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Algebra Formulas: Must-Know
Algebra formula flashcards for slope, quadratics, exponents, factoring, and school exam review.
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About this deck
This algebra formulas deck collects must-know formulas and identities for quick school review. It covers linear equations, quadratics, exponents, radicals, and other common algebra patterns.
Use it as a formula recall deck, then practice applying each formula in actual problems. Memorizing the formula is only the first step.
60cards
Middle school to high school algebralevel
algebra students, high school math learners, and exam reviewaudience
What you will learn
- Core linear equation formulas such as slope and point-slope form.
- Quadratic formulas, factoring patterns, and identities.
- Exponent and radical rules that appear often in algebra.
- Quick recognition of when a formula might apply.
How to study this deck
- Read the formula, then write one small example before marking the card correct.
- Separate cards you know by memory from cards where you only recognize the name.
- Review before problem sets or tests, then practice with real algebra exercises.
Recommended study setup
- Start with about 12 cards per session; the full deck is roughly 5 first-pass packs.
- Write, calculate, point to, or sketch the answer before flipping whenever the topic allows it.
- Use quiz mode after one recall pass; study notes appear only after you answer.
Scope
This deck is for formula recall. It does not replace worked examples, graphing practice, proofs, or full algebra lessons.
All 60 cards in this deck
| Front | Back |
|---|---|
| Slope formula | m = (y2 - y1) / (x2 - x1) |
| Slope-intercept form | y = mx + b |
| Point-slope form | y - y1 = m(x - x1) |
| Standard form of a line | Ax + By = C |
| Distance formula | d = sqrt((x2 - x1)² + (y2 - y1)²) |
| Midpoint formula | ((x1 + x2) / 2, (y1 + y2) / 2) |
| Quadratic formula | x = (-b ± sqrt(b² - 4ac)) / 2a |
| Discriminant | Δ = b² - 4ac (sign tells the number of real roots) |
| Vertex form of a parabola | y = a(x - h)² + k, vertex at (h, k) |
| Difference of squares | a² - b² = (a - b)(a + b) |
| Perfect square trinomial | a² + 2ab + b² = (a + b)² |
| Square of a difference | a² - 2ab + b² = (a - b)² |
| Sum of cubes | a³ + b³ = (a + b)(a² - ab + b²) |
| Difference of cubes | a³ - b³ = (a - b)(a² + ab + b²) |
| FOIL | (a + b)(c + d) = ac + ad + bc + bd |
| Exponent product rule | a^m · a^n = a^(m+n) |
| Exponent quotient rule | a^m / a^n = a^(m-n) |
| Exponent power rule | (a^m)^n = a^(mn) |
| Zero exponent rule | a^0 = 1, for a ≠ 0 |
| Negative exponent rule | a^(-n) = 1 / a^n |
| Fractional exponent | a^(1/n) = the nth root of a |
| Log product rule | log(ab) = log(a) + log(b) |
| Log quotient rule | log(a/b) = log(a) - log(b) |
| Log power rule | log(a^n) = n · log(a) |
| Change of base | log_b(x) = ln(x) / ln(b) |
| Arithmetic sequence nth term | a_n = a_1 + (n - 1)d |
| Geometric sequence nth term | a_n = a_1 · r^(n-1) |
| Compound interest | A = P(1 + r/n)^(nt) |
| Simple interest | I = Prt, where P is principal, r is rate, and t is time. |
| Absolute value equation | |x| = a means x = a or x = -a, for a >= 0. |
| Absolute value inequality | |x| < a means -a < x < a; |x| > a means x < -a or x > a. |
| Linear function form | f(x) = mx + b, where m is slope and b is the y-intercept. |
| Y-intercept | The value of y when x = 0. |
| X-intercept | The value of x when y = 0. |
| Parallel lines | Non-vertical parallel lines have the same slope. |
| Perpendicular lines | Non-vertical perpendicular lines have slopes whose product is -1. |
| System by substitution | Solve one equation for a variable, then substitute into the other equation. |
| System by elimination | Add or subtract equations to eliminate one variable. |
| Factoring out GCF | ab + ac = a(b + c). |
| Quadratic standard form | ax² + bx + c = 0. |
| Axis of symmetry | For y = ax² + bx + c, the axis is x = -b / (2a). |
| Vertex x-coordinate | For y = ax² + bx + c, h = -b / (2a). |
| Quadratic roots from factors | If (x - r1)(x - r2) = 0, then x = r1 or x = r2. |
| Completing the square pattern | x² + bx + (b/2)² = (x + b/2)². |
| Radical product rule | sqrt(ab) = sqrt(a) · sqrt(b), for nonnegative a and b. |
| Radical quotient rule | sqrt(a/b) = sqrt(a) / sqrt(b), for b > 0. |
| Rational exponent rule | a^(m/n) = the nth root of a^m. |
| Direct variation | y = kx, where k is the constant of variation. |
| Inverse variation | y = k / x, where k is constant and x != 0. |
| Function notation | f(a) means the output of function f when x = a. |
| Domain | The set of input values a function can use. |
| Range | The set of output values a function can produce. |
| Arithmetic series sum | S_n = n(a_1 + a_n) / 2. |
| Geometric series sum | S_n = a_1(1 - r^n) / (1 - r), for r != 1. |
| Percent change | Percent change = (new - old) / old × 100%. |
| Average rate of change | (f(b) - f(a)) / (b - a). |
| Scientific notation | a × 10^n, where 1 <= |a| < 10. |
| Inequality flip rule | Flip the inequality sign when multiplying or dividing by a negative number. |
| One-step equation inverse operations | Use the opposite operation to isolate the variable. |
| Literal equation | An equation with multiple variables that can be solved for one chosen variable. |
Frequently asked questions
Is this deck enough to study for an algebra test?
It helps with formula recall, but you should also solve practice problems so you know when and how to use each formula.
Does it include the quadratic formula?
Yes. It includes the quadratic formula along with other common algebra identities and equation forms.
Should formulas be memorized or derived?
For many school quizzes you need fast recall, but understanding where formulas come from makes them easier to apply correctly.
Is the Algebra Formulas: Must-Know flashcard deck free?
Yes. You can study it free in your browser on MazoCards. Create a free account to save progress, track streaks, and sync across devices.
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