United States · College BoardSyllabus
Maths syllabus, dot point by dot point
Every dot point in the United States Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Advanced Math
Module overview →- How do you rewrite algebraic expressions into equivalent forms by factoring, expanding, and using exponent rules?Equivalent expressions: factor and expand polynomials, simplify rational expressions, apply exponent and radical rules, and rewrite an expression to reveal a needed feature.11 min answer →
- How do you solve nonlinear equations in one variable, including quadratics, radicals, and exponential equations?Nonlinear equations in one variable: solve quadratics by factoring, the quadratic formula and completing the square, and solve radical, rational and exponential equations, checking for extraneous solutions.11 min answer →
- How do you recognise and interpret nonlinear functions such as exponential, polynomial, rational and radical functions?Nonlinear functions: distinguish linear from exponential growth, interpret polynomial, rational, radical and exponential functions and their graphs, and read key features and end behaviour.11 min answer →
- How do the three forms of a quadratic reveal its vertex, zeros and intercept, and how do you read a parabola?Quadratic functions and their graphs: use standard, factored and vertex form to read the y-intercept, the x-intercepts and the vertex, and connect the discriminant to the number of x-intercepts.11 min answer →
- How do you solve a system that pairs a linear equation with a nonlinear one, such as a line and a parabola?Systems of equations in two variables with a nonlinear equation: solve a line-and-parabola system by substitution, interpret the number of intersection points, and use the discriminant to count solutions.11 min answer →
Algebra
Module overview →- How do you solve linear equations in one variable and interpret what their solutions mean?Linear equations in one variable: solve equations that reduce to ax + b = c, handle equations with no solution or infinitely many solutions, and interpret solutions in context.10 min answer →
- How do you work with linear equations in two variables, moving between slope-intercept, standard and point-slope forms?Linear equations in two variables: graph and interpret lines, find slope and intercepts, convert between slope-intercept and standard form, and find the equation of a line from given information.11 min answer →
- How do you interpret and use linear functions, including slope as a rate of change and the meaning of the intercepts?Linear functions: interpret slope as a rate of change and the y-intercept as an initial value, use function notation, and build linear models from a rate and a starting amount.10 min answer →
- How do you solve linear inequalities in one or two variables, and what do their solution sets look like?Linear inequalities in one or two variables: solve and graph inequalities, remember to flip the sign when multiplying or dividing by a negative, and interpret feasible regions in context.10 min answer →
- How do you solve a system of two linear equations, and when does a system have no solution or infinitely many?Systems of two linear equations in two variables: solve by substitution and elimination, solve graphically, and determine when a system has one solution, no solution, or infinitely many.11 min answer →
Bluebook and Test Strategy
Module overview →- How is the Digital SAT Math section structured, and how should that shape your pacing?The Digital SAT Math format: 44 questions in 70 minutes across two modules, taken on the Bluebook app, with a calculator allowed throughout and a built-in reference sheet.9 min answer →
- How does the Digital SAT adapt Module 2 to your Module 1 performance, and what does that mean for strategy?The multistage adaptive design: Module 1 is the same for everyone, and Module 1 performance routes you to a harder or easier Module 2 that determines your achievable score band.9 min answer →
- How do you enter answers correctly on Digital SAT student-produced response (grid-in) questions?Student-produced response questions: the roughly one-quarter of Math questions where you type the answer, and the rules for entering integers, decimals, fractions, and negatives without mixed numbers or pi.9 min answer →
- What formulas does the Digital SAT reference sheet provide, and how do you use them quickly?The Math reference sheet provided on every Digital SAT question: circle and triangle area, the Pythagorean theorem, the special right triangles, common volumes, and the angle and radian facts.9 min answer →
- How can the built-in Desmos graphing calculator turn Digital SAT algebra and function questions into a few clicks?Using the built-in Desmos graphing calculator in Bluebook to solve equations, find intersections, read zeros, and check answers across the whole Math section.10 min answer →
Geometry and Trigonometry
Module overview →- How do you compute area and volume for the standard shapes and solids, including composite figures and scaling?Area and volume: compute area of rectangles, triangles and circles, volume of prisms, cylinders, spheres, cones and pyramids, handle composite figures, and use the reference sheet.10 min answer →
- How do you work with circle measurements: circumference, area, arc length, sector area, and radian measure?Circles: use circumference and area, compute arc length and sector area as fractions of the whole, convert between degrees and radians, and apply central angle relationships.10 min answer →
- How do you use the distance and midpoint formulas, and read or build the equation of a circle in the coordinate plane?Coordinate geometry and circle equations: use the distance and midpoint formulas and write or interpret the standard-form equation of a circle, completing the square when needed to find the center and radius.11 min answer →
- How do you use angle relationships, parallel lines, and triangle properties including similarity to find unknown measures?Lines, angles, and triangles: use vertical, complementary and supplementary angles, parallel lines cut by a transversal, the triangle angle sum, and similar and congruent triangles to find unknowns.11 min answer →
- How do you use the Pythagorean theorem, special right triangles, and the trigonometric ratios to find sides and angles?Right triangles and trigonometry: apply the Pythagorean theorem, the special right triangles, the sine, cosine and tangent ratios (SOH-CAH-TOA), and the sine and cosine of complementary angles.11 min answer →
Problem-Solving and Data Analysis
Module overview →- How do you read one-variable data, compute and compare measures of center and spread, and reason about samples and statistical claims?One-variable data: mean, median, mode and range, standard deviation as spread, the effect of outliers, and inference from sample statistics including margin of error and evaluating statistical claims.11 min answer →
- How do you solve percent problems, including percent change, successive percentages, and reverse percentages?Percentages: compute a percent of a number, percent increase and decrease, percent change, successive percent changes, and find an original amount from a percentage (reverse percent).11 min answer →
- How do you compute probabilities and conditional probabilities, especially from a two-way frequency table?Probability and conditional probability: compute simple probability as favorable over total, read probabilities from two-way frequency tables, and compute conditional probability given a restricted group.10 min answer →
- How do you set up and solve ratio, rate, and proportion problems, including unit conversions?Ratios, rates, proportional relationships, and units: solve proportions, work with unit rates and constant of proportionality, and convert between units including compound units.11 min answer →
- How do you read scatterplots, fit a line or curve of best fit, and use a model to predict?Two-variable data: read scatterplots, choose a linear, quadratic or exponential model of best fit, interpret slope and intercept of a line of best fit, and use the model to predict and interpolate.11 min answer →