SAT Study

Median

the middle score in a distribution; half the scores are above it and half are below it

Mode

the most frequently occurring score(s) in a distribution

veered

change direction

Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p ?

p/((0.8)(1.08)) Take amount payed and divide by product of discount and sales tax

if the expression 6x^2/3x-6 is equivalent to 24/2x-6 + N what is n in terms of x?

plug in number for x and solve for n then determine which answer choice is equivalent to n 2x + 4

When asked for solutions of multiple inequalities

plug in values from each quadrant and determine which quadrants are included in the solution set values must work for both inequalities in order to be part of the solution set

The indefinite pronouns both, few, many, others, and several

plural

plural subject

plural verb exp: know, pay, spring

to effectively combine underlined sentences

precision and concision

deftness

skill

Probability

# of outcomes that fit requirements over # of possible outcomes

circle properties

(#/360)=(arc/circumference)=(sector area/area)

Midpoint Formula

(x₁+x₂)/2, (y₁+y₂)/2

√2x

(√2x)^2=2x

more circle properties

(part/whole) (central angle/360) (arc length/circumference) (sector area/ pi r^2)

midpoint

(x+x/2, y+y/2)

circle (h,k)

(x-h)^2+(y-k)^2=r^2

go punctuation

- Can link anything EXCEPT Two complete ideas -comma -NO punctuation

ax^2+bx+c

-b/a=sum of solutions c/a=product of solutions

stop punctuation

. and ;

In the figure above, if cos angle DBA=.3, what is the value of cos dba + sin dba

.6

extraneous solutions

0 in denominator or taking square root of a negative number

Reading Approach

1. Read the blurb 2. Select and understand your question 3. Read what you need 4. Predict the correct answer 5. POE

A rectangle was altered by increasing its length by 10 percent and decreasing its width by p percent. If these alterations decreased the area of the rectangle by 12 percent, what is the value of p ? A) 12 B) 15 C) 20 D) 22

1.10L+(1-p/100)=.88A solve for p p=22

2(5√2)

10√2

if 153=2(z+z)n, what is 2n(2z)-193

153=2n(2z) 153-193=-40

Find degrees in a polygon

180(n-2) n is the number of sides

1 radian

180/π

360=

2 pi

surface area rectangular solid

2(lw+wh+lh)

Which of the following is equivalent to 4^5^6

4^5^6 rewrite as 2^2^5^6 power to power rule so you get 2^5^3 rewrite as 3√2^5 for every three twos, one can come out 2^3√2^2=2^3√4

A train passes through the Appleton train station every 20 minutes. The first train each day passes through at 6 am and the last train passes at 10:40 pm. How many trains pass through the Appleton station in one day?

51 Don't forget to include the first train.

suface area cube

6s^2

Bowtie Method

7/9 - 1/6 7 x 6=42 42-9=33 9 x 6=54 33/54=11/18

i^2

=-1

4-i^2

=5

analogy

A comparison of two different things that are similar in some way

Which of the following cannot be an example of a function whose graph in the xy plane has two x intercepts?

A quadratic function with no real zeroes.

area of haxagon

A=((3rad 3)/2) times a^2

When two parallel lines are intersected by a third line

All the small angles are the same; all the big angles are the same; and any small angle + any big angle = 180°

Phrases for addition

Also, moreover, in fact, furthermore, in addition, similiarly, indeed, in other words, next, likewise, then, for example

Mean

Average

circumference

C=2(pi)r

which of the following accurately defines all values of p-1 if 15 ≤ p ≤ 30 and 7 ≤ p ≤ 19

Can't stack and subtract as that will flip sign so do 30-7=23 30-19=11 15-7=8 15-19=-4 Take two numbs from same inequality and subtract from other two extremes -4 ≤ (p-q) ≤ 23

Vertex form

Complete the square

The volume of conce C is 12 millimeters. What is the volume in cubic millimeters of a cone with one third of the radius and triple the height of cone C?

Cone Formula: V=1/3πr^2h V=1/3 π (r/3)^2 3h V=1/3 π (1/9) r^2 3h V=1/3 π r^2 1/3 The volume is 1/3 of volume of original cone 1/3 x 12=4

Percent Change

Difference/Original times 100

when to use fewer

Fewer is used when comparing countable things

contrast words

However, on the other hand, nonetheless, nevertheless, still, instead, despite this, meanwhile

For what value of x is the expression 2/(x-6)^2+4(x-7)+8 undefined?

If on the calculator section, graph the equation and find the x value that produces an error. x=4

y = a( x− 2)( x+ 4) In the quadratic equation above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (, ) c d . Which of the following is equal to d ?

If the parabola is factored, x vertex is the average of the zeroes zeroes: 2 and -4 Average of zeroes: -1 c=-1 Plug in c in for x d=-9

circle inscribed in square relationship

If the radius of the circle inside is 2, then the square faces on either end must have sides double the radius, or 4. The long dimension of the box will be 3 times the other two sides(4) which is = to 12.

g(x)=2-3^x The function g(x) is defined by the equation above. Which of the following is the graph og y=-g(x) in the xy- plane?

If you don't know graph you can plug in points. Y int of original is 1 so if you negate it new y int is -1.

Magnitude

Ignoring sign and paying attention to how big or small a number is

when to use less

Less is used when comparing non-countable things

When given a circle of many triangle and it tells you the center of the circle

Look for radii and two equal radii can tell you if a triangle is isosceles which will help you solve for angles

half stop punctuation

Must be preceded by a complete idea : and -

possesive pronouns

Our, Mine, Their, Ours, His, Hers, Your, Yours, Their, My, Its, Are

Determine if expressions are equal to one another

Plug in or solve for variable

When given a system of equations and asked what variable makes the system have one solution

Plug in the answer choices

pita

Plugging In The Answer

objective tone

Presenting information in a way that is not emotional or biased

R=f/n+f solve for f

Put R over 1 and cross multiply, then solve for f

Parallel Lines

Same Slope If two lines have same slope they have no solutions

Standard From ax+by=c

Slope=-a/b Y interecept=c/b

Infinite solutions or no solutions

Slopes of equations are equal.

diagonal formula

Super Pythagorean Theorem l^2 + w^2 + d^2 = (diagonal)^2 use to find length of square sides inscribed in circle once you find the radius

absolute value

The distance a number is from zero on a number line

if there is a dash before a phrase

chances are a dash should follow that phrase

For a polynomial p x( ), the value of p(3) is −2. Which of the following must be true about p x( ) ?

The remainder when p x( ) is divided by x − 3 is −2.

Which of the following must be true regarding d(x) if d(x) is a polynomial and d(-9)=1

When d9x0 is divided by x + 9, the remainder is 1

Growth and Decay Formulas

When the growth is a percent of the total population, use final amount=original amount(1+rate)^number of changes When the growth is a multiple of the total population, use final amount=original amount(multiplier)^number of changes

3y less than 7 x less than 3y + 4 which of the following consists of the x coordinates of all the points that satisfy the system of inequaties above?

When you see an inequality, PLUG IN. Make x and y = to something that will make the system of equations true. Answer: x less than 3.

Quadratic Equation

Y=ax^2+bx+c

Standard Deviation

a measure of variability that describes an average distance of every score from the mean

innovation

a new way of doing something

population parameter

a numerically valued attribute of a model for a population

understanding proposition

make arguement more precise and effective

geometry parallel lines

alternate interior angles are =

constant rate

always the linear equation

Rational Equation

an equation containing at least one fraction whose numerator and denominator are polynomials polynomial denominators: multiply denominators by each side to get rid of it.

fanboy vertical line test

and is a fanboy so draw vertical line through and but is a fanboy so draw a vertical line through but

Linear Pair

angle + angle=180

as likely

as in

mood

attitude informational, command, persuasive

Standard Form

ax+by=c

3/3b+2b/b-3=2

b=3/5 use bowtie method to get fractions together multiple by denominators solve for b

commas come

before conjunction (and)

idiom but

but also

when a quadratic equation doesn't factor, you have two options:

completing the square (better option) quadratic formula

a+bi

complex number a is real b is imaginary

understanding focus kept or deleted

concise and precise

supporting an arguement

concise, precise, consistent

still

contrasting transition

sin x

cos (90-x)

two fractions equal to one another

cross multiply

Discriminant

d=positive=2 solutions d=0 one real solution d=negative=0 solutions

Distance Formula

d=√(x2-x1)^2+(y2-y1)^2

idiom defined

defined as

To find arc length

degrees of arc/360 x cirumference value

deviation

departure from the norm

ballparking

determing which answer choices are in a reasonable range of the solution

idiom different

different from

rate

distance/time

to find scale of graph

divide total by values on y axis

subject pronoun

does action

punctuation vertical line test

draw vertical line where punctuation is between two sentences if two complete ideas=stop punctuation (semincolon or period) one complete idea= (comma)

ample

enough or plenty

Regular Hexagon

equal angles 720 degrees cut into 6 triangles

inherently

essentially

factoring third degree equations

factor by group

impermanent

fades away, doesn't last

fanboys and semicolons

fanboys are not used with semicolons

idiom fear

fear of

instead of counting blocks to find slope

find two points on graph find rate of change in order to be safe as images are not drawn to scale always

if two sentences share similiar ideas and have the word furthermore

furthermore sentence comes second as it further elaborates upon a topic

when polynomial g(x) is divided by x-4, the remainder is 3. Which of the following statements about g(x) must be true?

g(4)=3

comma ,

go punctuation

incomplete to complete

go punctuation

no punctuation

go punctuation

to connect two incomplete ideas

go punctuation

y ≤-15x+3000 y≤ 5x In the xy‑plane, if a point with coordinates (a, b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?

graph two equations shade solutions set look in table for solutions or find solution by locating the intersection of the two equations.

at least

greater than or equal to

maximum of function

greatest y value

if the equation of a parabola is given in factored from

h is equal to the average of the roots of the equation

when equation of parabola is in standard form

h=-b/2a

connect complete and incomplete idea

half stop or go punctuation

colon :

half stop punctuation

dash -

half stop punctuation

confidence interval

how confident one is in the data

margin of error

how incorrect the data appears to be

nonetheless

however shows contrast

imaginary numbers

i^1=i i^2=-1 i^3=-i i^4=1

idiom regard

in regards to

affect

influence

=

is, are, were, did, does

idiom jealous

jealous of

no more than

less than or equal to ≤

chord

line of circle from one point to another diameter is the longest chord on a circle

To divide one polynomial by another

look at the leading terms in both polynomials. The value that results from dividing the leading term in the numerator by the leading term in the denominator is the first term of the quotient.

contempt

looking at someone with hatred or dishonor

if -5/3 ≤ p ≤ -3/2, which of the following accurately expresses values for -12s+9?

manipulate the middle of the equation to get -12s-9 multiply by -4 and then add one do the same for all three parts of inequality solution: 7 ≤ -12s +9 ≤ 23/3

ambivalence

mixed feelings about someone

which of the following complex number is equivalnt to expression with i

multiply by conjugate

with fractions on either side of inequality

multiply by denominators first so you don't mess up the sign of the inequality

unwanted denominators

multiply by unwanted denominators to get rid of them

3-5i/8+2i

multiply top and bottom by 8-2i which is conjugate

subject and verb

must agree in number

if 13 ≤ 31-2x ≤ 39, What represents all possible values of x

must isolate x -31 from all three parts divide by -2 from all three parts which flipps signs of inequality answer: -4 ≤ x ≤ 9

Mr. Kohl has a beaker containing n milliliters of solution to distribute to the students in his chemistry class. If he gives each student 3 milliliters of solution, he will have 5 milliliters left over. In order to give each student 4 milliliters of solution, he will need an additional 21 milliliters. How many students are in the class? A) 16 B) 21 C) 23 D) 26

n=3x+5 the 5 represents the extra mililiters n=4x-21 the 21 represents the mililiters that he does not have set expressions equal and solve for x which is the number of students in the class

novelty

new and unusual

ax^2+bx+c

no b term means its centered on the y axis c term is y intercept

complete idea first

no comma

idiom not

not only

consistency

number gender case

ambigious

open to more than one interpretation

m=1/2p

p=2/1m switch variables take reciprical

fractions

part/whole

when you divide hexagon into 6 triangles

pay attention to the degrees each line bisects (120) look for 30 60 90 triangles and remember area formula

from question to question

pay attention to what is changing and what you are being tested on

rhombus

perpendicular diagonals perpendicular slopes negative recipricals

active voice

person doing the action

180=

pi

circle area

pi r^2

Which choice most effectively combines the sentences at the underlines portion?

puncutation may change but the question is testing precision and concision shortest answer is most likely to be correct

s=rθ

r=radius s=length of arc θ=degrees of central angle (convert to radians)

passive voice

receiver of action

object pronoun

receives action

voice

refers to whether the subject of the sentence is also performing the action of the verb

Polynomial Remainder Theorem

remainder when polynomial f(x) is divided by a linear polynomial x-a is equal to f(a)

idiom responsibility

responsibility to

idiom responsible

responsible for

effect

result

slope

rise/run

s=r(theta)

s is arc length r is radius theta is central angles in RADIANS

kx-3y =4 4x −5y =7 In the system of equations above, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?

same solution=same slope put both equations in y=mx+b form find slope of second equation and set it equal to slope of first equation solve for k

modifiers

should be next to what they are describing

cos 60=x what is also equivalent to x

sin 30

Indefinite pronouns that end in -body

singular

Indefinite pronouns that end in -one

singular

each

singular

The indefinite pronouns all, any, more, most, none, and some

singular and plural

indefinite pronouns

singular exp: anybody, anyone, anything everybody, everyone, everything nobody, no one, nothing somebody, someone, something

singular subject

singular verb exp: knows, pays, springs

minimum of function

smallest y value

after taking square root

solution is always plus or minus

, plus and

stop punctuation

comma + but

stop punctuation

comma + fanboy

stop punctuation

semicolon

stop punctuation

solving systems of linear equation

stack and add distrubute -1 and subtract manipulate equations

a fast increase in a graph

steep slope

nevertheless

suggests a really amazing and unexpected connection

however

suggests at most mild surprise

An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?

sum of first ten ratings is 750 in order to have an average of 85 for for the first 20 ratings, the total sum is 1700 1700-750=950 950 is the sum of the next 10 ratings maximum 9 x 100=900 so the lowest rating is 50

ax^2+bx+c

sum of roots= -b/a x value of vertext=-b/2a

pronoun

takes the place of a noun exp: he, her, he, she

tangent vs radius

tangent is perpendicular to radius

antecedent

term for what pronoun refers to

punctuation changing

test stop and go puntuation vertical line test complete or incomplete sentences

Range

the difference between the highest and lowest scores in a distribution

syntax

the order in which words appear in

if two triangles are similiar

their corresponding angles are congruent

four items

three commas

Causation words

thus, as such, therefore, consequently, as a result

MADSPM

to Multiply exponents, Add them; to Divide exponents, Subtract them; when there are Parentheses, Multiply exponents (power to power)

moreover

to add information

Tangent Lines

touch at one point form a 90 degree angle with the radius

tangent to y axis

touches y axis at one point

idiom try

try to

three items

two commas

Isosceles Triangle

two sides of equal length, equal base angles

part whole questions

understand how parts of text relate to the text as a whole exp: an initial paragraph can introduce a mood, provide context, make a claim while the rest of the story can contradict initial ideas, support initial ideas

text structure questions

use POE

relating quantitive information to an arguement

use POE to eliminate incorrect answers

In the xy-plane, the line determined by the points (2, k) and (k , 32) passes through the origin. Which of the following could be the value of k ? A) 0 B) 4 C) 8 D) 16

use given coordinates and origin to find a potential slope k-0/2-0=k/2 32-0/k-0=32/k k/2=32/k solve for k cross multiply k=8

when given endpoint of radius and center of circle

use pythgorean theorem to find the radius

To find how many solutions a system of equations has

use the discriminant d=b^2-4ac

once you know h

value of k can be determined using k=f(h)

Parallel Structuring

when 2 polynomials are set equal to one another, the corresponding parts can often be set equal.

verb tense

when the action happened past, present, future

possesive nouns

will always have an 's or an s' shows ownership and modifies like an adjective

Vertext of parabola ax^2+bx+c

x vertex=-b/2a

The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth-grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. If there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.) A) 0.410 B) 0.357 C) 0.333 D) 0.250

x+y=18 5x+9y=122 x=10 y=8

triangle 30:60:90

x:x rad 3:2x

The sum of three numbers is 855. One of the numbers, x, is 50% more than the sum of the other two numbers. What is the value of x ? A) 570 B) 513 C) 214 D) 155

x=1.5(y+z) x+y+z=855 2/3x=y+z x+2/3x=855 x=513

y=k(x-4)(x+12) In the quadratic equation above, k is a constant such that k is not = to -. When the equation is graphed in the xy-plane, the graph is a parabola with vertex (m, n). Which of the following is equal to n?

x=4 and x=-12 (0,4)(0,-12) FInd midpoint which = (-4,0) m=-4 y=k(-4-4)(-4+12) y=-64k

circle (0,0)

x^2+y^2=r^2

x^a^2/x^b^2

x^a^2-b^2

point slope formula

y-y1=m(x-x1)

vertex form of a quadratic equation

y=a(x-h)^2+k a=postive parabola opens upward k=minimum a=negative parabola opens downward k=maximum

Slope Intercept Form

y=mx+b