Free Resources · SAT Math & Writing
Notes Library
A growing collection of free, in-depth study notes for the SAT — covering the full math reference scope plus key writing skills. Each note includes worked examples, diagrams, and (where helpful) interactive widgets you can experiment with directly in your browser. No login required. Designed for students preparing for the digital SAT and for anyone strengthening foundational math.
Foundations & Algebra
Numbers, Rates & Statistics
Percent change, rates, ratios, mean/median/mode, standard deviation basics, and probability fundamentals.
Reference Sheet
Algebra & Exponents
Solving equations, exponent rules, completing the square, and factoring techniques the SAT relies on.
Reference Sheet
Equivalent Expressions
Recognizing and producing equivalent forms — distribute, factor, FOIL, and apply exponent rules under pressure.
Teaching Note
Literal Equations
Solving for one variable in terms of others — the most under-practiced SAT algebra skill.
Teaching Note
Functions & Graphs
Linear Functions & Lines
Slope, slope-intercept form, standard form, parallel and perpendicular lines, and graph reading.
Reference Sheet
Quadratics & Parabolas
The three forms (standard, vertex, factored), discriminant, and reading parabola features from each.
Reference Sheet
Quadratic Functions
Deep teaching on quadratic behavior with an interactive vertex form widget — drag the parameters and watch the graph respond.
Teaching Note · Interactive
Functions & Transformations
Six parent function families and the four transformations (shifts, stretches, reflections, compressions) with live demos.
Reference Sheet · Interactive
Nonlinear Functions
Recognizing nonlinear functions from equations, graphs, and tables. Includes the linear-vs-exponential growth distinction.
Teaching Note
Linear vs. Quadratic Systems
Three scenarios for each system type, comparison table, and two interactive widgets to explore the geometry.
Teaching Note · Interactive
Geometry & Trigonometry
Circles
Equation of a circle, completing the square to find center and radius, arc length, sector area, and inscribed angles.
Reference Sheet
Areas & Volumes
Plane figures, polygon angles, triangle properties, and volume formulas for prisms, cylinders, spheres, cones, and pyramids — with labeled diagrams.
Reference Sheet · 16 Diagrams
Trigonometry
SOHCAHTOA, the complementary-angle identity, the Pythagorean identity, and degree-radian conversion — with side-by-side diagrams.
Reference Sheet · 7 Diagrams
SAT Writing & Conventions
How to use these notes
Reference sheets are designed for quick lookup — formulas, definitions, and worked examples for each topic. Teaching notes go deeper, walking through concepts step by step the way they would be taught in a tutoring session. Both are written for students preparing for the SAT, but the underlying math applies broadly to any algebra, geometry, or precalculus coursework.
Want 1-on-1 help?
These notes are free for everyone. If you'd like personalized tutoring on any of these topics — or full SAT/ACT prep — email brandon@shustutoring.com or call (561) 717-9750 to schedule a free consultation.