SAT Math Core Formula Handbook | SAT数学核心公式全梳理

📚 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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