Albert Einstein said, "If you can't explain it simply, you don't understand it well enough." I strongly believe that simple is better than complex. Simple is harder to achieve. I go out of my way to simplify subjects.
These are my notes created after giving the same lesson 4-5 times in one week. I am lazy and would rather provide a cheat sheet to my students than to write it all down once more. I include PDF documents so students can freely access them on their mobile devices. I include Microsoft Word documents so teachers can easily modify them to suit their needs.
| Basic Math | ||
| Harold's PEMDAS Cheat Sheet | Docx | Order of operations: PEMDAS & GEMS |
| Harold's Times Tables Cheat Sheet | Docx | Multiplication patterns, 12 x 12, and 25 x 25 times tables practice sheets |
| Harold's Prime Numbers Cheat Sheet | Docx | Prime numbers |
| Algebra | ||
| Harold's Algebra Cheat Sheet | Docx | Summarizes an Algebra textbook |
| Harold's Parent Functions: Algebraic & Conics Cheat Sheet | Docx | My parent functions and their inverses for algebraic, transcendental, and the conic sections. Also called Library of Functions. |
| Harold's Math Etiquette Cheat Sheet | Docx | Lists bad math etiquette, illegal math operations, and how to polish your work. |
| Harold's Math is Fun Cheat Sheet | Docx | Fun math graphs, images, jokes, quotes, and proofs from basic math to calculus. |
| Geometry | ||
| Harold's Geometry Shape Formulas Cheat Sheet | Docx | Perimeter, area, surface area, and volume formulas for 2D & 3D geometric shapes |
| Harold's Geometry Cheat Sheet | Docx | Parallel Lines with Traversals |
| Harold's Geometry Circle Theorems | Docx | Rules of circle geometry, including: angles, arcs, chords, secants, and tangent lines. |
| Precalculus | ||
| Harold's Parent Functions: Trig & Hyperbolics Cheat Sheet | Docx | My parent functions and their inverses for trigonometry and hyperbolics. Also called Library of Functions. |
| Harold's Parent Functions: Polar Cheat Sheet | Docx | My parent functions for polar coordinates. Also called Library of Functions. |
| Harold's Trigonometry Cheat Sheet | Docx | My trig supplement to Paul's Online Notes |
| Harold's Triangles Cheat Sheet | Docx | Law of Sines, Cosines and Tangents |
| Harold's Trig Proofs Cheat Sheet | Docx | My proofs of three (3) trig formulas that allow us to easily derive ALL the trig formulas |
| Harold's Precalculus Cheat Sheet | Docx | My rectangular, polar, and parametric coordinate equations for conics sections |
| Harold's Exponential Growth and Decay Cheat Sheet | Docx | My natural growth and decay formulas used in finance, radioactive decay half-lifes, and biology growth |
| Harold's Graphing Rationals Cheat Sheet | Docx | My tips on graphing rational polynomial functions P(x)/Q(x) |
| Harold's Illegals Cheat Sheet | Docx | My list of common illegal (undefined) math operations |
| Harold's Series Cheat Sheet | Docx | My arithmentic and geometric series, permutations, and combinations formulas |
| Harold's Partial Fraction Expansion (Precalculus) Cheat Sheet | Docx | My partial fraction expansion tips with a Precalculus example |
| Harold's Vectors Cheat Sheet | Docx | My vector formulas with illustrations and examples |
| Harold's Matrix Cheat Sheet | Docx | My matrix formulas with illustrations and examples |
| Harold's TI-84 Grid for Parametric Art | Docx | My template for creating parametric art on a TI-84 calculator |
| Calculus | ||
| Harold's Fundamental Theorem of Calculus Cheat Sheet | Docx | My attempt to make the Fundamental Theorems of Calculus easy to understand |
| Harold's Calculus Cheat Sheet | Docx | My list of all of the main formulas and techniques for AP Calculus BC |
| Harold's Calculus BC Cheat Sheet | Docx | My rectangular, polar, and parametric coordinate equations for conics and the calculus |
| Harold's Partial Fraction Expansion (Calculus) Cheat Sheet | Docx | My partial fraction expansion tips with an integration example |
| Harold's Series Convergence Tests Cheat Sheet | Docx | My sequences and series convergence and divergence tests on 1 page |
| Harold's Taylor Series Cheat Sheet | Docx | My Taylor (Maclaurin) Series with key examples |
| Harold's Infinite Series Cheat Sheet | Docx | My comprehensive list of Infinite Sums with examples |
| Harold's Infinite Products Cheat Sheet | Docx | My comprehensive list of Infinite Products with examples |
| Harold's Center of Mass Cheat Sheet | Docx | My Center of Mass in 1-D, 2-D, and 3-D for both Discrete and Continuous |
| Harold's Hyperbolics Cheat Sheet | Docx | My formulas for hyperbolic functions for precalcuolus through calculus |
| Harold's Calculus 3 Cheat Sheet | Docx | My rectangular, cylindrical, spherical, parametric, vector and matrix equations for conics and 3D calculus |
| Differential Equations | ||
| Harold's Differential Equations Cheat Sheet | Docx | First and second order ordinary differential equations (ODEs), Laplace and Fourier transforms. |
| Harold's PDE Cheat Sheet | Docx | First and second order partial differential equations (PDEs). |
| Harold's Differential Equation Models Cheat Sheet | Docx | My solutions to elegantly simple DiffEqs for exponential growth & decay, Newton's Law of Cooling, and population growth. |
| Harold's Euler's Method Example | Docx | DiffEq Euler's Method Example problem |
| Business Math | ||
| Harold's Finances Cheat Sheet | Docx | My basic financial equations for compounded interest and computing loan payments |
| Harold's Simplex Tableau Cheat Sheet | Docx | How to optimize a linear system of equations using the Simplex Method in Standard Form |
| Harold's Business Calculus Cheat Sheet | Docx | Minimum equations you must memorize for business calculus |
| Physics | ||
| Harold's Modified GUESS Method Cheat Sheet | Docx | My modified GUESS method for solving physics and other word problems |
| Harold's High School Physics Cheat Sheet | Docx | For the textbook Discovering Design with Physics, 1st Edition, Dr. Jay L. Wile (2023). |
| Harold's Physics Units of Measure Cheat Sheet | Docx | My physics units of measure, symbols, and prefixes |
| Harold's Physics Formulas Cheat Sheet | Docx | My physics equations organized to show similarities across disciplines |
| Harold's Physics of Projectiles Cheat Sheet | Docx | My classic kinematic solution of a cannonball's trajectory |
| Harold's Physics Kinematic Graphs Cheat Sheet | Docx | My using graphs to determine position, velocity and acceleration |
| Harold's Physics of Forces Cheat Sheet | Docx | My forces on an inclined plane solution |
| Harold's Physics of Forces with Pully Cheat Sheet | Docx | My forces on an inclined plane with a pully and a second weight solution |
| Harold's Electromagentic Spectrum Cheat Sheet | Docx | My electromagnetic spectrum with light and radio waves |
| Harold's Physics Optics Cheat Sheet | Docx | My physics diagrams for concave lenses, convex lenses, and convex mirrors |
| Harold's Physics Doppler Effect Cheat Sheet | Docx | My doppler effect of both sound and light |
| Harold's Center of Mass Cheat Sheet | Docx | My Center of Mass in 1-D, 2-D, and 3-D for both Discrete and Continuous |
| Chemistry | ||
| Harold's Chemical Elements and Compounds Spreadsheet | Periodic table, element data, lists of compound formulas and their uses (Excel XLSX) |
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| Harold's High School Chemistry Cheat Sheet | Docx | For the textbook Discovering Design with Chemistry, 1st Edition, Dr. Jay L. Wile (2015). |
| Electrical Engineering | ||
| Harold's Boolean Algebra Cheat Sheet | Docx | Boolean algebra, logic circuits, logic gates, truth tables |
| Harold's AC Circuits Cheat Sheet | Docx | Alternating current RLC circuits and impedance |
| Harold's Circuits: Flip-Flop Cheat Sheet | Docx | S-R, D, J-K, and T Flip-Flops |
| Computer Technology | ||
| Harold's AI Chatbots List | Docx | Lists the strengths of the top AI Chatbots as of Q1 2025 |
| Harold's Microsoft 365 Copilot Applications List | Docx | Lists all Microsoft 365 Copilot applications (Microsoft Suite) as of Q1 2025 |
| Statistics | ||
| Harold's Probability Cheat Sheet | Docx | My compilation of common probability formulas (SNHU MAT243) |
| Harold's Statistics: Descriptive Cheat Sheet | Docx | My AP Stats formulas with mean, variance, and statistical inference (SNHU MAT243) |
| Harold's Statistics: Distributions Cheat Sheet | Docx | My discrete and continuous Probability Distribution Functions (PDFs) (SNHU MAT243) |
| Harold's Statistics: Discrete Distributions Cheat Sheet | Docx | My discrete Probability Distribution Functions (PDFs) |
| Harold's Statistics: Hypothesis Testing Cheat Sheet | Docx | My Hypothesis Testing made simple (SNHU MAT243) |
| Harold's Statistics: Linear Regression Analysis Cheat Sheet | Docx | My simple and multiple linear regression models (SNHU MAT243) |
| Harold's Statistics: ANOVA and Chi Squared Cheat Sheet | Docx | My analysis of variance (ANOVA) and chi squared tests (SNHU MAT243) |
| Philosophy | ||
| Harold's Logic (Philosophy) Cheat Sheet | Docx | Logic tailored for Philosophy students |
| Discrete Math | ||
| Harold's Logic Cheat Sheet | Docx | The 8 basic logical symbols, laws, logical conditional, logical quantifiers (SNHU MAT 299 & MAT 230 Module 1) |
| Harold's Sets Cheat Sheet | Docx | Set notation, number sets, logic form of: set notation, numbers, geometry, and functions; Cartisian products, and set relations (SNHU MAT 299 & MAT 230 Module 1) |
| Harold's Counting Cheat Sheet | Docx | Counting methods, including sequences and sets (SNHU MAT 230 Module 3) |
| Harold's Directed Graphs Cheat Sheet | Docx | Directed graphs (digraphs) (SNHU MAT 230 Module 5) |
| Harold's Undirected Graphs and Trees Cheat Sheet | Docx | Undirected graphs and trees (SNHU MAT 230 Module 6) |
| Harold's Modular Arithmetic Cheat Sheet | Docx | Modular arithmetic: b = a (mod m) (SNHU MAT260) |
| Harold's Prime Numbers Cheat Sheet | Docx | Prime numbers (SNHU MAT 260 & MAT 230 Module 8) |
| Harold's Cryptology Cheat Sheet | Docx | Cryptology, encode, decode, symmetric, asymentric, public-private key, hash functions (SNHU MAT 260 & MAT 230 Module 8) |
| Harold's Big O Cheat Sheet | Docx | Analysis of algorithms for asymptotic complexity measurement O(n). |
| Advanced Math / Proofs | ||
| Harold's Proofs Cheat Sheet | Docx | Techniques to solve mathematical proofs. (SNHU MAT 299 & MAT 230 Module 2) |
| Harold's Real Analysis Cheat Sheet | Docx | All theorems and definitions of MAT 470 Ch 1-6, Real Numbers and Real Analysis (SNHU MAT 470 & MAT 230 Module 5) |
| Harold's Abstract Algebra Cheat Sheet (DRAFT) | Docx | Abstract Algebra (SNHU MAT415) |
| Harold's Complex Variables Cheat Sheet (DRAFT) | Docx | Applied Complex Variables (NYU MATH-UY-4434) |
| Harold's History of Mathematics Cheat Sheet | Docx | History of Math and Math Education (SNHU MAT-450) |
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Last updated 22 September 2025