Formula Sheet

Slope-intercept: y = mx + b

Point-slope: y − y₁ = m(x − x₁)

Standard form: Ax + By = C

Slope: m = (y₂ − y₁) / (x₂ − x₁)

For ax² + bx + c = 0:

x = (−b ± √(b² − 4ac)) / 2a

Discriminant: b² − 4ac determines number of solutions

Substitution: solve one equation for a variable, substitute into the other.

Elimination: add or subtract equations to cancel a variable.

aᵐ · aⁿ = aᵐ⁺ⁿ

(aᵐ)ⁿ = aᵐⁿ

a⁻ⁿ = 1/aⁿ

a^(1/n) = ⁿ√a

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

sin²θ + cos²θ = 1

180° = π radians

To convert: degrees × π/180 = radians

To convert: radians × 180/π = degrees

Mean: sum of all values ÷ number of values

Median: middle value when data is ordered

Mode: most frequently occurring value

Measures how spread out values are from the mean.

Low SD — values clustered near mean

High SD — values spread far from mean

On the SAT you compare SDs, not calculate them.

The range within which the true population value is likely to fall.

Confidence interval = sample statistic ± margin of error

Larger sample means smaller margin of error

P(event) = favorable outcomes / total outcomes

0 ≤ P(event) ≤ 1

P(not A) = 1 − P(A)

Percent = (part / whole) × 100

Percent change = (new − old) / old × 100

Line of best fit: ŷ = mx + b

Positive correlation: as x increases, y increases

Negative correlation: as x increases, y decreases

Before FANBOYS: use comma before for, and, nor, but, or, yet, so when joining two independent clauses.

After introductory element: use comma after an intro clause/phrase.

Non-essential clause: set off with commas (can be removed without changing meaning).

Items in a series: A, B, and C (Oxford comma preferred on SAT).

Singular subject takes a singular verb: The dog runs.

Plural subject takes a plural verb: The dogs run.

Tip: Ignore prepositional phrases between subject and verb. "The list of items is..."

Collective nouns (team, group) are usually singular.

Semicolon (;): joins two independent clauses — no conjunction needed.

Colon (:): introduces a list, explanation, or elaboration. Must follow a complete clause.

Pronoun must agree with its antecedent in number and gender.

Everyone is singular: Everyone has his or her book.

Ambiguous pronoun reference is always wrong — make it clear what the pronoun refers to.

Possession: singular nouns add 's (the cat's toy)

Plural nouns ending in s add ' (the cats' toys)

Contraction: it's = it is; they're = they are; you're = you are

No apostrophe: its (possessive), their, your, whose