DAT Math Formulas
Cos(A)
A/H
Cot(A)
A/O (1/tan)
Tim invests $1000 in an account that accrues 12% interest per year, compounded quarterly. After 15 months, how much interest has Tim earned?
A= P (1+r/n)^nt 15 months/12 months = 1.25 1000 * (1+.12/4)^4*1.25 1000 (1.03) ^ 5 = 1159.27 so he accrued $159.27 interest *** if you do not remember formula could do 1000*.12+1000=1120 so it would be something slightly larger than 120 since its 15 months not a year
area of rhombus
A=bh
Area of a circle
A=πr²
Diameter= 20 m Subtended arc= 50 Whats the distance
C= 2pir= 2pi*10= 20 pi (50/360) * 20pi = 2.8 pi
Circle A and Circle B are respectively defined in standard coordinate plane by equations (x+3)^2 + ( y -2) ^2 = 21 and (x+12)^2 + (y+2)^2 = 16 what is the shortest distance between the two centers of the circles?
Circle A's center is -3,2 Circle B's center is -12,-2 distance formula = sqr ( x2- x1) ^2 + (y2-y1) ^2 = sqr (-12-(-3))^2 + (-2-2)^2 = sqr (-9^2 + - 4^2) = sqr 97
Sin(A)=
Cos(90-A)
Distance Formula
D=(velocity)(time)
C to F conversion
F=9/5(C)+32
Compound Interest Formula
Future value= present value*(1+annual interest rate/number of periods)^number of periods*time
Sec(A)
H/A (1/cos)
Csc(A)
H/O (1/sin)
Simple Interest Formula
I=prt (principal* annual rate*Time in yrs)
Jaime is 6 years older than Tyroine now. In 2 years, Jaime will be one year less than twice Tyroines current age. What is Jaime's current age?
J= T + 6 (T=J-6) J+2= 2T-1 J+2= 2 (J-6) -1 J + 2 = 2J - 12 -1 2= J - 13 J= 15
degrees C to K
K=C+273
Dist between two points
Make right triangle and solve hypotenuse
Tan(A)
O/A
Sin(A)
O/H
A bag is filled with 20 pieces of candy A and 10 pieces of candy B. If you choose 2 pieces of candy at random without replacement, what is the probability of picking one piece of candy of each type?
Scenario where A is chosen first= 20/30*10/29=20/87 Scenario where B is chosen first = 10/30*20/29=20/87 Both scenarios together 20/87+20/87=40/87
Cos(A)=
Sin(90-A)
Variance
Stand. Dev. Squared
Three fair coins are tossed at once. What is the probability of getting 2 or more heads
There are 3 coins with 2 sides = 2*2*2= 8 possibilities Probability of getting 2 heads = 3!/(3-2!)2! = 3 Probability of getting 3 heads = 3!/ (3-3!) 3! = 1 Therefore there is a total of 4 possibilities of getting 2 or 3 heads and 8 total possibilities 4/8=1/2
If Corey gave 70 stickers to Jared and Jared gave 10 stickers to Megan then each of them would have the same amount. How many more stickers does Corey have than Megan?
To solve this we need to know the net change of each person Corey -70 Jared (+70-10)=+60 Megan +10 C-70=M+10 C-M=80 Corey has 80 more stickers than Megan
avg. velocity
Total distance travelled/time
Volume of a cylinder
V=πr²h
percent increase/decrease=
[(x2-x1)/x1]*100%
s^2 - 2s - 35+?
a+b= -2 a*b= -35 5-7=-2 5*-7= -35 s^2+5s-7s-35=0 (s+5)(s-7) s= -5 or 7
The mean and standard deviation of a set of data is given by m and s, respectively. If 10 additional data points are added exactly at the mean, which of the following is true a. m stays the same s decreases b. m stays the same s increases c. m decreases s stays the same d. both stay the same
a. m stays the same and s decreases
Law of Sines
a/sinA = b/sinB = c/sinC
Car travels 1/4 circle 10 miles from center Find the distance?
arc length= 90 radius = 10 90* (pi/180) = pi/2 radians S= pi*r = pi/2 * 10= 5 pi meters
Parabola
ax^2+bx+c vertex = -b/2a
cos(-A)
cosA
cos x-y=
cosx*cosy + sinx*siny
1+cot^2A=
csc^2A
Imaginary numbers i^0= I^1= i^2= i^3= i^4=
i^0-=1 I^1=i i^2=-1 i^3=-i i^4= 1
Volume of a rectangle
l*w*h
log rules log(mn) log(m/n) nlog(x) logbA
log (mn) = log(m) + log(n) log (m/n) = log(m) - log(n) log (m^n) = nlog(m) nlog(x) = Log(x^n) logbA= log a/ logb
log(675)=2x+3y
loga^2+logb^3 25*27 5 and 3
Combination Formula
n! / (n-r)! * r! - n is the total number and r is the sample number - order doesn't matter
Permutation Formula
n!/(n-r)! - order does matter
Area of ellipse
pi a b
Perpendicular lines are y= -5 +6
reciprocal slopes y= x/5 + 3
Convex polygon with n number of sides what is the sum of angles (s)
s= (n-2) (180)
Area of a equilateral triangle
s^2 * root 3/ 4
tan^2+1=
sec^2
2sin(x)cos(X) =
sin(2x)
sin(x)/cos(x)
tan(x)
How many ways can you arrange 4 identical footballs and 3 identical basketballs on a shelf?
total=7 7!/ 4! 3!= 35
What is greater Quantity A = 5x^2-20x+19 Quantity B = -2
x vertex = -b/2a 20/2(5)=2 5(2)^2-20(2)+19=-1 Quantity A is greater
³√x=
x^(1/3) * x^(1/2) = X^(3/6) + x^(2/6) = X^(5/6) = ⁶√X⁵
√x^(4/5) = 4
x^(4/5) = 16 x^(4/5)*^(5/4) = 16 ^ ( 5/4) x= ⁴√16⁵= 32
linear equation
y=mx+b y1-y2=m(x1-x2)
Area of a regular polygon
(.5)(# of sides(N))(sin360/N)(s^2)
Combined Work ex) If Tom gets a job done in 4 hours and Jerry gets it done in 3 hours, how many hours does it take to get the job done working together?
(1/A)+(1/B)= (1/T)
Area of a cylinder
(2pi*r*h) + (2pi* r^2)
Exponent Rules (X^b)(Y^b) X^b/Y^b) (X^n)(X^m) X^n/X^m (x^a)^b
(X^b)(Y^b) = (XY)^b (X^b/Y^b) = (X/Y)^b (X^n)(X^m) = X^n+m X^n/X^m = X^n-m (x^a)^b = x ^ a*b
x^2-1=
(x+1)(x-1)
Equation of a circle
(x-h)^2 + (x-k)^2 = r^2
sin(-A)
-sinA
sin^2(A) + cos^2(A)
1
Gaussian distribution 1 standard deviations 2 standard deviations 3 standard deviations
1 standard deviations= 68% 2 standard deviations+= 95% 3 standard deviations= 99.7%
1 yard ^2 = feet ^2
1 yard ^2= 3 feet ^2
cos(2A)
1-2sin^2A
cos(2x)
1-2sin^2X
standard deviation formula
1. Work out the Mean (the simple average of the numbers) 2.Then for each number: subtract the Mean and square the result. Then work out the mean of those squared differences. Take the square root of that
Interquaritle Range 4,4,10,11,15,7,14,12,6
1. order the numbers 4,4,6,7,10,11,12,14,15 2. middle of the first hlaf (4+6)/2=5 3. middle of second half (12+14)/2=13 4. find the IQR by subtracting one from the other 13-5=8 which is the interquartile range
1M=yd?
1.1 yards
Area of triangle
1/2bh
volume of a pyramid / square pyramid
1/3 (area base) h 1/3 s^2 h
volume of a cone
1/3 pi r^2 h
a^-n=
1/a^n
Combined Work Problems
1/t1+1/t2= 1/total time
How many ways can you arrange 7 people out of 10
10!/(10-7)! 7!= 10/3!7!= 10/3*2= 120
Numbers between 1-100 divisible by 3 and 4
100-=3*33 100=4*25 but both divisible by 3*4=12 100=12*8 33+25-8=50
Sum of interior angles
180(n-2)
1kg=ibs?
2.2 pounds
1in= cm?
2.5 centimeters
surface area of a rectangle
2lw+2wh+2lh
Area of hollow cylinder
2pi r^2
sin(2A)
2sin(A)cos(A)
How many ways can words of APPALOOSA be arranged?
3 A's 2 P's 2 O's 9 total letters 9!/3!2!2! = 15120 9*8*7*6*5*4*3*2*1/3*2*2*2
How to find an exterior angle
360/n= angle
At what point of the graph does 3x-4y=12 cross the x axis
3x-4(0)=12 3x=12 x=4 (4,0)
Volume of a sphere
4/3πr³
1Ib.=g?
454 grams
Area of a sphere
4πr^2
Liklihood of pulling 3 spades out of a deck of cards without replacement
52 cards total 13 cards in each suit 4 suits 13/52* 12/51 * 11/50 = 33/2550
How many ways can 6 cards be arranged
6*5*4*3*2*1=720
1 standard deviation of the mean
68% of data
The length of symptoms of the flu is normally distributed with an average of 7 days and a standard deviation of 2 days. What is the probability someone with the flu will experience symptoms for less than 5 days?
7 days is the normal and the standard deviation is 2 days so if someone experiences symptoms for less than 5 days they are 1 standard deviation from the mean so 68% of the population is 1 standard deviation from the mean and the person is therefore 32% below and above the mean but you only want the value for what is below therefore it is 16% another way to look at this 1-.68/2=16%
Probability of 3 out of 8 heads
8!/3!5! = 8*7*6/3*2= 56
2 standard deviations of the mean
95% of data
3 standard deviations of the mean
99.7%
Isoceles triangle fact
B=h
If 40% of the population owes a bike, 10% of the population owes a skateboard, and 5% of the population owns both, what percent of the population owns either a skateboard or a bike or both?
Assume the population is out of a 100 since 5 people own both you can assume that out of the equation so 40-5=35 and 10-5=5 35+5+5=45 45/100=45%
