ALG.01
Laws of Exponents
Law
Example
Domain 1 of 4 · Algebra
Algebra
Linear equations, systems, exponent rules and the algebraic building blocks almost every SAT Math question leans on.
● ~35% of Math · 13–15 questionsALG.02
Fractional Exponents & Roots
A radical with index n and inner power m converts directly to a fractional exponent — the fastest way to simplify nested roots on the calculator section.
ALG.03
Special Products Perfect squares & difference of squares
ALG.04
Complex Fractions
ALG.05
Cross Multiplication
ALG.06
Linear Equations — Number of Solutions
→Infinitely many solutions
→No solution
→One solution
ALG.07
Absolute Value Equations
→1 solution
→2 solutions
→No solution
ALG.08
Functions — Domain & Intercepts
ALG.09
Slope & Linear Equations
Point-slope form — build the equation of a line from a slope m and one known point (x₁, y₁).
ALG.10
Parallel & Perpendicular Lines
ALG.11
Reading a Line's Slope
ALG.12
Percent Translations
Phrase
Translates to… / Example
p% of x
p% greater than x
p% less than x
ALG.13
Percent Change
ALG.14
Work Formula
Work equals rate multiplied by time — the backbone of every "how long will it take" rate question.
ALG.15
Systems of Linear Equations — Number of Solutions
→Infinitely many solutions
→No solution
Any other relationship between the coefficients gives exactly one solution — the two lines cross at a single point.
ALG.16
Distance & Midpoint Formulas
Distance is the Pythagorean theorem applied to two coordinate points; the midpoint is just the average of the x's and the average of the y's.
Domain 2 of 4 · Advanced Math
Advanced Math
Quadratics dominate this domain: the three forms, how roots relate to coefficients, and what the discriminant tells you before you solve anything.
● ~35% of Math · 13–15 questionsADV.01
Three Forms of a Quadratic
Standard form
Vertex form
Factored form
ADV.02
Sum & Product of the Roots
Straight from the standard-form coefficients — no need to solve for x₁ and x₂ first.
ADV.03
Vertex Coordinates
The vertex's x-coordinate is also the exact midpoint of the two roots.
ADV.04
The Discriminant
→2 real solutions
→1 real solution
→No real solutions
ADV.05
Direction of the Parabola
→Opens upward ⋃
→Opens downward ⋂
ADV.06
Function Transformations
Transformation
Visual Effect
Shift up by k units
Shift down by k units
Shift left by h units
Shift right by h units
Reflect over the x-axis (flip upside down)
Stretch vertically by a factor of c (becomes skinnier)
Shrink vertically by a factor of c (becomes fatter)
Domain 3 of 4 · Problem-Solving & Data Analysis
Problem-Solving & Data Analysis
Ratios, rates, and the statistics vocabulary the SAT expects you to read off a table, box plot, or scatterplot on sight.
● ~15% of Math · 5–7 questionsPSD.01
Density
PSD.02
Center & Spread
PSD.03
Five-Number Summary & Box Plots
Min, Q1, Median, Q3, Max — the box spans the middle 50% of the data (Q1 to Q3); the whiskers reach the min and max.
PSD.04
Population, Sample & Margin of Error
PSD.05
Scaling Similar Figures
Ratio Relationship
Example, side ratio 1 : 5
If every linear dimension scales by k, area scales by k² and volume scales by k³.
PSD.06
Probability
Count the outcomes that satisfy the event, divide by the total number of possible outcomes.
Domain 4 of 4 · Geometry & Trigonometry
Geometry & Trigonometry
Angles, triangles, circles, area, volume, and right-triangle trig — the full shape-and-space toolkit for the SAT's most visual questions.
● ~15% of Math · 5–7 questionsGEO.01
Sum of Interior Angles
n is the number of sides of the polygon.
GEO.02
The Pythagorean Theorem
GEO.03
Special Right Triangles
45–45–90: legs are equal, hypotenuse is a leg times √2. 30–60–90: sides sit in the ratio x : x√3 : 2x.
GEO.04
Triangle Congruence
GEO.05
Equilateral Triangle Area
Where a is the length of a side.
GEO.06
Projection Formulas
Dropping the altitude to the hypotenuse creates three similar right triangles — these geometric-mean relationships follow directly.
Area of the triangle — both expressions equal twice the area, divided by 2.
GEO.07
Circles
GEO.08
Equation of a Circle
The standard-form equation of a circle — center (h, k), radius r. Comes straight from the distance formula: every point (x, y) on the circle is exactly r away from the center.
GEO.09
Arcs & Sectors
An arc's degree measure equals its central angle θ. Arc length and sector area both scale that same fraction θ/360 of the full circle.
GEO.10
Circle Angle Theorems
A central angle is always double the inscribed angle that subtends the same arc.
GEO.11
Right-Triangle Trigonometry SOH · CAH · TOA
GEO.12
Trigonometric Identities
The Pythagorean identity holds for any angle x — it comes straight from the Pythagorean theorem on the unit circle.
Mnemonic — All Students Take Calculus: going counter-clockwise through quadrants I–IV, All ratios positive, then Sine, Tangent, Cosine are positive in turn.
GEO.13
Area & Perimeter
GEO.14
Volume & Surface Area
GEO.15
General Volume Principle
Works for any prism or cylinder — find the area of the base, multiply by height.
GEO.16
Curved & Pointed Solids
For any pyramid or cone — square, triangular, or otherwise — volume is one-third the base area B times the height.
