United States · College BoardQ&A
MathsQ&A by dot point
A short Q&A bank for every United States Maths syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Advanced Math
- Equivalent expressions: factor and expand polynomials, simplify rational expressions, apply exponent and radical rules, and rewrite an expression to reveal a needed feature.0Q&A pairs
- 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.0Q&A pairs
- Nonlinear functions: distinguish linear from exponential growth, interpret polynomial, rational, radical and exponential functions and their graphs, and read key features and end behaviour.0Q&A pairs
- 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.0Q&A pairs
- 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.0Q&A pairs
Algebra
- 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.0Q&A pairs
- 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.0Q&A pairs
- 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.0Q&A pairs
- 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.0Q&A pairs
- 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.0Q&A pairs
Bluebook and Test Strategy
- 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.0Q&A pairs
- 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.0Q&A pairs
- 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.0Q&A pairs
- 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.1Q&A pairs
- Using the built-in Desmos graphing calculator in Bluebook to solve equations, find intersections, read zeros, and check answers across the whole Math section.0Q&A pairs
Geometry and Trigonometry
- 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.1Q&A pairs
- 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.0Q&A pairs
- 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.0Q&A pairs
- 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.0Q&A pairs
- 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.0Q&A pairs
Problem-Solving and Data Analysis
- 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.0Q&A pairs
- 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).0Q&A pairs
- 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.0Q&A pairs
- Ratios, rates, proportional relationships, and units: solve proportions, work with unit rates and constant of proportionality, and convert between units including compound units.1Q&A pairs
- 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.0Q&A pairs