TSI Assessment (TSIA2) math coverage: Brilliant lesson mapping by subcategory

This page maps the mathematics content of the Texas Success Initiative Assessment (TSIA2) to the Brilliant lessons that teach it. Search by subcategory or skill to find the closest match. A subcategory is listed only where Brilliant content fully or in part addresses it directly.

The College Board publishes no codes for TSIA2's content, so the codes below are Brilliant's own shorthand: the prefix is the content category — QR Quantitative Reasoning, AR Algebraic Reasoning, GSR Geometric and Spatial Reasoning, PSR Probabilistic and Statistical Reasoning — and the number is the subcategory's position in the specification's own Table 1. To check one against the source, count into that category's list.

TSIA2 Mathematics is two tests. Every test taker sits the 20-item College Readiness Classification test first; anyone scoring below the state's college-readiness standard is routed into a 48-item Diagnostic test. Seven subcategories — QR.1 to QR.3, GSR.1, GSR.2, PSR.1 and PSR.2 — appear on the Diagnostic test only, so the lessons listed against them build skills the classification test does not itself measure.

Quantitative Reasoning

TSIA2 subcategory	What the content subcategory asks	Brilliant targeted skill
QR.1	Perform basic math operations with whole numbers and integers, decimals, and fractions. The student will use mathematical symbols to represent words that represent those symbols, and add, subtract, multiply, and divide whole numbers, decimals, and fractions. (Diagnostic only)	Fractions — Adding fractions with different denominators, Adding related fractions, Adding same-denominator fractions, Adding unrelated fractions, Multiplying fractions, Multiplying whole numbers by 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, Calculating distance with subtraction, Counting signed tile values, Evaluating expressions step by step, Subtracting on the number line, Subtracting positive and negative numbers, Subtracting with signed tiles; Exponents and Radicals — Applying order of operations with exponents, Evaluating expressions inside radicals, Evaluating fraction bar expressions, Evaluating multi-operation expressions, Evaluating nested grouping expressions, Evaluating powers and roots with arithmetic
QR.3	Compare numbers in a variety of forms, including decimals, fractions, and percents. The student will compare and order whole numbers, decimals, and fractions, including on a number line. (Diagnostic only)	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; Negative Numbers — Comparing positive and negative numbers
QR.4	Compare magnitudes of rational and irrational numbers. The student will apply math operations to rational and irrational numbers.	Exponents and Radicals — Estimating magnitude with powers of ten, Estimating non-perfect square roots, Estimating with scientific notation, Expressing numbers in scientific notation, Locating consecutive powers on number lines, Locating cubes on number lines, Locating multiples of powers, Locating negative powers on number lines
QR.5	Solve problems with ratios, proportions, and percents. The student will apply ratios, proportions, and percents to solve problems.	Proportional Reasoning — Adjusting ratios in mixtures, Comparing ratios with unit rates, Finding the scale factor, Finding totals from ratios, Finding unit rates, Identifying equivalent ratios, 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, Writing compound change expressions, Writing percent change expressions; Geometry and Measurement — Find the scale factor and unknown lengths; Real-World Algebra — Finding a percent of an amount, Scaling prices
QR.6	Solve proportional relationship problems in context (e.g., linear relationships in financial literacy and numeracy). The student will formulate a solution to a real-world situation based on the solution to a mathematical problem.	Proportional Reasoning — Checking for proportionality, Comparing unit prices, Predicting with a proportional model, Relating totals, rates, and amounts; Linear Relationships — Find the input that reaches a target value, Graphing real-world relationships; Linear Equations — Interpret a linear solution in context, Modeling with linear equations; Real-World Algebra — Using a formula, Writing formulas with variables
QR.7	Identify, manipulate, and interpret linear equations, inequalities, and expressions. The student will recognize and use algebraic properties, concepts, procedures, and algorithms to combine, transform, evaluate, and interpret expressions and equations.	Visual Algebra — Building expressions from rate and start, Combining pattern expressions, Comparing pattern growth rates, Writing expressions for each shape, Writing rules for growing patterns, Writing separate even and odd rules; Linear Relationships — Calculating rates of change, Classify a relationship as linear and proportional, Computing slope, Finding constant change, Finding starting values, Graphing from point-slope form, Graphing linear inequalities, Graphing lines from intercepts, Graphing lines from slope, Identifying inequality solutions, Interpreting intercepts, Writing linear inequalities, Writing point-slope equations, Writing slope-intercept equations, Writing standard form equations; Solving Equations — Chaining reasoning across equations, Checking value constraints, Combining like terms, Combining terms in equations, Constructing balanced equations, Deriving new equations, Deriving variable inequalities, Determining inequality direction, Distinguishing inequality types, Distributing over a sum, Distributing over groups, Evaluating mathematical statements, Factoring common factors, Factoring into groups, Graphing inequalities, Identifying equation results, Reasoning with grouped expressions, Transforming equations, Translating words to inequalities, Writing balanced equations, Writing equations from scales, Writing grouped equations, Writing inequalities from scales; Linear Equations — Combining terms with decimals, Evaluating linear expressions, Finding the greatest common factor, Graphing compound inequalities, Identifying inequality solutions, Substituting negative values, Writing and simplifying expressions, Writing compound inequalities, Writing percent change expressions; Proportional Reasoning — Comparing proportional graphs, Graphing proportional relationships, Writing proportional equations; Linear Systems — Graphing inequality constraints, Writing equations from constraints, Writing inequality systems; Negative Numbers — Rewriting subtraction as addition; Geometry and Measurement — Write an equation relating labeled angles; Introduction to Functions — Writing numeric function rules

Algebraic Reasoning

TSIA2 subcategory	What the content subcategory asks	Brilliant targeted skill
AR.1	Solve linear equations, inequalities, and systems of linear equations. The student will recognize and use algebraic properties, concepts, procedures, and algorithms to solve equations, inequalities, and systems of linear equations, as well as make connections among graphical, tabular, and algebraic representations.	Linear Systems — Checking points in inequalities, Classifying inequality solutions, Counting solutions to a system, Eliminating by adding equations, Finding solutions by graphing, Graphing inequality solutions, Identifying inequality solutions, Interpret the solution of a system in context, Reading points on a graph, Scaling equations to eliminate, Set up a system from a scenario, Solving systems by graphing, Testing points in equations; Solving Equations — Choosing what to substitute, Finding inequality solutions, Finding unknown values, Finding value ranges, 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; Linear Equations — Classifying equations by solutions, Combining fractional terms, Combining groups of expressions, Combining like terms to solve, Combining negatives to solve, Comparing deals with percentages, Dividing by negatives in inequalities, Finding missing values with negatives, Finding unknown values, 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
AR.2	Evaluate linear functions. The student will evaluate a linear function for a particular value.	Linear Relationships — Evaluating linear equations, Reading linear patterns; Introduction to Functions — Following function rules, Identifying function rules, Matching input-output pairs
AR.3	Solve quadratic and exponential relationship problems in context (e.g., exponential decay/growth, compound interest, and depreciation). The student will formulate a solution to a real-world situation based on the solution to a mathematical problem.	Quadratics — Finding the best possible value, Finding when objects arrive, Interpreting results in context, Predicting whether a target is reached, Understanding motion equations, Writing equations for motion, Writing equations for real situations; Exponential Functions — Graph and compare compound interest functions, Write a compound growth or decay expression, Write a function for a growth or decay scenario
AR.4	Identify and manipulate quadratic, polynomial, exponential, rational, and radical equations and expressions. The student will recognize and use algebraic properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions and equations.	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, Distinguishing negation from negative bases, Dividing with prime factorizations, Evaluating cube roots and higher roots, Evaluating cubes, Evaluating general fractional exponents, Evaluating negative-base powers, Evaluating perfect squares, Evaluating powers of negative one, Evaluating square roots, Evaluating unit fraction exponents, Evaluating whole-number powers, Evaluating zero-exponent expressions, Identifying exponential bases, Multiplying and dividing in scientific notation, Multiplying square root expressions, Multiplying with prime factorizations, 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, Writing expressions from patterns; Polynomials — Adding polynomials, Factoring out monomials, Factoring power differences, Multiplying monomials, Multiplying polynomials, Subtracting polynomials, Working with multivariable polynomials; Equations and Curves — Adding rational expressions, Rewriting equivalent equations, Simplifying by factoring, Simplifying fractional exponents, Simplifying rational expressions, Simplifying with exponent rules, Simplifying with exponent rules; Visual Algebra — Breaking patterns into parts, Identifying equivalent expressions, Seeing squares inside patterns, Writing equivalent expressions, Writing exponential expressions, Writing expressions as length times width; Exponential Functions — Build a decay function with a fractional base, Deduce an exponential function from two points, Evaluate an exponential expression, Express decay with a negative exponent, Find the base of an exponential function, Identify exponential decay from a dot pattern, Identify exponential growth from a dot pattern, Set the coefficient of an exponential function; 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, 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
AR.5	Solve equations and evaluate functions (e.g., quadratic, polynomial, exponential, rational, and radical). The student will recognize and use algebraic properties, concepts, procedures, and algorithms to solve equations and evaluate functions, as well as make connections among graphical, tabular, and algebraic representations.	Polynomials — Applying parity properties, Connecting roots and factors, Deducing roots from symmetry, Evaluating polynomials, Evaluating power functions, Factoring biquadratic polynomials, Finding roots from graphs, Finding the y-intercept, Identifying transformed features, Matching equations to graphs, Matching graphs to factored form, Reading polynomial graphs, Solving by factoring; Exponential Functions — 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, Evaluate an exponential at negative x-values, Evaluate an exponential at non-integer x-values; Quadratics — Checking solutions by substitution, Completing squares with fractions, Connecting intercepts to factors, 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, Isolating squared variables, Plotting points on parabolas, Reading solutions from graphs, Solving by completing the square, Solving equations by factoring, Solving shifted square equations, Solving with square roots, Using the quadratic formula, Writing equations from graphs, Writing vertex form equations; Equations and Curves — Evaluating equations at points, Evaluating squaring and square roots, Finding intersection points, Finding points on a curve, Identifying power function graphs, Identifying transformed graphs, Matching equations to graphs, Matching rational functions to graphs, Verifying points on curves; Logarithms — Find the exponent in an exponential equation; Introduction to Functions — Reading continuous function graphs

Geometric and Spatial Reasoning

TSIA2 subcategory	What the content subcategory asks	Brilliant targeted skill
GSR.2	Identify and define types of angles. The student will identify and define angles including supplementary, complementary, and vertical angles. (Diagnostic only)	Geometry and Measurement — Find unknown angles around a point or on a line
GSR.4	Find perimeter, area, surface area, and volume using a variety of methods, including estimation. The student will recognize, identify, and validate properties of two- and three-dimensional figures, as well as calculate perimeter, area, surface area, and volume of figures.	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, Use the one-third relationship for pyramids and cones
GSR.5	Use transformations to investigate congruence, similarity, and symmetry. The student will identify and apply transformations to figures.	Coordinate Transformations — Combining rotations, Combining rotations and translations, Combining scaling and sliding, Combining translations, Computing 180-degree rotations, Computing axis reflections, Computing diagonal reflections, Computing quarter-turn rotations, Connecting reflections and rotations, Finding lines of symmetry, Finding rotational symmetry, Identifying types of symmetry, Proving congruence, Proving similarity, Recognizing mirror images, Reflecting across any line, Reflecting across axes, Reversing reflections, Reversing rotations, Reversing translations, Rotating around any point, Rotating around the origin, Rotating by reflecting twice, Rotating clockwise, Scaling around any point, Scaling from the origin, Sliding points and shapes, Translating by reflecting twice, Translating by rotating twice, Translating by scaling twice, Translating with coordinates; Geometry and Measurement — Match corresponding angles in similar shapes, Relate areas of similar shapes using scale factor
GSR.6	Apply right triangle relationships and basic trigonometry. The student will apply right angle relationships and use basic trigonometric ratios to solve problems.	Coordinate Geometry — Applying the Pythagorean theorem to areas, Finding side lengths with the Pythagorean theorem; Trigonometric Functions — Finding special right triangle sides
GSR.7	Make connections between geometry and algebraic equations. The student will make connections between geometry and algebra.	Coordinate Geometry — Calculating a circle's radius, Calculating distance from coordinates, Calculating rectangle area, Calculating right triangle area, Finding compound shape area, Identifying equivalent area expressions, Plotting shifted circles, Using the circle equation at the origin, Using the general circle equation, Writing area expressions with variables, Writing distance expressions with variables; Clustering & Classification — Finding distance with several variables; Linear Relationships — Finding perpendicular slopes, Writing parallel line equations, Writing perpendicular line equations; Coordinate Plane — Measuring gridline distance, Plotting horizontal and vertical lines; Equations and Curves — Writing circle and ellipse equations

Probabilistic and Statistical Reasoning

TSIA2 subcategory	What the content subcategory asks	Brilliant targeted skill
PSR.1	Sort and count data. The student will sort and count data. (Diagnostic only)	Exploring Data Visually — Group a data table to summarize categories
PSR.3	Compute and interpret probability. The student will compute and interpret the probability of an event and its complement.	Probability in Data — Adding probabilities of separate outcomes, Estimating chances without data; Probability and Chance — Calculating probability, Changing probability by removing options, Comparing the likelihood of outcomes, Finding the probability of both events, Finding the probability of either event, Finding the probability something won't happen
PSR.4	Compute and describe measures of center and spread of data. The student will compute and describe summary statistics of 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, 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
PSR.5	Classify data and construct appropriate representations of data. The student will identify appropriate representations of data based on its type.	Exploring Data Visually — Choosing the right chart, Reading histograms; Everyday Statistics — Matching data to box plots
PSR.6	Analyze, interpret, and draw conclusions from data. The student will determine types of data, analyze given information, and determine a solution.	Exploring Data Visually — Compare boxplots across datasets, Describe the relationship in a scatter plot, Describing how two things relate, Filter a data table with conditions, 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, Making a data-backed recommendation, 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 line graphs, Reading pie charts, Reading scatter plots, Spotting trends over time; Everyday Statistics — Comparing data above and below the mean, Comparing data sets with box plots, Reading box plots, Spotting outliers; Regression — Detecting hidden groups in data; Probability in Data — Estimating probabilities from past data; Clustering & Classification — Interpreting clusters

How this page is built

Every skill in Brilliant's math skill hierarchy is mapped to the single content subcategory it aligns with most closely, using the College Board's TSIA2 Mathematics Test Specifications, version 1.4, prepared for the Texas Higher Education Coordinating Board as the authority for what each content subcategory requires and where its boundaries fall. Skills that build toward a content subcategory without teaching its stated content are excluded, so a skill appears here only where it addresses the content subcategory directly.

Each skill links to a lesson where it is practiced, and hovering a skill shows the description learners see for it. This page is regenerated from the mapping, so it reflects the current state rather than a fixed snapshot.