SAT prep

English and math

Percent Change

(Original - New Value / Original ) x 100

Adding Percent

• To show an increase you add one to the percent

EX: x+15% → x(1.15)

Subtracting Percents

• To show a decrease you should subtract the percent from 1

EX: x-15% → x(1-0.15) = x(0.85)

Repeated ercent Change

• If somethign changes multiple times → MULTIPLY

EX: Increase by 10% twice: 1.10 × 1.10

Sum of roots

-b / a

Product of roots

c / a

Vertex form of a Parabola

y=a(x-h)²+k

• (h,k) is the vertex

Y-coordinate of Vertex

-b / 2a

• To find x value, plug the value back into the function for y

Point Slope form

y-y₁=m(x-x₁)

• (x_1, y₁)

Arc length

2πr(angle/360

Sector Area

πr²(angle/360)

Tangent

• Always meets at one point and forms a 90* agle with radius

• The tangents slope is perpendicular to the radius → negative reciprocal of radius’ slope

Equation of circles

(x-h)²+(x-k)²=r²

• (h,k) is the center of the circle

• r is the radius → If the number isnt squared: square root it to find radius

Complete Sentance

1. Subject - Who are what the sentance is about

2. Verb - The action or state of being

3. Full idea is expressed: It must make sense by itself

Incomplete sentances depend on something else

Comma

• Before FANBOYS (for, and, nor, but, or, yet, so)

• After introductory sentances

  • After school, I studied.

• Around non-essential information → Extra info that can be removed and wont change the meaning of the text

• In a list

Comma Splice: Adding a comma between to complete sentances

Semi Colons

• To connect to complete setnaces that are closely linked in meeting → If a period makes sense, so will a semicolon

• Goes before transition words

• Used in complex lists that include more than one word

Dash

• Adding extra information: Its stronger than a comma.

  • My mother—who hates cooking— never cooks.

• To emphasize something important

  • I only had one goal—to get a good grade.

• To introduct a list: slighly less formal than a colon

  • He packed everything—clothes, shoes, and books.

Colons

• Explains something that comes after it

The part before the colon must be a complete sentance.

• To introduce a list, example, or quote.

Apostrophes - Possesion

Singular - Add ‘s to a singular noun

• EX: Dog’s leash

Plural - Add ‘ the a plural noun

• EX: The dogs’ park

Subject-Verb Agreement

The subject and verb must match in number

• Singular subject → singular verb

• Plural subject → plural verb

The verb tense must stay consistant throughout the sentance

Have been

Past actions that affect the present

Cause and Effect

Thus, Accordingly, Hence, Consequently, to this end

Contrast Trasition words

Nevertheless, Regardless, Still

Sequence (Order / Time) Transition

Subsequently- after or later