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The 10 starter formulas
Each card in the starter deck contains one essential formula with a memory hint. Study them with spaced repetition to build formula fluency.
| Formula | Plain-text notation | Memory hint |
|---|---|---|
| Quadratic Formula | x = (-b ± sqrt(b^2 - 4ac)) / (2a) |
Negative b, plus/minus the square root of the discriminant, all over 2a — solves any ax² + bx + c = 0 |
| Slope Formula | m = (y2 - y1) / (x2 - x1) |
Rise over run — the change in y divided by the change in x between two points |
| Slope-intercept Form | y = mx + b |
m is slope, b is the y-intercept where the line crosses the y-axis |
| Pythagorean Theorem | a^2 + b^2 = c^2 |
The sum of the squares of the two legs equals the square of the hypotenuse in any right triangle |
| Distance Formula | d = sqrt((x2 - x1)^2 + (y2 - y1)^2) |
Square root of the sum of squared differences — the Pythagorean theorem applied in 2D coordinate space |
| Area of Circle | A = pi * r^2 |
Pi times radius squared — radius-squared accounts for how area grows with distance from center |
| Area of Triangle | A = (1/2) * base * height |
Half of base times height — a triangle is exactly half a rectangle with the same base and height |
| Area of Rectangle | A = length * width |
Length times width — the simplest area formula and foundation for all 2D shape areas |
| Simple Interest | I = P * r * t |
Principal times rate times time — linear growth with no compounding |
| Percentage Change | % change = ((new - old) / old) * 100 |
Subtract old from new, divide by old, multiply by 100 — measures relative shift as a percent |
No LaTeX or MathJax rendering: This tool uses plain-text notation on purpose. Formulas like x^2, sqrt(x), and 1/2 are clear, fast to load, work offline, and render identically on every device. If you need prettier mathematical typography, export your deck to Anki or another tool that supports LaTeX.
Before & After: Writing formula cards that stick
Good formula cards test whether you can identify *when* to use a formula, not just recall it. Here's what transforms a weak card into a strong one.
Weak card ✗
Front: Pythagorean Theorem
Back: a^2 + b^2 = c^2
Problem: You can memorize the formula, but when do you use it? Is c always the hypotenuse? What if the triangle is obtuse? This card tests pattern recognition only.
Strong card ✓
Front: A right triangle has legs 3 and 4. What is the hypotenuse?
Back: 5. Use Pythagorean: a^2 + b^2 = c^2 → 3^2 + 4^2 = 9 + 16 = 25 → c = sqrt(25) = 5
Why it works: You must (1) identify this is a right-triangle problem, (2) recall the formula, (3) substitute correctly. This forces deeper thinking than bare memorization.
The starter deck gives you the formulas; you can edit the backs to add worked examples for your own practice problems. The stronger the card, the better the learning.
How to study math formulas effectively
Flashcards alone aren't enough. Combine formula memorization with practice problems to build real skill.
Memorize, then derive
Use flashcards to lock down the formula. Then prove why it works—solve problems that require deriving it from first principles. Understanding the derivation prevents mistakes and builds confidence.
Test on application, not just recall
Don't just memorize "a^2 + b^2 = c^2." Instead, study: "A right triangle has legs 5 and 12. Find the hypotenuse." This forces you to identify which formula to use, a critical skill on exams.
Study formulas in clusters
Group related formulas together: all area formulas in one deck, all distance/slope formulas in another. Seeing them side-by-side helps you learn which to apply in different contexts.
Use worked examples as memory bridges
Attach a simple worked example to each card. When you flip a card and see the example, it jogs your memory for the derivation and reinforces *why* the formula works, not just *what* it is.
Rate honestly to target weaknesses
When you rate a card "Again," that formula goes back into the queue. Cards you rate "Easy" are shelved longer. Trust the algorithm—it automatically focuses on the formulas you struggle with most.
Sources
- OpenStax — Algebra and Trigonometry 2e
- OpenStax — College Algebra 2e Key Equations
- Anki Manual — Importing text files
- Quizlet Help — Importing content
- SuperMemo — Minimum Information Principle
Learn more study techniques
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Spaced repetition
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Active recall
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Flashcard maker
Our general-purpose flashcard tool with full import/export. Perfect for any subject—not just math.
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Pomodoro timer
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Questions
Why study formulas with flashcards instead of just memorizing them?
Flashcards force active recall—you must retrieve the formula from memory, not just recognize it in a textbook. This produces stronger, longer-lasting memory. Spaced repetition ensures you review formulas just before you're about to forget them, which is when learning is most efficient.
Should I memorize formulas or derive them?
Both. Memorizing formulas saves time during exams and problem-solving. Understanding the derivation ensures you can apply the formula correctly and catch errors. Use flashcards for memorization; complement them with practice problems to build understanding.
Can I add my own formulas or formulas from my class?
Yes. The starter deck contains 10 essential formulas, but you can add, edit, or replace them anytime. Type any formula using plain-text notation: ^ for exponents, sqrt() for square roots, and standard symbols for operations.
What does plain-text notation mean? Why no LaTeX?
This tool uses plain text on purpose. No LaTeX or MathJax rendering means faster load times, offline access, and simpler cards. Notation like x^2 and sqrt(x) is clear and universal across all platforms. If you need prettier math typography, export your deck to Anki or another tool that supports LaTeX.
How do I know if I'm memorizing formulas correctly?
You're ready when you can (1) recall the formula instantly, (2) identify which formula solves a given problem, and (3) explain why each part of the formula is there. If you hesitate or have to think hard, rate it "Hard"—these cards need more practice.
Can I import formulas from another app?
Yes. Export your deck as CSV and open it in any app that accepts CSV (Quizlet, Anki, etc.). The reverse works too: export from those apps and import here. One card per row: formula front, definition/hint back.