice; Equations and Curves — Graphing the square root function, Identifying symmetric points, Using hyperbola symmetry
G.608	Find the coordinates of a point rotated 90° about the origin	Coordinate Transformations — Combining rotations, Computing quarter-turn rotations, Reversing rotations, Rotating around the origin, Rotating clockwise; Complex Numbers — Dividing by i, Rotating by multiplying by i
G.609	Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle)	Quadratics — Finding maximum and minimum values, Finding the axis of symmetry, Finding the vertex, Finding vertices using symmetry; Coordinate Geometry — Plotting shifted circles, Using the circle equation at the origin, Using the general circle equation; Equations and Curves — Writing circle and ellipse equations

Score range 33–36 (G 7xx)

ACT standard	What the standard asks	Brilliant targeted skill
G.701	Use relationships among angles, arcs, and distances in a circle	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
G.702	Compute the area of composite geometric figures when planning and/or visualization is required	Coordinate Geometry — Finding compound shape area
G.703	Use scale factors to determine the magnitude of a size change	Polar Coordinate Plane — Applying rotations and dilations; Geometry and Measurement — Find the scale factor and unknown lengths, Relate areas of similar shapes using scale factor; Coordinate Transformations — Scaling around any point, Scaling from the origin, Translating by scaling twice
G.705	Solve multistep geometry problems that involve integrating concepts, planning, and/or visualization	Coordinate Transformations — Combining rotations and translations, Combining scaling and sliding, Combining stretches with transformations, Connecting reflections and rotations

Statistics and Probability

Score range 16–19 (S 3xx)

ACT standard	What the standard asks	Brilliant targeted skill
S.302	Calculate the average given the number of data values and the sum of the data values	Everyday Statistics — Updating the mean with new data
S.303	Read basic tables and charts	Clustering & Classification — Encoding an image as numbers; Exploring Data Visually — Reading and comparing bar charts, Reading histograms, Reading line graphs, Reading scatter plots
S.304	Extract relevant data from a basic table or chart and use the data in a computation	Predicting with Probability — Adding up probabilities to a threshold, Finding the chance of a range, Reading a probability plot; Exploring Data Visually — Find frequencies and percentiles from a histogram, Find percents of a whole from a pie chart, Read and compare bars on a bar chart, Reading pie charts
S.305	Use the relationship between the probability of an event and the probability of its complement	Probability and Chance — Finding the probability something won't happen

Score range 20–23 (S 4xx)

ACT standard	What the standard asks	Brilliant targeted skill
S.403	Determine the probability of a simple event	Probability and Chance — Calculating probability; Probability in Data — Estimating probabilities from past data
S.404	Describe events as combinations of other events (e.g., using and, or, and not)	Probability in Data — Adding probabilities of separate outcomes, Combining probabilities with a formula; Probability and Chance — Finding the probability of both events, Finding the probability of either event, Using Venn diagrams
S.405	Exhibit knowledge of simple counting techniques	Probability and Chance — Counting possible outcomes

Score range 24–27 (S 5xx)

ACT standard	What the standard asks	Brilliant targeted skill
S.501	Calculate the average given the frequency counts of all the data values	Everyday Statistics — Finding the mean (the average) of a data set, Finding the mean of uneven data
S.502	Manipulate data from tables and charts	Exploring Data Visually — Create a new column from existing columns, Creating new data columns, Filter a data table with conditions, Group a data table to summarize categories; Clustering & Classification — Normalizing data to the same scale
S.503	Compute straightforward probabilities for common situations	Probability and Chance — Comparing the likelihood of outcomes
S.504	Use Venn diagrams in counting	Probability and Chance — Counting outcomes across overlapping events
S.506	Recognize that when a statistical model is used, model values typically differ from actual values	Regression — Predicting from a model equation

Score range 28–32 (S 6xx)

ACT standard	What the standard asks	Brilliant targeted skill
S.601	Calculate or use a weighted average	Probability and Chance — Calculating expected value, Calculating expected value for multiple events, Comparing expected values; Everyday Statistics — Combining groups to find the mean
S.602	Interpret and use information from tables and charts, including two-way frequency tables	Everyday Statistics — Comparing data above and below the mean; Clustering & Classification — Comparing similarity on a scatter plot, Reading a heat map of weights; Exploring Data Visually — Spotting trends over time
S.604	Compute a probability when the event and/or sample space are not given or obvious	Probability and Chance — Changing probability by removing options; Probability in Data — Finding probabilities of multi-step outcomes
S.605	Recognize the concepts of conditional and joint probability expressed in real-world contexts	Predicting with Probability — Judging how much evidence matters
S.606	Recognize the concept of independence expressed in real-world contexts	Probability and Chance — Finding probability of two unrelated events; Probability in Data — Identifying when events affect each other

Score range 33–36 (S 7xx)

ACT standard	What the standard asks	Brilliant targeted skill
S.701	Distinguish between mean, median, and mode for a list of numbers	Everyday Statistics — Comparing mean, median, and mode, Finding the median, Seeing how outliers affect the mean, Updating the median with new data
S.702	Analyze and draw conclusions based on information from tables and charts, including two-way frequency tables	Predicting with Probability — Comparing a group to everyone, Comparing two distributions; Exploring Data Visually — Describing how two things relate, Judging how strongly things relate, Making a data-backed recommendation; Regression — Detecting hidden groups in data; Clustering & Classification — Interpreting clusters, Predicting the class of new data, Spotting the variable that takes over; Probability in Data — Judging how often a rule fails
S.704	Exhibit knowledge of conditional and joint probability	Predicting with Probability — Applying Bayes' theorem, Combining cases into one probability; Probability in Data — Combining probabilities across cases, Finding conditional probabilities from data, Finding probability of two related events, Updating probabilities with new evidence; Probability and Chance — Finding probability given a condition

How this page is built

Every skill in Brilliant's math skill hierarchy is mapped to the single standard it aligns with most closely, using ACT's published College and Career Readiness Standards for Mathematics (© 2022 ACT, Inc.) 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.