SAT MATH

Harmonic mean

2v1v2/v1+v2

percentage

(part/whole)100

JOE BLOGGS

if you see answers that look alike and 2 that dont, pick the ones that look alike

mass in terms of denisty and volume

M=vd

Circumfrence (2 formulas)

C=2πr C=πd

Area of a circle

A=πr²

Volume of a cube

V=edge³

Final Velocity Formula

V^f=V1+at

f(x)=x+7

g(x)=x²+3

f(g(x))=?

f(x²+3)=(x²+3)+7  (plug g(x) into all x’s of f(x)

F(x²+3)=x²+10

Mode

number that is most frequent in data

Median

Middle number. If there are 2 middle numbers add them and divide by 2

Mean

add up all numbers, then divide by number of numbers. 

Range

Biggest number - Smallest number

how many times would you have to write 59?

10 times

Standard deviation

High Deviation: more spread out. Less numbers close to the mean

Low: close to the mean average

49x²-ax+25=(7x-b)² 

what is a/b 

49x²-ax+25=49x²-14bx+b²

-ax=-14bx

-a=-14b

a=14b

14=a/b

A farmer has 2500 square meters of land

How nay square feet of land does the farmer have

1ft=0.3048m

asking for square meters not meters

1ft²=(0.3048)²= 0.092903

2500/0.092903

26910ft²

1km²

1,000,000 m²

A proposal for a new town hall was included in a ballot for a local town election. It was reported that 4 times as many people voted in favor of building the new town hall than people who were against the building of the new town hall. If 12,000 people voted in the election, how many people voted against building the new town hall?

x= against

4x= for

4x+x=12000

5x=12000

x=2400

The function f is defined as f(x)=2x+3. The function g is defined as g(x)=x²−5. What is the value of f(g(3))?

1. find g(3) —> g(3)= 3²+5

2. g(3)=4

3. plug 4 into f(x)

4. f(4)=2(4)+3=11

5. final answer is 11

Area of a right triangle

A=1/2bh

Probablility Formula

Desired Outcomes/Total Outcomes

Sector Area Formula 

—>

Functions f, g, and h represent equations of lines in the xy-plane. The line of function f is defined by the equation f(x)=3x−5. The line of function g is defined by the equation g(x)=4x−12. Function h defines a line that is parallel to the line of function f and intersects with the line of function g at x=0. What is the equation of function h?

same slope as line f= 3x

intersects with line g at x=0 means yint=-12

so line has to be 3x-12

In triangle ABC, AB=8, BC=12, and AC=10. Triangle ]DEF is similar to triangle ABC where AB corresponds to DE and BC corresponds to EF. If the length of DE is 66, What is the length of EF?

use proportions

8/6=12/x

If f(x)=3x+2 and g(x)=4x, what is the value of 2f(3)+3g(2)?

2f(3)

1. f(3)=11

2. 2(11)=22

3g(2)

1. g(2)=8

2. 8(3)=24

24+22=46

The graph of the function f in the xy-plane shown is a parabola. Which of the following accurately defines f?

vertex form: y= a(x-h)²+k

vertex= (4,-5) —> a(x-4)²-5

point on graph=(5,3)

3=a(5-4)²-5 ——> 3=a-5

a=8 ——> y=8(x-4)²-5

The functions k and l are defined as follows: k(x)=4x−3, l(x)=3x−1−k(x). What is the value of l(0)?

1. k(0)=-3

2. l(0)=3(0)-1-(-3)

3. l(0)=2

Point Q is located at the center of a circle that has an area of 196π. If Q has the coordinate (7,12) what is the equation of the circle?

center: (7,12)

a=πr²

196π=πr²

196=r²

r=14

Sam has two jobs. Job A pays 15 dollars per hour, while job B pays 20 dollars per hour. In a given week, Sam worked a total of 40 hours and earned 710 dollars. How many hours did Sam spend working job A during this week?

a+b=40

solve for a so substitute a in for b —> b=40-a

15a+20b=710

15a+20(40-a)=710

a=18

OR JUST GRAPH IT

F=GMm/r²

r= distance between 2 points

A and B are ? units away

C and D 3x closer than A and B are

C and D = r/3 ——> 1/3 as much distance as AB

GMm/r/3²

GMm/r²/9

GMm/r² (9)

distance =9

OR

say C and D is 3

3x closer = AB =9

A circle has center O, and points Q and R lie on the circle. The measure of arc QR is 30°, and the circumference is 60 inches. What is the length of arc QR, in inches?

C(length)=60in.

QR(length)= x

QR(degrees)= 30

C(degrees)=360

30/360=x/60

x=5

Percentage Increase Formula

—>

A cylinder has a height of 5 units and a radius of r units. If the cylinder's radius was increased by a factor of 3, what is the volume of the new cylinder is terms of r and π?

V=5πr²

radius increased by 3

π(3r)² (5)

π9r²(5)—> 45πr²

Problem

Substitute x+w into f(x) to find g(x).

consecutive odd integers

consecutive even integers

consecutive integers

x (x+2) (x+4) (x+6)

x (x+2) (x+4) (x+6)

x (x+1) (x+2) (x+3)

2x²+3x+10 find the product of roots

product of roots = C/A c=10 a=2

QUESTION

1. multiply by t²s to get rid of fractions

2. 5ts-8t²=10s——> -8t²+5ts-10s=0

3. a=-8 b=-5s c=-10s

4. Discrimant Formula(to find how many values/ solutions) b²-4ac

5. (-5s)²-4(-8)(-10s)

6. 25s²-320=0

7. FACTOR s(25s-320)=0

8. s=0 25s-320=0——> s=12.8

9. s>0 t>0 s>12.8=13

Exponential Formula y=a(b)^x

a= initial value (y int)

b= factor ( usually a decimal)

x= exponent

compound interest formula( new value after percentage increase)

A= final amount

r= initial amount

p= percent

compound interest question

A machine can complete a task in 91 minutes and 48 seconds. If its working rate is increased by p%, it would complete the task in 54 minutes. What is the value of p?

turn 48 seconds into minutes 48/60=0.8 —> 91.8

a= 1/54

r= 1/91.8 

1/54= (1+p/100)1/91.8

1+p/100= 91.8/54

1+p/100= 1.7

p/100=0.7

p=70

conversions

• 128 fluid ounces in 11 gallon.

  • 88 fluid ounces in 11 cup

  • 22 cups in 11 pint

  • 22 pints in 11 quart

  • 44 quarts in 11 gallon

  • 3 feet in a meter

  • 3 feet in a yard

• 2.54 centimeters in 1 inch

• 100cm in 1 meter

f(x)=5bx²+abx+10x+2a

a and b are constants

if x=-18/5 only solution to f(x)=0

what is f(42/5)

factor (a+5x)(bx+2)

x=-18/5

a+ 5(-18/5)       b(18/5 +2)

a= 18    b=5/9

f(42/5) ——> plug back into original equation

f(42/5)= 18+5(42/5) (5/9(42/5)+2)

f(42/5)= 400

if you have a graphing question with a missing number(a b c) and its multiple choice what should you do?

Plug the number in with desmos. See which number matches.

what kind of function is this

rational

Jasmine purchased a stock whose price increases by 1.38% every month. Which of the following functions represents the price of the stock after x years if the original price was $5.34?

5.34(0.0138)^12x

x^a+x^b=

x^a+b

x^a/x^b

x^a-b

(x^a)^b

x^a(b)

x^1/a

(^a√x)¹

x^-a

1/x^a

x⁰

1

for n angles

180(n-2)

Density Formula

D=m/v

Isocolese triangle

2 equal sides(angles and side lengths)

angles across from each other

are equal

mean x n(number of numbers)=

Sum

Horizontal shift h units to the right

f(x-h)

Verticle shift up k units

f(x)+k

20 % of x

0.2x

Increase x by 20% 

1.2x

Decrease x by 20 %

0.8x

what is 150% more than 10

25

• The value of a collectible comic book increased by 167% from the end of 2011 to the end of 2012.

• Then it decreased by 16% from the end of 2012 to the end of 2013.

• We want to find the net percentage increase in value from the end of 2011 to the end of 2013.

167%=2.67

decrease by 16%= 0.84

2.67(0.84)=2.2428V

2.248V - V= 1.2428

1.248(100)=124.28

solve

(x+5)²+(y-2)²=81

expand

(x² + 10x + 25) + (y² - 4y + 4) = 81

x²+y²+10x-4y+29=81

29-81=-52

tangent to circle

means its perpendicular

find the slope then find its oppisite reciprical thats the answer

tangent circle question

tangent circle question

slope = -3

degrees in terms of radians

d= r(180/pi)

radians in terms of degrees

r= d(pi/180)

prove similarity

SSS

AA

SAS

vertex formula

a(x-h)²+k

AOS

-b/2a

vertex formula 2

vertex= x1+x2/2

sum of solutions

-b/a

product of solutions

c/a

discriminant formula

d=b²-4ac

determine the number and type of solutions (or roots) for a quadratic equation of the form

D>0 there are two distinct real roots

D=0 there is exactly one real root

D<0 there are no real roots

even odd parent functions

odd powers go through x axis (x-2)

even powers bounce off x axis (x-6)²

sin and cos relationship

sin(x)= cos(90-x)

is

=

of

multiplication

more

less

addition

subtraction

at least

≥

if angles a+b=90

then cos(a)=sin(b)

altitude

creates 90 degree angle

Altitude Question

use 30 60 90 rule

word problem

change in y/change in x= 8/1 slope = 8

plug in (2,18) to find y int 

y=2

box plots

—>

exponential question

use the table button on desmos

but two points in

change it to exponential function

and it will give you the slope

triangl question

70/63=60/x

x=54

f(0)

y int

solve for g(0) first

g(0)=14t

plug (24,0) into original equation

0=(24+14)(t-24)

0=t-24

t=24

g(0)=14(24)

g(0)=336

inequality question

graph inequality

make table

test each x

find points > than 16,24,32

x=2014

y=2018

y= 1.27x

x=(p/100)y

set them equal to each other

y=x(100/p)

x(100/p)=1.27x

100/p=1.27

p=100/1.27

p=78.74

NOT WHAT YOU THINK

f(x)=5 

5= 9/7x+8/7

plug into desmos

turn h(28)=15 into a point —→ (28,15)

same with h(26)=12 (26,12)

solve for slope—→ -7/2

plug (26,12) into y=-7/2x+b to find y int

OR

graph in a table

click add regression

During word problems read what the question is asking first

“Given that” questions

maple trees/ tall trees(20 feet or taller)

reread question before going on 

y=f(x+3)-4

ax²+21sqrt(x)

combine

f(x+3)-4=a(x+3)²+21sqrt(x+3)-4

identify point on graph : (1,18)

18=a(1+3)²+21sqrt(4)-4

a=-5/4