Math Formulas
53 cards
5 min read
Review these 53 cards — active recall, FSRS spaced repetition, and SAT-format quizzing.
53 cards — scan the full deck below, or import the TSV into Anki.
| Prompt | Answer |
|---|---|
| Quadratic formula | x = (-b ± √(b² - 4ac)) / 2a |
| Discriminant formula | b² - 4ac |
| Discriminant: two real solutions? | b² - 4ac > 0 |
| Discriminant: one real (repeated) solution? | b² - 4ac = 0 |
| Discriminant: no real solutions? | b² - 4ac < 0 |
| Vertex x-coordinate of y = ax² + bx + c | x = -b / 2a |
| Vertex form of a parabola | y = a(x - h)² + k, where (h, k) is the vertex |
| Slope formula (given two points) | m = (y₂ - y₁) / (x₂ - x₁) |
| Slope-intercept form of a line | y = mx + b (m = slope, b = y-intercept) |
| Point-slope form of a line | y - y₁ = m(x - x₁) |
| Standard form of a line | Ax + By = C |
| Slope of a line parallel to a given line | Same slope (m₁ = m₂) |
| Slope of a line perpendicular to a given line | Negative reciprocal of the original slope (m₁ · m₂ = -1) |
| Linear system: when does it have no solution? | Same slope, different y-intercepts (parallel lines) |
| Linear system: when does it have infinite solutions? | Same slope and same y-intercept (identical lines) |
| Distance formula | d = √[(x₂ - x₁)² + (y₂ - y₁)²] |
| Midpoint formula | ((x₁ + x₂)/2, (y₁ + y₂)/2) |
| Circle equation (center-radius form) | (x - h)² + (y - k)² = r², center (h, k), radius r |
| Exponential growth model | y = a(1 + r)^t (a = initial amount, r = growth rate, t = time) |
| Exponential decay model | y = a(1 - r)^t (a = initial amount, r = decay rate, t = time) |
| Compound interest formula | A = P(1 + r/n)^(nt) |
| Percent change formula | Percent change = (New - Original) / Original × 100 |
| SOHCAHTOA | sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent |
| sin(x) = cos(?) | cos(90° - x) — sine and cosine of complementary angles are equal |
| Radian to degree conversion | degrees = radians × (180/π) |
| Degree to radian conversion | radians = degrees × (π/180) |
| Arc length formula (central angle in degrees) | arc length = (θ/360°) × 2πr |
| Sector area formula (central angle in degrees) | sector area = (θ/360°) × πr² |
| Sum of the roots of ax² + bx + c = 0 | -b/a |
| Product of the roots of ax² + bx + c = 0 | c/a |
| Difference of squares factoring | a² - b² = (a + b)(a - b) |
| Perfect square trinomial (addition) | a² + 2ab + b² = (a + b)² |
| Perfect square trinomial (subtraction) | a² - 2ab + b² = (a - b)² |
| Sum of cubes factoring | a³ + b³ = (a + b)(a² - ab + b²) |
| Difference of cubes factoring | a³ - b³ = (a - b)(a² + ab + b²) |
| Exponent rule: multiplying same base | x^a · x^b = x^(a+b) |
| Exponent rule: dividing same base | x^a / x^b = x^(a-b) |
| Exponent rule: power of a power | (x^a)^b = x^(ab) |
| Exponent rule: negative exponent | x^(-a) = 1/x^a |
| Exponent rule: zero exponent | x^0 = 1 (for x ≠ 0) |
| Exponent rule: fractional exponent | x^(a/b) = (b-root of x)^a, i.e., the b-th root of x, raised to the a power |
| Conditional probability rule | P(A|B) = P(A and B) / P(B) — restrict the denominator to the given condition |
| Probability of independent events (both occur) | P(A and B) = P(A) × P(B) |
| Mutually exclusive events: P(A or B) | P(A or B) = P(A) + P(B) |
| General addition rule: P(A or B) | P(A or B) = P(A) + P(B) - P(A and B) |
| Average speed formula | Average speed = Total distance / Total time |
| Weighted average formula | (sum of each value × its weight) / (sum of the weights) |
| Direct variation | y = kx (y increases proportionally with x) |
| Inverse variation | y = k/x (product of x and y stays constant) |
| Imaginary unit: i² | i² = -1 |
| Completing the square: what to add to x² + bx = c | Add (b/2)² to both sides to create a perfect square trinomial |
| Function transformation: y = f(x) + k | Shifts the graph up (k > 0) or down (k < 0) |
| Function transformation: y = f(x - h) | Shifts the graph right (h > 0) or left (h < 0) |
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