Day 2 of 90 Days of Free SAT Prep Lessons! By a 1590 SAT Scorer! Math Equations and Grammar Rules!!!

SAT Math Formulas and Equations
📌 The session covered key SAT math formulas, starting with the slope-intercept form of a line: $y = mx + b$, where $b$ is the $y$-intercept and $m$ is the slope.
📐 The vertex form of a quadratic equation is $y = a(x-h)^2 + k$, where the vertex is located at the point $(h, k)$.
➗ The distance formula is derived from the Pythagorean theorem: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, which can be simplified to $\sqrt{\text{run}^2 + \text{rise}^2}$.
➗ The quadratic formula to find roots ($x$-intercepts where $y=0$) for $ax^2 + bx + c = 0$ is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Exponent Rules
➕ When multiplying exponents with the same base ($z^x \cdot z^y$), add the exponents: $z^{x+y}$.
➖ When dividing exponents with the same base ($\frac{z^x}{z^y}$), subtract the exponents: $z^{x-y}$.
✖️ When raising a power to another power ($(z^x)^y$), multiply the exponents: $z^{xy}$.

Algebraic Patterns (Factoring)
➖ The difference of perfect squares factorization is $x^2 - y^2 = (x-y)(x+y)$.
➕ The perfect squares trinomial (positive middle term) expands to $(x+y)^2 = x^2 + 2xy + y^2$.
➖ The negative perfect squares trinomial expands to $(x-y)^2 = x^2 - 2xy + y^2$.

SAT Writing: Grammar Rules
✍️ Subject-Verb Agreement: The number (singular/plural) of the verb must match the number of its subject.
💡 A common indicator for a singular verb is an 's' ending that can be dropped (e.g., "he runs" vs. "they run").
👥 Collective Nouns (like *congress* or *band*) are treated as singular subjects and require singular verbs, even if they represent a group of individuals.

SAT Writing: Sentence Structure and Modification
❌ Prepositional phrases (e.g., *of clarinet players*) must be ignored when determining subject-verb or subject-pronoun agreement number.
✂️ Sentence Fragments lack a complete thought or a crucial component like a verb, making them stand-alone sentences.
🔗 Comma Splice: Incorrectly joining two independent clauses with only a comma (no coordinating conjunction/FANBOYS).
🛑 Run-on Sentence: Two independent clauses joined with no punctuation or only a coordinating conjunction without a preceding comma.
➡️ Modifiers must be placed directly next to the word they modify; introductory modifiers require a comma after them.

Key Points & Insights
➡️ Note-Taking is Crucial: The presenter stresses writing down key formulas (Slope-Intercept, Vertex Form, Distance, Quadratic, Exponent Rules, and Perfect Square Patterns) for memorization.
➡️ Prioritize Accuracy Over Pacing (Initially): Focus the first few weeks on mastering the material and achieving high accuracy before moving on to timing and pacing strategies for the SAT.
➡️ Identify Sentence Errors Quickly: Master identifying comma splices, run-ons, and fragments as these are frequent, high-value error types in the SAT Writing section.
➡️ Check Pronoun Agreement: Pronouns must clearly refer to their antecedent and agree in number; always ignore prepositional phrases when checking this agreement.

📸 Video summarized with SummaryTube.com on Jan 22, 2026, 08:00 UTC