SAT Class 1

Absolute Value:

• |x - 3| = 5: The absolute value represents distance from 0.

• |x - a| = b: The distance between x and a is b.

• |x + a| = b: Distance between x and -a is b.

• Example: |x - 3| = 5 → The distance between x and 3 is 5.

Inequalities and Equations:

• | -2x + 1 | < 1: Inequality involving absolute value.

• Convert inequality to an equality: | -2x + 1 | = 1.

Subtraction = Distance:

• The distance between two numbers is calculated by subtraction.

• Example: |x - 3| = 9 → Distance between 3 and 9 is 6, or 9 - 3 = 6 and 3 - 9 = -6.

Mathematical Example with Distances:

• AC = a

• CE = b

• a + b = 25

• AB = a, BC = a

• 3aABC = 3a

• 3a + 3b = 3(a + b) → Substitute: 3(25).

Parallelism:

• Parallel = Agreement: Things that are parallel align in some way.

Clauses in Sentences:

• Independent Clause (IC): A complete thought. Example: "I went to the park."

• Dependent Clause (DC): Cannot stand alone, depends on IC. Example: "wanting to go to the park."

• Clauses contain a subject and a verb.

Articles:

• Articles are "a," "an," and "the."

• French Articles: le, la, les.

• Function of Article: Noun announcer. Example: "I went to the mall." or "I went to the beautiful mall."

Adjectives vs. Adverbs:

• Adjective (adj): Describes a noun. Example: "beautiful."

• Adverb (adv): Describes how, when, where, or why. Example: "beautifully."

• Example: "I went to the very beautiful mall."

• Difference between "lavish" (adj) and "lavishly" (adv).

Verb Examples:

• "Go" as a verb.

• "Walk" is an action (verb).

Sentence Construction:

• "I took a walk.": Simple sentence with subject, verb, and object.

• "I was tired.": Subject + linking verb + adjective.

Logic:

• Logic = The flow of facts.

• Common sense = Facts.

• Example of logic: "If A, then B."