Original practice questions, modeled on public College Board skill descriptors — not College Board material.
SP Score Prepped
Drill by score band: 400–500 500–600 600–700 700–800

Difficulty hub

Hard SAT Math Questions

This page lists the 140 questions in the site's 500-question bank tagged hard difficulty, grouped by topic and by score band. Every count below comes from the site's question bank (data/questions.json).

Hard questions by score band

140 hard questions across 20 topics; they fall in 2 score bands (600-700: 20, 700-800: 120).

Other difficulty hubs

TopicSub-skill pagesHard questionsDrill
Absolute Value EquationsAbsolute Value Inequalities, Solving Basic Absolute Value Equations, Distance Interpretation of Absolute Value, Graphing Absolute Value Functions77 hard questions
Circles, Arcs, and SectorsArc Length and Sector Area, Equation of a Circle, Circle Geometry in Context, Inscribed Angles and Tangent Lines77 hard questions
Complex NumbersAdding and Subtracting Complex Numbers, Complex Conjugates and Division, Multiplying Complex Numbers, Powers of i77 hard questions
Exponential Functions and Exponent RulesComparing Exponential and Linear Models, Applying Exponent Rules, Exponential Growth and Decay Models, Fractional and Radical Exponents77 hard questions
Function Notation and CompositionEvaluating Functions, Function Composition, Reading Functions from Graphs and Tables, Inverse Functions77 hard questions
Linear Equations in One VariableEquations with Fractional Coefficients, Solving Literal Equations, Multi-Step Solving, Translating Words to Equations77 hard questions
Linear Functions and Their GraphsBuilding Linear Functions from Tables, Parallel and Perpendicular Slopes, Writing Equations from Points and Slopes, Slope and y-Intercept Interpretation77 hard questions
Linear InequalitiesCompound and Absolute Value Inequalities, Graphing Solution Sets, Interpreting Inequality Word Problems, Solving One-Variable Inequalities77 hard questions
Mean, Median, and ModeComputing and Manipulating the Mean, Mean Versus Median, Mode, Range, and Spread, Weighted Averages77 hard questions
Parallel and Perpendicular LinesIdentifying Slopes from Equations, Midpoint and Distance Formulas, Writing Parallel Line Equations, Writing Perpendicular Line Equations77 hard questions
Percentages and Percent ChangePercent Increase and Decrease, Percent of a Quantity, Percent in Word Problems, Successive Percent Changes77 hard questions
Polynomial OperationsFactoring Higher-Degree Polynomials, Multiplying Polynomials, Polynomial Long and Synthetic Division, Remainder and Factor Theorems77 hard questions
Probability and Two-Way TablesCompound and Independent Events, Conditional Probability, Simple Probability, Probability from Two-Way Tables77 hard questions
Quadratic EquationsCompleting the Square, Factoring Quadratic Expressions, Applying the Quadratic Formula, Quadratic Word Problems77 hard questions
Rational ExpressionsAdding and Subtracting Rational Expressions, Complex Fractions, Solving Rational Equations, Simplifying Rational Expressions77 hard questions
Ratios and ProportionsRate and Density Problems, Scaling Recipes, Maps, and Models, Setting Up Proportions, Similar Figures and Proportional Sides77 hard questions
Right Triangle TrigonometryPythagorean Theorem, SOH-CAH-TOA, Special Right Triangles, Complementary Angle Trig Identities77 hard questions
Systems of Linear EquationsSolving Systems by Elimination, Systems with No Solution or Infinite Solutions, Solving Systems by Substitution, Systems from Word Problems77 hard questions
Units and Unit ConversionConverting Compound Units, Dimensional Analysis, Metric Prefix Conversions, Conversions Embedded in Word Problems77 hard questions
Volume and Surface AreaComposite Solids, Cylinders and Cones, Rectangular Solids, Spheres77 hard questions