📚 SAT Math Core Formula Handbook | SAT数学核心公式全梳理
The SAT Math section tests your ability to apply a compact set of formulas across algebra, problem solving, data analysis, and advanced math. This handbook organizes the essential formulas you must know, with concise explanations and consistent notation.
SAT 数学部分考查你在代数、问题解决、数据分析与高等数学中运用一组精炼公式的能力。本文系统梳理你必须掌握的核心公式，并附上简明解释与统一记号。
1. Linear Equations and Slope | 线性方程与斜率
The slope of a line through two points (x₁, y₁) and (x₂, y₂) is given by:
过两点 (x₁, y₁) 与 (x₂, y₂) 的直线斜率为：
m = (y₂ - y₁) / (x₂ - x₁)
Point-slope form: y - y₁ = m(x - x₁). Slope-intercept form: y = mx + b. Standard form: Ax + By = C, with slope -A/B.
点斜式：y - y₁ = m(x - x₁)。斜截式：y = mx + b。标准式：Ax + By = C，其斜率为 -A/B。
Parallel lines have equal slopes; perpendicular lines have slopes whose product is -1.
平行线斜率相等；垂线斜率之积为 -1。
2. Distance and Midpoint | 距离与中点
The distance between (x₁, y₁) and (x₂, y₂) is:
点 (x₁, y₁) 与 (x₂, y₂) 之间的距离为：
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
The midpoint M of the segment joining the two points is:
连接两点的线段中点 M 为：
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
These formulas are essential for coordinate geometry problems.
这两个公式是坐标几何问题的基础。
3. Quadratic Functions and Roots | 二次函数与根
A quadratic equation in standard form is ax² + bx + c = 0. Its roots are given by:
标准形式的二次方程为 ax² + bx + c = 0，其求根公式为：
x = (-b ± √b² - 4ac) / (2a)
The discriminant Δ = b² - 4ac determines the nature of roots: Δ > 0 gives two distinct real roots; Δ = 0 gives one repeated root; Δ < 0 gives no real roots.
判别式 Δ = b² - 4ac 决定根的性质：Δ > 0 有两个不等实根；Δ = 0 有一个重根；Δ < 0 无实根。
Vertex form: y = a(x - h)² + k, with vertex (h, k). Axis of symmetry: x =
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