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
Complementary or supplementary? 📐
These two terms are easy to mix up, but the difference comes down to the sum of the angles:
Complementary angles add to 90°.
Supplementary angles add to 180°.
An easy way to remember: complementary angles complete a right angle, while supplementary angles complete a straight angle.
Save this for a quick geometry review!
#ComplementaryAngles #SupplementaryAngles #Geometry #LearnMath #MathHelp
1 day ago | [YT] | 2
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Understand The Math
Tabular integration is a shortcut that organizes the derivatives, integrals, and alternating signs to make repeated integration by parts much easier.
Watch the full lesson here: https://youtu.be/gAbh1cXfqug
5 days ago | [YT] | 5
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Understand The Math
Need help with parabolas?
Learn about the vertex, focus, directrix, and axis of symmetry—and how to write the equation of a parabola.
Watch the full lesson here: https://youtu.be/l_OSqvr_sgQ
1 week ago | [YT] | 4
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Understand The Math
What is Singular Value Decomposition?
SVD factors a matrix into three matrices: U, Σ, and Vᵀ. 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
1 week ago | [YT] | 1
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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
1 week ago | [YT] | 3
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Understand The Math
Need help remembering the trig ratios?
Use SOHCAHTOA:
SOH → sine = opposite / hypotenuse
CAH → cosine = adjacent / hypotenuse
TOA → tangent = opposite / adjacent
Save this for later!
2 weeks ago | [YT] | 1
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Understand The Math
Finding the area between two curves?
Remember: with dx, use top − bottom. With dy, use right − left.
This video walks through both methods step by step.
https://youtu.be/dGpbfgMWQXU
2 weeks 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 P—and how this leads to the limit definition of the derivative.
Watch the full lesson here: https://youtu.be/p4bk1oOzNYA
2 weeks 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
2 weeks 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
3 weeks ago | [YT] | 4
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