SAT Math
the digital SAT Math domains
111 of 136 skills covered
✓ covered · ◐ partial · ○ not yet · — excluded
Domain 1: Algebra (≈35% of the test, 13–15 questions)
| skill | lessons | ||
|---|---|---|---|
| 1 | Solve one-step and multistep linear equations (integer, fractional, decimal coefficients) | Solving Linear Equations, Equations with Brackets, Equations with Fractions, Algebraic Notation | ✓ covered |
| 2 | Variables on both sides; parentheses/distribution | Equations with the Unknown on Both Sides, Equations with Brackets, Expanding Brackets | ✓ covered |
| 3 | Create a linear equation modelling a context and solve it | Forming Equations, Writing Formulas from Words | ✓ covered |
| 4 | Determine the number of solutions of a linear equation (0, 1, infinitely many) | How Many Solutions an Equation Has | ✓ covered |
| 5 | Find the coefficient/constant giving no solution or infinitely many solutions | Choosing a Coefficient to Fix the Solution Count | ✓ covered |
| 6 | Interpret the solution of a linear equation in context | Forming Equations | ✓ covered |
| 7 | Create/write a linear equation in two variables modelling a relationship | Writing Formulas from Words | ✓ covered |
| 8 | Compute and interpret slope, x- and y-intercepts, in and out of contextMissing: the x-intercept of a line — the string "x axis" appears nowhere in the catalog | Coordinate Geometry, Gradient from Two Points, Distance-Time Graphs | ◐ partial |
| 9 | Find a line's equation from two points, a point + slope, a table, or a graphMissing: from a point and a slope, and from a graph | The Equation of a Line Through Two Points, Writing Formulas from Words | ◐ partial |
| 10 | Convert between forms of a linear equation (slope-intercept, standard, point-slope) | Writing a Line as Ax + By = C, Point-Slope Form of a Line | ✓ covered |
| 11 | Connect algebraic representation and graph | y = mx + c, Coordinate Geometry, Simultaneous Equations | ✓ covered |
| 12 | Slope criteria for parallel and perpendicular lines | Gradients of Parallel and Perpendicular Lines, Parallel and Perpendicular Lines | ✓ covered |
| 13 | Identify coordinates of points on a line; verify a point lies on a lineMissing: verifying whether a given ordered pair satisfies a given line | The Coordinate Plane, Coordinate Geometry | ◐ partial |
| 14 | Interpret the meaning of a part of a linear equation in context | Writing Formulas from Words, Distance-Time Graphs, Coordinate Geometry | ✓ covered |
| 15 | Function notation for linear functions; evaluate f(x); find input for a given output | Function Notation, Inverse Functions | ✓ covered |
| 16 | Create a linear function modelling a constant rate of change | Writing Formulas from Words | ✓ covered |
| 17 | Interpret slope and y-intercept of a linear function in context | Distance-Time Graphs, Writing Formulas from Words, y = mx + c | ✓ covered |
| 18 | Interpret a specific input-output pair in context | Writing Formulas from Words | ✓ covered |
| 19 | Connect table, graph, equation and verbal description of a linear functionMissing: graph → table and graph → verbal; no lesson closes the loop across all four | Writing Formulas from Words, y = mx + c | ◐ partial |
| 20 | Compute the constant average rate of change over an interval | Gradient from Two Points | ✓ covered |
| 21 | How a translation of a linear function affects equation and graphbut only on y = x²; the linear case is never shown | Transforming Graphs | ◐ partial |
| 22 | Compare two linear functions in different representationsMissing: comparison across differing representations (one as a graph, one as a table/equation) | Gradients of Parallel and Perpendicular Lines | ◐ partial |
| 23 | Solve a system by substitution | Simultaneous by Substitution | ✓ covered |
| 24 | Solve a system by elimination | Simultaneous by Elimination, Solving Simultaneous Equations by Scaling | ✓ covered |
| 25 | Solve a system graphically; interpret as an intersection | Simultaneous Equations, Intersections of Graphs | ✓ covered |
| 26 | Create a system of two linear equations modelling a context, and solve it | Writing a Pair of Equations from a Word Problem | ✓ covered |
| 27 | Number of solutions of a system; parameter values for each case | How Many Solutions a Pair of Equations Has, Choosing a Coefficient in a Pair of Equations | ✓ covered |
| 28 | Solve for a combination of the variables (e.g. x + y) | Solving for x + y Without Finding x and y | ✓ covered |
| 29 | Interpret the solution of a system in context | Writing a Pair of Equations from a Word Problem | ✓ covered |
| 30 | Solve linear inequalities in one variable, including the negative-divide flip | Inequalities, Two-Step Inequalities | ✓ covered |
| 31 | Create a linear inequality representing a constraint in a context | Forming an Inequality in Two Variables | ✓ covered |
| 32 | Graph a linear inequality in two variables; half-plane; boundary included or not | Graphing an Inequality in Two Variables | ✓ covered |
| 33 | Solve and graph systems of two linear inequalities; points in the solution region | The Overlap of Two Inequality Regions | ✓ covered |
| 34 | Determine whether an ordered pair satisfies an inequality or a systemone-variable | Integer Solutions of Inequalities | ◐ partial |
| 35 | Interpret a solution/non-solution in context, incl. greatest/least possible valuesStill missing: greatest/least possible values asked IN a context | Integer Solutions of Inequalities, Forming an Inequality in Two Variables | ◐ partial |
Domain 2: Advanced Math (≈35% of the test, 13–15 questions)
| skill | lessons | ||
|---|---|---|---|
| 36 | Add, subtract, multiply polynomials; combine like terms | Like Terms, Expanding Brackets, Expanding Two Brackets | ✓ covered |
| 37 | Expand products incl. special products (square of a binomial, difference of squares) | Expanding Two Brackets, Algebraic Identities | ✓ covered |
| 38 | Factor: GCF, trinomials, difference of squares, grouping | Factoring by Common Factor, Factoring Quadratics, Factoring Quadratics with a Leading Coefficient | ✓ covered |
| 39 | Rewrite rational expressions: simplify, common denominator, ± × ÷, polynomial/synthetic divisionMissing: division of one rational expression by another, and worked examples with algebraic denominators — the fraction lessons are still x/2 + x/3 rather than (x+1)/(x−2) | Algebraic Fractions, Adding and Multiplying Algebraic Fractions, Long Division of Polynomials | ◐ partial |
| 40 | Laws of exponents (product, quotient, power, negative, zero, rational) | Laws of Indices, The Power of a Power Rule, Zero and Negative Indices, Fractional Indices | ✓ covered |
| 41 | Radical ↔ rational-exponent notation; simplify radicals | Fractional Indices, Radicals, Adding and Multiplying Radicals, Rationalizing the Denominator, Squares and Square Roots, Cubes and Cube Roots | ✓ covered |
| 42 | Rewrite exponential expressions to reveal equivalent growth/decay ratesMissing: the actual rewrite — changing the compounding interval (annual ↔ monthly) or the base to display an equivalent rate. "monthly"/"annual" appear in no lesson of this strand | Laws of Indices, The Power of a Power Rule, Exponential Growth, Exponential Decay, Percentage Increase | ◐ partial |
| 43 | Complete the square; convert among standard, factored and vertex forms | Completing the Square, Factoring Quadratics, Expanding Two Brackets | ✓ covered |
| 44 | Use structure to rewrite complex expressions (treat a sub-expression as one quantity) | Treating a Bracket as a Single Quantity | ✓ covered |
| 45 | Solve a formula/literal equation for a variable of interest | Changing the Subject of a Formula, Making a Twice-Appearing Letter the Subject | ✓ covered |
| 46 | Determine unknown coefficients by equating two equivalent expressions | Finding Unknown Coefficients by Matching | ✓ covered |
| 47 | Determine the most suitable form of an expression to display a featureMissing: the which-form-for-this-feature question — planned as the exam-item lesson "Choosing the Form of a Quadratic" | Completing the Square, Solving by Factoring, Sketching from Vertex and Factored Form | ◐ partial |
| 48 | Solve quadratics by factoring / zero-product property | Solving by Factoring, Factoring Quadratics, Factoring Quadratics with a Leading Coefficient | ✓ covered |
| 49 | Solve quadratics by square roots, completing the square, and the quadratic formula | The Quadratic Formula, Completing the Square, Squares and Square Roots, Deriving the Quadratic Formula | ✓ covered |
| 50 | Discriminant: number/nature of real solutions, incl. parameter values giving 0/1/2 | The Discriminant and the Nature of the Roots, Always Positive or Always Negative Quadratics, When a Line Meets, Touches or Misses a Curve | ✓ covered |
| 51 | Solve absolute value equations | Solving Absolute Value Equations | ✓ covered |
| 52 | Solve radical equations, rejecting extraneous solutions | Solving Equations with a Square Root | ✓ covered |
| 53 | Solve rational equations with restrictions and extraneous solutionsStill missing for this row: the same check on a rational EQUATION — fractional-equations never tests its roots against the denominator it cleared | Fractional Equations, Solving a Rational Inequality | ◐ partial |
| 54 | Solve polynomial equations in or reducible to factored form | Solving by Factoring, Factor and Remainder Theorem | ✓ covered |
| 55 | Solve exponential equations | Solving Exponential Equations, Growth and Decay Problems | ✓ covered |
| 56 | Solve a linear + nonlinear system algebraically and graphically | Intersections of Graphs, Quadratic and Cubic Graphs, A Linear Equation Paired with a Quadratic | ✓ covered |
| 57 | Interpret intersection points as the solutions of a system | Intersections of Graphs, Simultaneous Equations | ✓ covered |
| 58 | Parameter values giving a specified number of solutions (e.g. a line tangent to a parabola) | When a Line Meets, Touches or Misses a Curve, Always Positive or Always Negative Quadratics | ✓ covered |
| 59 | Sum or product of the roots without solving | The Sum and Product of the Roots | ✓ covered |
| 60 | Function notation with nonlinear functions; evaluate; find inputs for given outputsMissing: finding the INPUT for a given nonlinear output — every generator runs forwards from x | Function Notation, Quadratic Graphs, Quadratic and Cubic Graphs, Reciprocal Graphs, Exponentials and Logarithms, Domain and Range, The Graph of y = |x| | ◐ partial |
| 61 | Domain restrictions of rational and radical functions | Domain and Range | ✓ covered |
| 62 | Key features of quadratics: vertex, max/min, axis of symmetry, zeros, y-interceptMissing: "axis of symmetry" as a NAMED term and reading a quadratic's y-intercept | Completing the Square, Solving by Factoring, Quadratic Graphs, Sketching from Vertex and Factored Form | ◐ partial |
| 63 | Choose the most suitable form of a quadratic and convert between formsMissing: the choosing half — planned as the exam-item lesson "Choosing the Form of a Quadratic" | Completing the Square, Factoring Quadratics, Sketching from Vertex and Factored Form | ◐ partial |
| 64 | Create and use quadratic functions to model contextsMissing: projectile/revenue modelling and interpreting a vertex as a maximum in context — "projectile" and "revenue" occur nowhere | Forming Quadratic Equations | ◐ partial |
| 65 | Key features of exponentials: initial value, growth/decay factor, percent change per interval | Exponential Growth, Exponential Decay, Compound Interest, Depreciation, Percentage Increase | ✓ covered |
| 66 | Create and use exponential growth/decay models | Growth and Decay Problems, Compound Interest, Depreciation, Exponential Growth, Exponential Decay | ✓ covered |
| 67 | Distinguish linear vs exponential vs quadratic situations | Simple versus Compound Interest, Exponential Growth, y = mx + c | ✓ covered |
| 68 | Zeros and factors: f(a) = 0 ⇔ (x − a) is a factor; remainder = f(a) | Factor and Remainder Theorem, Solving by Factoring | ✓ covered |
| 69 | Interpret key features of a nonlinear graph in contextMissing: maxima/minima and end behaviour of a nonlinear model read in a real context | Distance-Time Graphs, Speed-Time Graphs, Interpolation and Extrapolation, The Gradient of a Curve | ◐ partial |
| 70 | Connect equation, table, graph and verbal description of a nonlinear functionMissing: table ↔ graph and verbal ↔ graph for nonlinear functions; the table-of-values route exists only for linear | Quadratic and Cubic Graphs, Quadratic Graphs, Reciprocal Graphs | ◐ partial |
| 71 | Effect of translations/transformations on equation, graph and key features | Transforming Graphs, Completing the Square | ✓ covered |
| 72 | Interpret a constant, coefficient, factor, term or input-output pair of a nonlinear modelMissing: interpreting a coefficient or factor of a nonlinear function that models a context | Compound Interest, Writing Formulas from Words | ◐ partial |
| 73 | Compute and compare the average rate of change of a nonlinear function over an interval | The Average Rate of Change Over an Interval | ✓ covered |
| 74 | Identify/match graphs of quadratic, exponential, absolute value and polynomial/rational functions | Quadratic Graphs, Quadratic and Cubic Graphs, Reciprocal Graphs, Exponentials and Logarithms, Logarithmic Graphs, The Graph of y = |x|, Taking the Modulus of a Whole Expression, Replacing x with a Modulus | ✓ covered |
Domain 3: Problem-Solving and Data Analysis (≈15% of the test, 5–7 questions)
| skill | lessons | ||
|---|---|---|---|
| 75 | Ratios and equivalent ratios (part-to-part, part-to-whole) | Ratio, Part-to-Whole Ratios, Tidying a Ratio, Three-Part Ratios, Bar Models for Ratio | ✓ covered |
| 76 | Compute and apply unit rates | Rates, Comparing Unit Rates, The Unitary Method | ✓ covered |
| 77 | Set up and solve proportions, incl. scale drawings and maps | Proportion by Unit Value, Map Scales, Scale Factor, Direct Proportion | ✓ covered |
| 78 | Proportional relationships y = kx; constant of proportionality | Direct Proportion, The Constant of Proportionality, Inverse Proportion | ✓ covered |
| 79 | Unit conversions within and between measurement systems, incl. multistepMissing: conversions between systems — no imperial units appear (feet, pounds, gallons all return nothing) | Converting Lengths, Converting Units of Area, Meters, Centimeters and Kilometers, Grams and Kilograms, Milliliters and Liters, Reading Scales | ◐ partial |
| 80 | Derived units (speed, density, unit price); dimensional analysis | Speed, Average Speed, Density, Rates, Rate, Total, Units, Comparing Unit Rates | ✓ covered |
| 81 | Multistep problems combining ratios, rates, proportions and conversions | Proportion by Unit Value, Combining Two Ratios, Before-and-After Ratio Problems, Ratios with a Constant Part, Rate, Total, Units | ✓ covered |
| 82 | Percent of a quantity; find part, whole, or percent | Percentage, Finding a Percent, Reverse Percentages | ✓ covered |
| 83 | Convert among fractions, decimals and percents | Fractions, Decimals and Percents, Ratio, Fraction, Percent, 0.5 Is a Half | ✓ covered |
| 84 | Percent increase, decrease and percent change | Percentage Increase, Percentage Change, Taking a Percent Off | ✓ covered |
| 85 | Successive/compound percent change; discount, markup, tax, tip, simple interest | Taking a Percent Off, Simple Interest, Compound Interest, Depreciation | ✓ covered |
| 86 | Reverse percentage — original value from a changed value | Reverse Percentages | ✓ covered |
| 87 | Interpret and compare percentages from data tables | Comparing with Percent, Reading Tables, Two-Way Tables | ✓ covered |
| 88 | Read one-variable displays: dot plots, histograms, frequency tables, bar graphs, box plots | Dot Diagrams, Histograms, Frequency Density, Tally and Frequency Tables, Bar Charts, Reading Bar Charts, Box and Whisker, Stem and Leaf, Pie Charts | ✓ covered |
| 89 | Mean, median, mode, range, incl. from a frequency table | The Mean, Median and Mode, Range and IQR, Averages from a Frequency Table, Mean of Grouped Data | ✓ covered |
| 90 | Compare two data sets using centre and spread | Comparing Data Sets, Measures of Spread, Range and IQR, Standard Deviation | ✓ covered |
| 91 | Standard deviation conceptually — which distribution has greater spread | Measures of Spread, Standard Deviation, Standard Deviation: Ungrouped, Standard Deviation: Grouped | ✓ covered |
| 92 | Effect of changes to a data set on mean/median/range; outliers | Measures of Central Tendency | ✓ covered |
| 93 | Choose the measure of centre appropriate to a skewed distribution | Measures of Central Tendency, Comparing Data Sets | ✓ covered |
| 94 | Read scatterplots and line graphs; identify points and trends | Scatter Plots, Line Graphs, Time Series | ✓ covered |
| 95 | Describe association: positive/negative, linear/nonlinear, strong/weak | Correlation, Scatter Plots | ✓ covered |
| 96 | Fit a line of best fit; predict; compare predicted vs actual | Line of Best Fit, Interpolation and Extrapolation, The Least-Squares Regression Line, Predicting from a Regression Line | ✓ covered |
| 97 | Interpret the slope and intercepts of a linear model of data in context | The Least-Squares Regression Line | ✓ covered |
| 98 | Select the appropriate model type for data: linear vs exponential vs quadraticMissing: any question that selects a model for given data or a given context | Simple versus Compound Interest | ◐ partial |
| 99 | Interpret the parameters of a fitted model; evaluate how well it fits | The Least-Squares Regression Line, Pearson’s Correlation Coefficient, Critical Values of r | ✓ covered |
| 100 | Probability of a simple event as favourable ÷ total | Single-Event Probability, Sample Space, The Probability Scale | ✓ covered |
| 101 | Relative frequencies and probabilities from frequency and two-way tables | Two-Way Tables, Experimental Probability, Tally and Frequency Tables, Probability in Set Notation | ✓ covered |
| 102 | Conditional probability, incl. from two-way tables | Conditional Probability, Conditional Probability Notation, Conditional Probability from Tables | ✓ covered |
| 103 | Complement of an event | Complementary Events, The Chance of At Least One | ✓ covered |
| 104 | Use probabilities to predict expected counts in a group | Expected Counts from a Chance, The Law of Large Numbers | ✓ covered |
| 105 | Use a sample statistic to estimate a population parameter | Populations and Samples, Point Estimates, Capture and Recapture | ✓ covered |
| 106 | Interpret margin of error; interval of plausible values | Confidence Intervals | ✓ covered |
| 107 | What affects margin of error (larger sample → smaller margin) | Standard Error | ✓ covered |
| 108 | Role of random sampling in producing representative estimates | Sampling Methods | ✓ covered |
| 109 | Distinguish observational studies from experiments | Observational Studies and Experiments | ✓ covered |
| 110 | What each design supports: random assignment → causation; random sampling → generalisation | Observational Studies and Experiments, Sampling Methods, Correlation Is Not Causation | ✓ covered |
| 111 | Identify the population results extend to; spot overreaching conclusionsMissing: naming the specific population an estimate may be generalised to | Observational Studies and Experiments, Sampling Methods, Correlation Is Not Causation | ◐ partial |
Domain 4: Geometry and Trigonometry (≈15% of the test, 5–7 questions)
| skill | lessons | ||
|---|---|---|---|
| 112 | Perimeter and area of triangles, rectangles, parallelograms, trapezoids, polygons, composites | Area and Perimeter, Area of a Triangle, Area of a Parallelogram, Area of a Trapezium, Area of Composite Shapes | ✓ covered |
| 113 | Circumference and area of circles | Circumference and Diameter, Area of a Circle | ✓ covered |
| 114 | Volume and surface area of prisms, cylinders, pyramids, cones, spheres; find a missing dimensionMissing, narrowed 2026-08-26: volume-of-a-cuboid now reverses (layers = volume ÷ base) and cubes-and-cube-roots finds a cube's edge from its volume; the cylinder/cone/sphere reverse cases still run forwards only | Volume of a Cuboid, Prisms and Cylinders, Pyramids and Cones, Spheres, Surface Area of a Cuboid, Surface Area of a Cylinder, Cones and Spheres, Nets, Cubes and Cube Roots | ◐ partial |
| 115 | Scale factors: effect on perimeter, area and volume | Scale Factor, Scaling Area, Scaling Area and Volume, Ratio of Areas, Ratio of Volumes | ✓ covered |
| 116 | Multistep real-world problems modelled by 2D/3D figures | Area of Composite Shapes, Prisms and Cylinders, Nets, Plans and Elevations, Density | ✓ covered |
| 117 | Vertical angles, linear pairs, complementary/supplementary, angles at a point | Angles at a Point, Angles on a Line, Vertically Opposite Angles, Angles | ✓ covered |
| 118 | Parallel lines cut by a transversal | Angles in Parallel Lines, Parallel and Perpendicular Lines | ✓ covered |
| 119 | Triangle angle sum and the exterior angle theorem | Angles in a Triangle | ✓ covered |
| 120 | Properties of isosceles and equilateral triangles (base angles, equal sides)Missing: the base-angles-are-equal property of an isosceles triangle — "isosceles" appears in no geometry lesson's teaching | Exact Sine, Cosine and Tangent at 30, 45 and 60°, Rhombus and Kite | ◐ partial |
| 121 | Interior/exterior angle sums of polygons | Angles in a Polygon, The Interior Angle of a Regular Polygon | ✓ covered |
| 122 | Congruence and similarity of triangles; proportional sides of similar figures | Congruence Tests, Similarity Conditions, Similar Shapes, Ratio of Areas | ✓ covered |
| 123 | Multistep problems combining scale factors, similarity and angle theoremsMissing: indirect measurement — no shadow/flagpole problem exists, and no question chains similarity with an angle theorem | Similar Shapes, Scale Factor, Map Scales, Enlargement with a Center | ◐ partial |
| 124 | Pythagorean theorem and converse, incl. inside larger figures | Pythagoras’ Theorem, Finding a Shorter Side with Pythagoras’ Theorem, Proving Pythagoras by Dissection, The Distance Between Two Points, The Slant Height of a Cone, The Converse of Pythagoras’ Theorem | ✓ covered |
| 125 | Special right triangles: 45-45-90 and 30-60-90 side ratios | Exact Sine, Cosine and Tangent at 30, 45 and 60° | ✓ covered |
| 126 | Sine, cosine, tangent as right-triangle side ratios | Sine, Cosine and Tangent | ✓ covered |
| 127 | Use right-triangle trigonometry to find sides or angles | Solving Right Triangles, Finding an Angle from a Ratio, Elevation and Depression | ✓ covered |
| 128 | Cofunction relationship sin(x°) = cos(90° − x°) | Sine and Cosine of Complementary Angles, Complementary Angles | ✓ covered |
| 129 | Similarity of right triangles relates trigonometric ratios | Sine, Cosine and Tangent, Similarity Conditions, Similar Shapes | ✓ covered |
| 130 | Unit-circle trigonometry beyond acute angles | Sine and Cosine of Angles Past 90 Degrees, Trigonometric Identities, Every Solution of a Trigonometric Equation | ✓ covered |
| 131 | Convert between degrees and radians | Radians, Arc Length and Sector Area | ✓ covered |
| 132 | Equation of a circle in the xy-plane; centre and radius, incl. by completing the square | The Equation of a Circle, Center and Radius by Completing the Square | ✓ covered |
| 133 | Central angles, arc measures and arc lengths | Arcs and Sectors, Arc Length and Sector Area, Chords, Arcs, Sectors and Segments, Angle at the Center | ✓ covered |
| 134 | Sector areas from central angles | Arcs and Sectors, Arc Length and Sector Area | ✓ covered |
| 135 | Properties of radii, diameters, chords, tangents, central and inscribed angles | Angle in a Semicircle, Angle at the Center, Angles in the Same Segment, Cyclic Quadrilaterals, Tangent Properties, The Alternate Segment Theorem, Chords and the Center | ✓ covered |
| 136 | Combine circle properties with other geometry | The Alternate Segment Theorem, Tangent Properties, Angle in a Semicircle, The Slant Height of a Cone | ✓ covered |
Other syllabuses: Singapore PSLE Mathematics · Singapore O-Level Mathematics · GCSE Mathematics (Higher) · Singapore A-Level H2 Mathematics