Thành thạo Đại số 1 từ những nguyên lý cơ bản
Phương trình bậc nhất, bất phương trình, hàm số, phương trình bậc hai và đa thức. Chuẩn theo Khung Chương trình Massachusetts cho Đại số I.
Đại Số 1 — Công Thức Cốt Lõi (Tra Cứu Nhanh)
Mọi công thức bạn cần cho Đại số 1 Regents trên một trang — phương trình tuyến tính, độ dốc, hệ, bậc hai, quy tắc lũy thừa.
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.