Harold's Cheat Sheets


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 Times Tables Docx My 25 x 25 multiplication table with practice sheet and tips
     
Algebra    
Harold's Parent Functions Cheat Sheet Docx My parent functions and their inverses for algebra, trig and the conics. Also called Library of Functions.
     
Geometry    
Harold's Geometry Cheat Sheet Docx Parallel Lines with Traversals
     
Precalculus    
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 and Illegals Cheat Sheet Docx My list of common illegal math operations and tips on graphing P(x)/Q(x)
Harold's Series Cheat Sheet Docx My arithmentic and geometric series, permutations, and combinations formulas
Harold's Partial Fractions (Precalculus) Cheat Sheet Docx My partial fractions expansion tips with an example
Harold's Vectors Cheat Sheet Docx

My vector 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 Notes 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 Fractions (Calculus) Cheat Sheet Docx My partial fractions 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 Maclaurin and Taylor Series with many examples
Harold's Calculus 3 Cheat Sheet Docx My rectangular, cylindrical, spherical, parametric, vector and matrix equations for conics and 3D calculus
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
     
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 Physics Units Cheat Sheet Docx My physics units of measure, symbols, and prefixes
Harold's Physics Cheat Sheet Docx My physics equations organized to show similarities
Harold's Physics of Projectiles Cheat Sheet Docx My classic kinematic solution of a cannon ball'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
     
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: 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)
     
Discrete Math    
Harold's Logic Cheat Sheet Docx

The 7 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 Boolean Algebra Cheat Sheet Docx Boolean algebra, logic gates, truth tables
Harold's Flip-Flop Cheat Sheet Docx S-R, D, J-K, and T Flip-Flops
     
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)

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Last updated 5 December 2022