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SAT^® Mathematics

Digital SAT Mathematics equips students with the algebra, advanced math, geometry, trigonometry, and data‑analysis skills required for the College Board’s 2024 digital exam, emphasizing recall, application, and problem‑solving.

Who Should Take This

High‑school juniors and seniors preparing for the Digital SAT, as well as tutoring professionals seeking curriculum alignment, benefit from this course. It targets learners with foundational high‑school math knowledge who need systematic practice to master definitions, formulas, and strategic reasoning for higher‑stakes testing.

What's Included in AccelaStudy® AI

Adaptive Knowledge Graph

Practice Questions

Lesson Modules

Console Simulator Labs

Exam Tips & Strategy

20 Activity Formats

Course Outline

76 learning goals

1 Algebra

5 topics

Linear Equations in One Variable

Define what constitutes a linear equation in one variable and identify the standard forms, including ax + b = c and equations requiring distribution and combining like terms.
Solve linear equations in one variable involving distribution, combining like terms, variables on both sides, and fractional or decimal coefficients, then interpret the solution in the context of a word problem.
Analyze the structure of a simplified linear equation to determine whether it has one solution, no solution, or infinitely many solutions based on the resulting identity or contradiction.

Linear Equations in Two Variables

Identify slope-intercept form (y = mx + b), point-slope form, and standard form (Ax + By = C) of linear equations, and describe what each parameter represents graphically.
Calculate the slope of a line given two points, a graph, or a table, and determine the equation of a line given slope and a point or two points, converting between forms as needed.
Interpret the slope and y-intercept of a linear equation in the context of a real-world situation, explaining what each value means in terms of the problem's variables.

Linear Functions

Define a linear function and recognize its key characteristics, including constant rate of change, domain and range over the real numbers, and graphical representation as a straight line.
Use function notation f(x) to evaluate a linear function at a given input, find the input that produces a given output, and interpret f(a) = b in context.
Determine the x-intercept and y-intercept of a linear function from its equation, graph, or table, and explain the meaning of each intercept in a real-world context.
Analyze how changes to the slope or y-intercept of a linear function affect its graph, predicting the graphical result of increasing, decreasing, or negating each parameter.

Systems of Two Linear Equations

Describe the three possible outcomes for a system of two linear equations: one unique solution (intersecting lines), no solution (parallel lines), and infinitely many solutions (coincident lines).
Solve a system of two linear equations using substitution or elimination, selecting the more efficient method based on the structure of the equations and interpreting the solution graphically.
Analyze the solution of a system of linear equations in a real-world context, explaining what the intersection point represents and evaluating whether the solution is feasible given the problem's constraints.
Analyze the coefficients of a system of two linear equations to determine without solving whether the system has one solution, no solution, or infinitely many solutions.

Linear Inequalities

State the rules for solving linear inequalities, including the rule that multiplying or dividing by a negative number reverses the inequality sign.
Solve linear inequalities in one variable and represent the solution set on a number line using open and closed circles and appropriate shading.
Interpret a system of linear inequalities in two variables graphically, identifying the solution region as the intersection of half-planes on the coordinate plane.
Analyze a word problem to set up and solve a linear inequality or system of inequalities, interpreting the solution set in terms of the constraints described.

2 Advanced Math

4 topics

Equivalent Expressions

List the exponent rules (product, quotient, power, zero exponent, negative exponent) and the properties used for simplifying polynomial and rational expressions.
Apply the distributive property, FOIL method, and special product patterns to expand polynomial expressions, and apply factoring techniques including GCF, difference of squares, and trinomial factoring to rewrite them.
Apply factoring to simplify rational expressions by canceling common factors in the numerator and denominator, identifying restrictions on the variable that prevent division by zero.
Apply exponent rules to simplify and rewrite exponential expressions, including expressions with fractional and negative exponents.
Analyze whether two algebraic expressions are equivalent by applying multiple simplification strategies and comparing the resulting forms.

Nonlinear Equations

Recognize the standard form (ax^2 + bx + c = 0), vertex form (a(x - h)^2 + k = 0), and factored form (a(x - r)(x - s) = 0) of quadratic equations and state the quadratic formula.
Solve quadratic equations by factoring, applying the quadratic formula, and completing the square, selecting the most efficient method based on the equation's structure.
Use the discriminant (b^2 - 4ac) to determine the number and nature of solutions of a quadratic equation without solving it.
Solve radical equations by isolating the radical and squaring both sides (checking for extraneous solutions), and solve absolute value equations by considering both positive and negative cases.
Analyze a nonlinear equation to determine which solution strategy is most appropriate, evaluating the trade-offs between algebraic manipulation and graphical approaches using the Desmos calculator.

Nonlinear Functions

Identify the key features of quadratic functions including vertex, axis of symmetry, direction of opening, x-intercepts (zeros), y-intercept, and maximum or minimum value.
Identify the key characteristics of exponential functions including growth versus decay, initial value, growth or decay factor, and asymptotic behavior.
Determine the vertex, axis of symmetry, and intercepts of a quadratic function from its equation in standard, vertex, or factored form.
Interpret the parameters of an exponential function f(x) = a * b^x in the context of a real-world growth or decay scenario, including population growth and depreciation.
Analyze polynomial, rational, and radical functions to determine domain and range restrictions caused by division by zero and even roots of negatives, and evaluate the functions at given inputs using function notation.
Compare the rates of change of linear, quadratic, and exponential functions over the same interval, explaining why exponential growth eventually exceeds polynomial growth.

Function Transformations

Describe the four basic types of function transformations: vertical and horizontal translations, vertical and horizontal stretches and compressions, and reflections across the x-axis and y-axis.
Apply transformation rules to write the equation of a transformed function given the parent function and a description of the translation, reflection, or stretch, and predict the graphical effect.
Analyze a graph to identify the sequence of transformations applied to a parent function and write the resulting equation in the appropriate form.

3 Problem-Solving and Data Analysis

5 topics

Ratios, Rates, and Proportions

Define ratios, rates, and proportions, and identify the difference between a ratio (part-to-part or part-to-whole) and a rate (quantity per unit of another quantity).
Solve proportion problems by setting up and cross-multiplying equivalent ratios, including problems involving scale factors, maps, and recipes.
Calculate unit rates from given information and use unit rates to solve problems involving speed, pricing, density, and other rate contexts.

Percentages and Unit Conversion

State the formulas for calculating percentages, percent increase, percent decrease, and successive percent changes applied to a base value.
Solve percent problems and apply dimensional analysis to convert between units of measurement, setting up conversion factors to cancel unwanted units systematically.
Analyze multi-step percent problems involving successive discounts, markups, tax, and tip, determining the final value after multiple percent changes.

One-Variable Data Analysis

Define measures of center (mean, median, mode) and measures of spread (range, interquartile range, standard deviation) and describe what each measure reveals about a data set.
Recognize common data displays including histograms, box plots, dot plots, and stem-and-leaf plots, and identify the information each display conveys about the distribution.
Calculate the mean, median, and range of a data set from a list, table, or box plot, determine the quartiles and interquartile range, and assess how adding or removing a data point changes these measures.
Compare two data distributions using measures of center and spread, determining which distribution has greater variability or a higher typical value.
Evaluate how outliers and skewness affect the mean and median of a distribution, determining which measure of center is most appropriate for a given data set.

Two-Variable Data Analysis

Describe what a scatterplot represents, identifying the explanatory (independent) and response (dependent) variables, and recognizing positive, negative, and no association.
Interpret the slope and y-intercept of a line of best fit in the context of the data, explaining what each value predicts about the relationship between the variables.
Assess predictions made using a line of best fit by distinguishing between interpolation within the data range and extrapolation beyond it, evaluating the reliability and limitations of each approach.
Distinguish between correlation and causation in two-variable data, identifying confounding variables and explaining why association alone does not establish a causal relationship.

Probability and Statistical Inference

Define probability as the ratio of favorable outcomes to total outcomes and state the basic probability rules including the complement rule and the addition rule for mutually exclusive events.
Calculate simple, compound, and conditional probabilities from frequency tables, two-way tables, and described scenarios involving independent and dependent events.
Evaluate the margin of error in a survey or poll, assessing how sample size affects the precision of the estimate and what the confidence interval represents.
Evaluate statistical claims by assessing study design, identifying whether random sampling and random assignment were used, recognizing sources of bias, and determining whether conclusions about causation or generalization are valid.

4 Geometry and Trigonometry

4 topics

Area, Perimeter, and Volume

List the formulas for area and perimeter of common polygons including rectangles, triangles, parallelograms, trapezoids, and regular polygons.
State the formulas for volume and surface area of prisms, cylinders, cones, spheres, and pyramids as provided on the SAT reference sheet.
Calculate the area and perimeter of polygons and composite figures by decomposing complex shapes into simpler components and applying the appropriate formulas.
Calculate the volume of three-dimensional solids using the appropriate formula, including problems that require unit conversion or algebraic manipulation to find a missing dimension.
Analyze problems requiring optimization of area, perimeter, or volume under given constraints, such as maximizing area for a fixed perimeter or determining dimensions from a given volume.

Lines, Angles, and Triangles

State the properties of angles formed by parallel lines cut by a transversal, including corresponding, alternate interior, alternate exterior, and co-interior (same-side interior) angles.
Identify the properties of triangles including the triangle angle sum theorem (interior angles sum to 180 degrees), the exterior angle theorem, and the triangle inequality theorem.
Apply angle relationships to find unknown angle measures in figures involving parallel lines, transversals, and triangles using algebraic equations.
Determine unknown side lengths and angle measures using properties of similar and congruent triangles, including setting up proportions from corresponding sides and applying congruence criteria (SSS, SAS, ASA, AAS).
Analyze complex geometric figures composed of multiple triangles and angle relationships to determine unknown measurements through multi-step reasoning.

Right Triangles and Trigonometry

State the Pythagorean theorem and its converse, and recognize the common Pythagorean triples (3-4-5, 5-12-13, 8-15-17) and their multiples.
Define the trigonometric ratios sine, cosine, and tangent for acute angles in a right triangle, and state the side-length ratios for 30-60-90 and 45-45-90 special right triangles.
Apply the Pythagorean theorem and trigonometric ratios to find unknown side lengths and angle measures in right triangles, including problems embedded in real-world contexts such as distance and height.
Evaluate when to apply special right triangle ratios (30-60-90 and 45-45-90) versus trigonometric functions, and determine exact side lengths using the appropriate method in geometry and coordinate geometry problems.
Analyze problems that require combining the Pythagorean theorem with trigonometric ratios or coordinate geometry to find distances, heights, or angles in multi-step scenarios.

Circles

State the standard form equation of a circle (x - h)^2 + (y - k)^2 = r^2 and identify the center and radius from the equation.
List the formulas for circumference, area, arc length, and sector area of a circle, and define central angle, inscribed angle, and the relationship between them.
Determine the center and radius of a circle from an equation in general form by completing the square, and write the equation of a circle given its center and radius.
Calculate arc length and sector area given the radius and central angle, and apply the inscribed angle theorem to find unknown angle measures in circles.
Analyze problems involving the intersection of a line and a circle, determining the number of intersection points by substituting the linear equation into the circle equation and examining the discriminant.

Scope

Included Topics

All four content domains of the Digital SAT Mathematics section (College Board, effective March 2024): Algebra (~35%), Advanced Math (~35%), Problem-Solving and Data Analysis (~15%), and Geometry and Trigonometry (~15%).
Algebra: linear equations in one variable, linear equations in two variables, linear functions (slope, intercept, rate of change), systems of two linear equations in two variables (substitution, elimination, graphical interpretation), and linear inequalities in one or two variables.
Advanced Math: equivalent expressions involving polynomials, rational expressions, and exponential expressions; nonlinear equations including quadratic equations (factoring, quadratic formula, completing the square), polynomial equations, radical equations, and absolute value equations; nonlinear functions including quadratic, exponential, polynomial, rational, and radical functions; function notation, domain and range, and function transformations (translations, reflections, stretches).
Problem-Solving and Data Analysis: ratios, rates, and proportional relationships; percentages and percent change; unit conversion and dimensional analysis; one-variable data analysis (mean, median, mode, range, standard deviation, data distributions, box plots, histograms, dot plots); two-variable data analysis (scatterplots, line of best fit, correlation, interpolation and extrapolation); probability and conditional probability; inference from sample statistics and margin of error; evaluating statistical claims and study design.
Geometry and Trigonometry: area and perimeter of polygons and composite figures; volume of prisms, cylinders, cones, spheres, and pyramids; lines, angles, and triangle properties (angle sum, exterior angle, similar and congruent triangles); right triangle trigonometry (sine, cosine, tangent, Pythagorean theorem, special right triangles); circles including standard form equations, arc length, sector area, central and inscribed angles, and tangent lines.
Digital SAT Math question format: all multiple-choice (four answer choices), no grid-in or student-produced response questions, built-in Desmos graphing calculator available for all questions, adaptive two-module structure where Module 2 difficulty adjusts based on Module 1 performance.

Not Covered

Calculus concepts including limits, derivatives, integrals, and infinite series.
Advanced statistics beyond the SAT scope: hypothesis testing procedures, chi-square tests, ANOVA, regression analysis with multiple predictors, and confidence interval construction beyond basic margin of error.
Matrix operations, vectors, complex number arithmetic beyond i-squared equals negative one, and abstract algebra.
Proof-based geometry, formal geometric constructions with compass and straightedge, and non-Euclidean geometry.
Pre-2024 SAT Math content no longer tested: grid-in response format and extended thinking problems.
Content from the Digital SAT Reading and Writing section.

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SAT® Mathematics