Comprehensive High-Level SAT Prep Guide: Grammar, Math, and Reading Strategies


SAT Grammar: Independent Clauses and Punctuation Hierarchy

  • Systematic Approach: Grammar should be approached like math (1+1=21 + 1 = 2) rather than relying on how a sentence "sounds" or "vibes."

  • The Independent Clause (IC) Checklist: A group of words that can stand alone as a sentence must meet three criteria:

    1. A Subject: The thing doing the action (e.g., "John").

    2. A Main Verb: The primary action that is not an infinitive (starts with "to"), a relative clause (starts with "that"), or a gerund (ends in "ing"). Note: "He runs" is a complete IC.

    3. No Wasabi Word: It cannot start with a dependent word like: "while," "when," "since," "after," etc.

  • Separating Two Independent Clauses: There are only three valid ways:

    1. Period: [IC]. [IC].

    2. Semicolon: [IC]; [IC].

    3. Comma + FANBOYS: [IC], [and/but/or/nor/for/yet/so] [IC].

  • Separating Independent and Dependent Clauses (IC + DC): Usually done with a comma (95%95\% of the time) or no punctuation at all.

Detailed Punctuation Use Cases

  • The Period ($.$): Used strictly for separating two independent clauses.

  • The Comma ($,$): There are five primary uses:

    1. Lists: Separating items in a sequence of three or more.

    2. FANBOYS: Used before a coordinating conjunction (most commonly "and"/"but") to join two ICs.

    3. Non-essential Information: Comma before and after information that can be deleted without changing the sentence's logical meaning. (Example: Chimamanda Negoi Adichi, whose 2013 novel won rewards, has become influential. The name is essential if the person hasn't been identified yet, such as in "Biologist Hopi Hora.")

    4. Introductory Information: Placing a comma after a DC that begins a sentence (e.g., "After analyzing soil samples, the team…").

    5. Adjectives: Replacing "and" between two adjectives (e.g., "effective, fun way").

  • The Semicolon ($;$): Used to separate two ICs or for "Complex Lists" (lists where items already contain internal commas, such as "Lagos, Nigeria; Nairobi, Kenya; and Accra, Ghana").

  • The Colon ($:$): Used for an "Extension"/elaboration. High likelihood of being correct in answer choices. The part after the colon must explain or elaborate upon the part before it. (e.g., "…one of the ocean's most elusive phenomena: bioluminescence.")

  • The Question Mark ($?$): Only used if the sentence begins with a question word (Which, Why, How, Do). Inside a sentence, it only works if a colon creates a new starting point.

  • The Dash ($-$): Functions either like non-essential information commas (one dash before and one after) or like a colon (used for an extension).

  • Transition Word Placement (However):

    • If Sentence A contradicts the first half of Sentence B: "Sentence A. However; Sentence B (Part 1)."

    • If the first half of a sentence contradicts the second half: "Sentence B (Part 1); however, Sentence B (Part 2)."

    • If no independent clauses surround it, use commas like non-essential info: ", however,".

SAT Verbs: The Three Main Rules

  • Rule 1: Focus on the First Word: When choices are verbs like "has played" or "are playing," look only at the first word ("has," "are").

  • Rule 2: Singular vs. Plural:

    • Nouns: S at the end = Plural.

    • Verbs: S at the end = Singular.

    • Singular Verbs: "is," "has," "was," "walks."

    • Plural Verbs: "are," "have," "were," "walk."

    • The Odd One Out Rule: If three choices are plural and one is singular, the singular one is almost always correct (and vice versa).

  • Rule 3: Main Verb Identification: A sentence usually needs exactly one main verb. Non-main verbs often start with "to"/"that" or end in "ing."

    • If a main verb exists, pick a non-main verb for the blank. If no main verb exists, the blank must be a main verb.

  • Edge Case: "A [Subject] of [Word]": The subject is the word before "of" (e.g., "Line of words" is singular, not plural).

  • Edge Case: "Neither/Nor": Match the verb to the second item listed (the one after "nor").

  • Verb Tense (Time): Use context clues. "Will" indicates future tense. Match the surrounding verbs (if surroundings are past, use past).

  • The "Had" Rule: Use "had" for an event that happened before another past event ("Past before past").

Modifiers, Pronouns, and Possession

  • Modifiers: The descriptive phrase before a comma must perfectly match the subject immediately after the comma. (e.g., "Free, fast, and available 24/7, AI chatbots…").

  • Pronouns: Must match the noun in number (Singular vs Plural) and case:

    • Subjective: I, he, she.

    • Objective: me, him, her, them.

    • Possessive: my, mine, its.

  • Possession Punctuation:

    • 's: Singular (e.g., "Girlfriend's account").

    • s': Plural (e.g., "Phones' notifications").

Desmos Graphing Calculator Mastery

  • The Power of Desmos: Over 50%50\% of math questions can be solved using Desmos alone.

  • Function Basics: Think of functions as inputs and outputs.

    • Linear: y=mx+by = mx + b (increases by a stable amount).

    • Quadratic: y=ax2+bx+cy = ax^2 + bx + c (parabola shape).

    • Exponential: y=a×bxy = a \times b^x (number with an exponent).

  • Interface Shortcuts:

    • Constants: Type a letter (a, b, c) and click "Slider" to slide through values.

    • Calculations: Literal typing of expressions gives instant answers.

    • Statistics: Type "mean", "median", "stdev", "min", "max", or "gcd" followed by a list of numbers in parentheses.

    • Trigonometry: Type "sin", "cos", "tan". Use the wrench icon to switch between radians and degrees.

    • Intercepts and Vertex: Click directly on the points on the graph for coordinates.

  • Single Variable Equations: Solve by looking for where the line crosses the x-axis.

  • Systems of Equations/Inequalities:

    • Intersection = Solution.

    • No intersection = Zero solutions; Same line = Infinite solutions.

    • Inequalities: Look for the double-shaded region. Solid lines indicate "greater than or equal to" (≥\ge) or "less than or equal to" (≤\le).

Desmos Regression Techniques

  • Regression Without a Table: Used when you have more unknowns than equations (e.g., 3 variables but only 2 equations).

    1. Treat x and y as constants by typing x1x_1 and y1y_1.

    2. Use the tilda (∼\sim) instead of an equal sign.

    3. Join multiple equations using brackets: [2x1z+y1∼3,x1−z∼y1z][2x_1 z + y_1 \sim 3, x_1 - z \sim y_1 z].

    4. "All real numbers of x": Use x1=[1..10]x_1 = [1..10] to test multiple values.

    5. Constraints: Add curly brackets for specific conditions (e.g., {t>0,a>1}\{t > 0, a > 1\}).

  • Regression With a Table: Type "table" to generate points.

    • Linear: y1∼mx1+by_1 \sim mx_1 + b.

    • Quadratic: y1∼ax12+bx1+cy_1 \sim ax_1^2 + bx_1 + c.

    • Vertex Form: y1∼a(x1−h)2+ky_1 \sim a(x_1 - h)^2 + k (where (h,k)(h, k) is the vertex point).

    • Circle Equation: (x1−h)2+(y1−k)2∼r2(x_1 - h)^2 + (y_1 - k)^2 \sim r^2 (where (h,k)(h, k) is the midpoint and rr is the radius). Note: You must re-type the result as a standard equation with "=" to visualize the circle on the graph.

Reading Passage Strategy

  • The Translation Technique: After every individual sentence, summarize it in plain, simple English (the "Feynman Technique"). Avoid using the passage's sophisticated terminology.

  • Predict: Read the prompt and answer the question in your own words before looking at the A/B/C/D choices to avoid trap answers.

  • Eliminate: Every single word in an answer choice must be supported by the passage. If one word is wrong, the whole choice is gone.

  • Stay Close: If two choices are similar, pick the one that makes the fewest assumptions.

  • Note-Taking Escape Hatch: If a passage is extremely dense, take notes on the main idea only. Keep it to 4 or 5 words maximum and deliberately brief (e.g., "SM teen ID sigh worried").

  • Context for Vocabulary: You don't need to know every word (e.g., "aromatic hydrocarbons") to answer questions. Use the surrounding facts to treat the word like a variable.

Standard SAT Reading Question Types

  • Central Ideas and Details: Identifying the main point or specific facts.

  • Inferences: Completing the passage based on logical progression found in the text.

  • Text Structure and Purpose: Determining why a specific sentence or paragraph exists and what action it performs.

  • Command Of Evidence: Finding the data point or evidence that most directly supports a specific claim (e.g., "sea urchin increase causes kelp decline").

  • Cross-Text Connection: Comparing two passages and determining how Author B would likely respond to Author A's claims.

The Five Patterns of Wrong Answers

  1. Contradiction: The choice says the exact opposite of the passage.

  2. Half-Right: Part of the choice is factually correct, but another part is wrong.

  3. Out of Scope: The choice introduces information not discussed (e.g., mentioning "sea otters" when they aren't in the text).

  4. Too Extreme: Using absolute language like "always," "never," or "only" when the passage is more nuanced.

  5. Wrong Question: The choice is factually true according to the passage but does not actually answer the specific question being asked.