Digital SAT notes: every topic explained

All 29 subtopics of the digital SAT, each with the kinds of question that keep coming up, how to spot and answer each one, and the traps to avoid. Free.

Math

Algebra

Linear equations in one variable: Solving equations with one unknown, like 3x+5=20, and using them to model and answer real-world questions.
Linear equations in two variables: Writing, reading and graphing equations like 4x+3y=24 or y=mx+b, whose solutions form a straight line.
Linear functions: Working with functions like f(x)=mx+b: evaluating them, building them from words, tables and graphs, and explaining what their parts mean.
Systems of two linear equations in two variables: Solving two linear equations together, setting them up from word problems, and deciding when a system has one solution, no solution or infinitely many.
Linear inequalities in one or two variables: Writing and solving inequalities like 15s+25p≤120, and deciding which values or points satisfy them.

Advanced Math

Nonlinear functions: Working with functions whose graphs curve, mostly exponential models and quadratics: writing them from a description, reading key points from their graphs, and explaining what their numbers mean.
Nonlinear equations in one variable and systems of equations in two variables: Solving equations where the variable is squared, under a root, inside absolute value bars or in a denominator, finding where a line meets a curve, and rearranging formulas to isolate one letter.
Equivalent expressions: Rewriting an expression in a different form that is still equal to it: expanding, combining like terms, factoring, using exponent rules, and working with fractions that have x in them.

Problem-Solving and Data Analysis

Ratios, rates, proportional relationships, and units: These questions test whether you can compare amounts with ratios and rates, scale them up or down, and change units without losing track of what each number means.
Percentages: These questions test whether you can find a percent of a number, work out what percent one number is of another, and handle percent increases, decreases and chains of percents.
One-variable data: Distributions and measures of center and spread: These questions test whether you can find and compare the mean, median, mode, range and standard deviation of a data set, read from a list, table or graph, and predict how they change when the data change.
Two-variable data: Models and scatterplots: These questions test whether you can read scatterplots and line graphs, use a line or curve of best fit to make predictions, interpret its slope, and choose the kind of model (linear, quadratic or exponential) that fits the data.
Probability and conditional probability: These questions test whether you can find the probability of an event from counts or tables, including conditional probability, where you only look at one group, and work backward from a probability to a count.
Inference from sample statistics and margin of error: These questions test whether you can use a random sample to estimate something about a whole population, and interpret what a margin of error does and doesn't tell you.
Evaluating statistical claims: Observational studies and experiments: These questions test whether you can judge what a survey or study really shows: which population its results apply to, whether its sample is biased, and what can and can't be concluded from it.

Geometry and Trigonometry

Area and volume: Find the area, perimeter, volume or surface area of a shape, often by working backward from one measurement to another, and see how these change when a shape is scaled up or down.
Lines, angles, and triangles: Use angle facts about crossing lines, parallel lines and triangles to find missing angles, and use similar or congruent triangles to find missing sides.
Right triangles and trigonometry: Find missing sides and angles in right triangles using the Pythagorean theorem, the special right triangles, and the sine, cosine and tangent ratios.
Circles: Read and write equations of circles in the xy-plane, and use the radius, arcs, central angles, tangent lines and radians to find lengths and angles.

Reading and Writing

Information and Ideas

Central Ideas and Details: These questions check whether you can say what a short passage is mainly about, find a specific detail it states, and see what its details clearly point to.
Inferences: These questions give you a short passage that ends in a blank and ask which choice most logically completes it, using only what the passage has set up.
Command of Evidence: These questions ask you to choose the evidence (a finding, a quotation, or data from a table or graph) that best supports, weakens or illustrates a specific claim.

Craft and Structure

Words in Context: Words in Context questions test whether you can choose the word that fits a sentence exactly, or work out what a word means in the way one particular text uses it.
Text Structure and Purpose: Text Structure and Purpose questions ask why a text was written, how it is organized, or what job one underlined sentence or phrase does within it.
Cross-Text Connections: Cross-Text Connections questions give you two short texts on the same topic and ask how the authors or researchers would respond to, agree with, or differ from each other.

Expression of Ideas

Rhetorical Synthesis: Rhetorical Synthesis questions give you a student's bullet-point notes and a goal, and ask which sentence uses the notes to meet that goal.
Transitions: Transitions questions ask you to pick the word or phrase that correctly shows how a sentence connects to the idea right before it.

Standard English Conventions

Boundaries: Boundaries questions ask you to pick the right punctuation, or no punctuation at all, at the point where two parts of a sentence meet.
Form, Structure, and Sense: Form, Structure, and Sense questions test whether the words in a sentence fit together: verbs that match their subjects and the timeline, pronouns and nouns in the right number and possessive form, and opening phrases that sit next to the thing they describe.