Free step-by-step math lessons with guided notes to help you truly understand math.
Welcome to Understand The Math, where you'll find clear explanations, worked examples, and free guided notes designed to help you build confidence and succeed in math.
Whether you're studying algebra, trigonometry, precalculus, calculus, linear algebra, or differential equations, you'll find lessons that focus on building real understanding, not just memorizing formulas.
Created by Dr. Cheryl Hile, a former Penn State mathematics professor with more than 25 years of university teaching experience and a Ph.D. in Engineering Science and Applied Mathematics.
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Understand The Math
What is Singular Value Decomposition?
SVD factors a matrix into three matrices: U, Ξ£, and Vα΅. This graphic shows the decomposition and the role each matrix plays.
Watch my step-by-step example to see how SVD works: https://youtu.be/f8DVtPvqtwc
6 hours ago | [YT] | 0
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Understand The Math
Need to find the midpoint or distance between two points?
Here are the midpoint and distance formulas, along with an example of each.
Save this for later
4 days ago | [YT] | 3
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Understand The Math
Need help remembering the trig ratios?
Use SOHCAHTOA:
SOH β sine = opposite / hypotenuse
CAH β cosine = adjacent / hypotenuse
TOA β tangent = opposite / adjacent
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6 days ago | [YT] | 1
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Understand The Math
Finding the area between two curves?
Remember: with dx, use top β bottom. With dy, use right β left.
This video walks through both methods step by step.
https://youtu.be/dGpbfgMWQXU
1 week ago | [YT] | 8
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Understand The Math
How do we find the slope of a tangent line?
This graphic shows how the slope of a secant line approaches the slope of the tangent line as Q moves toward Pβand how this leads to the limit definition of the derivative.
Watch the full lesson here: https://youtu.be/p4bk1oOzNYA
1 week ago | [YT] | 10
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Understand The Math
Need help finding volumes of solids of revolution?
These reference sheets show how to use the disk and washer methods when revolving a region about the x-axis, y-axis, or another horizontal or vertical line.
Watch my step-by-step examples here: https://youtu.be/1cp2Y7oWTz0
1 week ago | [YT] | 5
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Understand The Math
The FOIL Method helps you remember which terms to multiply: First, Outer, Inner, Last.
Watch my step-by-step example to see how it works!
https://youtu.be/P_B6YBGKwVU
1 week ago | [YT] | 4
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Understand The Math
π Linear Systems Cheat Sheet!
A linear system can have no solution, exactly one solution, or infinitely many solutions.
This cheat sheet shows what each case looks like graphically.
Save this for your next algebra review!
Want the full step-by-step lesson? Watch the video here:
https://youtu.be/OjQTEmZ8uOk
#LinearSystems #Algebra #MathCheatSheet
2 weeks ago | [YT] | 6
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Understand The Math
π Fraction Cheat Sheet!
Need a quick review of adding, subtracting, multiplying, and dividing fractions? Save these cheat sheets for later!
Want the full step-by-step lesson? Watch the video here:
https://youtu.be/LyMESqKEVnY
2 weeks ago | [YT] | 5
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Understand The Math
Working on integration by parts? Hereβs a cheat sheet with the formula, steps to follow, and the ILATE shortcut for choosing (u).
Want to see integration by parts in action? In this video, I work through 6 examples step by step and also show the tabular integration shortcut:
https://youtu.be/LvJ-N6A7FeU
Save this cheat sheet for when you need it! π
3 weeks ago | [YT] | 4
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