从第一原理掌握 代数1
一次方程、不等式、函数、二次函数和多项式。
Algebra 1 核心公式 —— 快速查阅
一页囊括 Algebra 1 Regents 所有公式 —— 一次方程、斜率、方程组、二次式、指数规则。
Linear Equations: The Five-Step Method That Solves Every “Find x”
Every solve-for-x problem on the Algebra 1 Regents comes down to the same five moves — distribute, combine, isolate, divide, check. Master the order and you'll handle one-step through both-sides equations on autopilot.
Linear Inequalities: Solving, Graphing, and the One Sign-Flip Rule
Inequalities solve like equations — except for one twist. Multiply or divide by a negative and the inequality sign flips. Master that single rule and you'll solve every Regents inequality on autopilot.
Slope & Linear Graphs: Rise Over Run, Three Equation Forms
Slope is rate of change — and rate of change is the entire point of Algebra 1. Master the slope formula, the three line equations (slope-intercept, point-slope, standard), and when to use each.
Systems of Equations: Three Methods, One Intersection Point
A system of equations asks where two lines cross. Three ways to find that point — graphing, substitution, elimination — and how to recognize when there are zero, one, or infinite solutions.
Functions & Notation: f(x), Domain, Range, and the Vertical Line Test
A function is a rule that takes one input and gives one output. Master f(x) notation, domain/range, and the vertical line test — the foundation for every equation and graph in Algebra 1.
Polynomials & Factoring: FOIL, GCF, and the Three Patterns
Multiply binomials with FOIL, then run the process backward to factor. Three patterns cover most Regents factoring questions: GCF, trinomial (x² + bx + c), and difference of squares.
Quadratic Functions: Parabolas, Vertex Form, and the Quadratic Formula
Every quadratic graphs as a parabola. Master vertex form to read the vertex on sight, and the quadratic formula to find the roots when factoring fails.
Exponential Functions: Growth, Decay, and the Doubling Rule
When the rate of change is proportional to the amount, you have exponential. Master the y = a · b^x form, half-life, compound interest, and the visual difference between linear and exponential.
Arithmetic & Geometric Sequences: Find the nth Term
Arithmetic sequences add the same number each step (linear pattern). Geometric sequences multiply by the same number each step (exponential pattern). Two formulas, one strategy: identify, then plug in.
Statistics & Data Analysis: Mean, Median, Mode, and the Correlation Coefficient
Mean, median, and mode summarize a data set in one number — but they tell different stories. Plus correlation vs causation, and how to read a correlation coefficient.