More Tips/Equations

Who vs whom

Plug in they for who and them for whom to see which works

Which vs that

Comma before which (ALWAYS)

No comma before that

Direct relationship

Divide

Inverse relationship

Multiply

Square root function

all positive solutions

Distance formula

√(x_{2 ^-} x₁)² + (y_{2 ^-} y₁)²

Like the pythagoream theorem

Midpoint formula

(avg x, avg y)

Standard form slope

Ax + By = C

m = -A/B

Standard Form x intercept

C/A

Standard form y intercept

C/B

Zero slope

horizontal line

Undefined slope

vertical line

Compound inequality

separate into 2 inequalities to solve separately easier

CHECK

that graphs start at 0

what the question is actually asking for

Average rate formula

total distance/total time

DRT questions

D = R * T

given 2 trips of same D —> system of equations

Ratio questions

ratio, multiplier, actual table

make multiplier the same

Absolute value

|x-b| = a (b is midpoint and a is variance)

Absolute value with variable

split into 2 equations

1 is normal without | |

other flip the sign on everything outside of | |

Radicals

separate number until you get the number of the radical

√18 = √2 × 3 × 3 = 3√2 (since there was 2 3s and the radical was 2 you take out the 3)

x coordinate of vertex

-b/2a

review

difference of squares

factoring when a isnt 1

factoring more than normal quadratic

a² + 2ab + b²

(a + b)(a + b)

a² - 2ab + b²

(a - b)(a - b)

a² - b²

^{RECOGNIZE THIS}

(a + b)(a - b)

Standard form roots

sum of roots = -B/A

product of roots = C/A

discriminant

b² - 4ac

<0 no solutions

=0 1 solution

>0 2 solutions

Transformations order

left/right

reflection

up/down

sum of interior angles

180(n-2)

n = number of sides

sum of exterior angles

always 360

supplementary

add up to 180

Circle Circumference

2πr

Circle Area

πr²

Cube suErface area

6s²

Equilateral triangle area

A= (s²√3)/4

Trapezoid area

A = (b₁ + b₂)/2 *h

Arc length

(x^o/360^o)2pir

Area of sector

(x^o/360^o)pir²

incomplete transversals

sum of 3 interior angles add up to 360

triangles rules

any side must be shorter than sum of other 2 sides

measure of an exterior angle = sum of remote interior angles

congruent triangle rules

SSS, SAS, AAS, ASADisnsity

mass/volume

density

pythagoream triples

3-4-5

5-12-13

7-24-25

8-5-17

9-40-41

2pi to degrees

360

sin(x) to cos

cos(90-x)

sin(theta) to cos

cos(pi/2 - theta)

Trig positive negative quadrants

ASTC

1234

Drawing angle

Angle comes off of x axis

Circle standard form

(x-h)² + (y-k)² = r²

Circle general form

CONVERT TO STANDARD

Reading comprehension strategy

Question

Underline/highlight

Identify

Cross out answers

Keep best answer

Other reading strategies

Identify subject, verb, independent clause, dependent clause, extra info, etc

find method

Find one error

Identify repeated error

Note difference in remaining

Decide which is correct

Period and semicolon are the ONLY difference between andwers

Elimínate both

Misplaced modifiers

When extra information about a noun is too far from it in the sentence and can be confusing

“Based on cats, Netflix aired the show Cats”

(Netflix isn’t based on cats)

Inference pattern

Topic/claim

Contrary statement

Implication

DONT INFER TOO MUCH

Complementary angles

Add up to 90 degrees