Math Cheat Sheet + Formulas

Question 1

What is PEMDAS?

Answer 1

Parentheses
Exponet
Multiplication/Division
Addition/Subtraction

Question 2

x^0
x^1
x^-m
x^m/n

Answer 2

1
x
1/x^m
n√x^m

Question 3

(a+b)^2
(a-b)^2
(a-b)(a+b)

Answer 3

a^2+2ab+b^2
a^2-2ab+b^2
a^2-b^2

Question 4

(a+b)^3

(a-b)^3

Answer 4

(a+b)(a^2-ab+b^2) (a^3+3a^2b+3ab^2+b^3)

a-b)(a^2+ab+b^2) (a^3-3a^2b+3ab^2- b^3

Question 5

Quadratic Formula

Answer 5

x = (1/2a)(−b ± √(b^2 − 4ac)
used to find roots of polynomials:
ax^2+bx+c=0

Question 6

arithmetic sequence

Answer 6

# Sequence in which the distance between each entry is constant (addition)
a, a+d, a+2d, a+3d,..
nth term = a + d(n-1)

Question 7

geometric sequence

Answer 7

# Sequence in which the distance between each entry is a multiple of the one before it (multiplication)
a, ar, ar^2, ar^3,..
nth term = ar^(n-1)

Question 8

determinant of matrix

Answer 8

|m|

ad)-(bc

Question 9

rationalize the denominator
1/√7
1/3^√7

Answer 9

1/√7(√7/√7) = √7/7
1/3^√7(3^√7^2/3^√7^2) = 3^√7^2/7

Question 10

formulas for slope of a line

Answer 10

(y{2} - y{1})/(x{2} - x{1})
tan theta
m
rise/run

Question 11

Pythagorean Theorem

Answer 11

a^2 +b^2 = c^2
distance formula is the same but sides a and b are replace with the distance between two points
common triples:
3-4-5 (6, 8, 10)
5-12-13
7-24-25
8-15-17

Question 12

midpoint

Answer 12

(x{1}+x{2}/2 , y{1}+y{2}/2)

Question 13

CIRCLE
equation
Circumference
Area
center
radius
Angles inside a circle:
Circumference/center angles
diameter angles
arc/theta relation
Tangent

Answer 13

x^2 +y^2 - 6x - 4y = 3
2(3.14)r
(3.14)r^2
(h,k)
(x-h)^2 + (y-k)^2 = r^2
angle origin on the circumference = Theta
angle origin on center = 2Theta
**If rays go to the same point
angles starting on circumference and both ending at two points directly across from each other (diameter), both angles will be 90 deg.
AB/2(3.14)r = Theta/360 deg.
Tangent touches @ one point, creates right angle with radius. Two tangents that meet at one point will have the same length

Question 14

PARABOLA
standard
intercept
vertex

Answer 14

y = ax^2 +bx +c
y = a(x-p)(x-q)
y = a(x-h)^2 +k

Question 15

ELLIPSE
equation of an ellipse
Center
major/minor axis

Answer 15

(x-h)^2/a^2   +   (y-k)^2/b^2   =  1
****major axis is the first term in the equation
(h, k)
minor = 2b
major = 2a

Question 16

TRIANGLE
perimeter
area(right)
area(any)
area(equilateral)
30-60-90 ratios
45-45-90 ratios
sum of interior angles
equilateral
Isosceles
scalene

Answer 16

a+b+c
1/2bh
1/2absinC = 1/2bcsinA = 1/2casinB
(1/2)(a)(a√3/2)
s : s√3 : 2s
s : s : s√2
<a></a>

Question 17

SQUARE
perimeter
diagonal

Answer 17

s^2 OR 4s

s√2

Question 18

TRAPEZOID

area

Answer 18

h(1/2*b{1}+b{2})
height times base average
**sneaky || line question

Question 19

POLYGONS
#diagonals
sum of INTERIOR angles
EACH interior angle
sum of EXTERIOR angles

Answer 19

(1/2)*(n(n-3))
(1/2)*((n-2)*180) = X
X /n
360 degrees for all polygons 
(1/n)*360

Question 20

CUBE
surface area
Volume
2D diagonal
3D diagonal

Answer 20

6s^2
s^3
s√2
s√3

Question 21

SPHERE
Surface area
volume

Answer 21

4(3.14)r^2

(4/3)*(3.14)r^3

Question 22

CYLINDER
Surface Area
Lateral Area
Volume

Answer 22

2(3.14)rh + 2(3.14)r^2
2(3.14)rh
(3.14)r^2h

Question 23

CONIC TRIANGLE
Surface Area
Lateral Area
Volume

Answer 23

(3.14)r^2 + (3.14)rl
(3.14)rl
(1/3)*(3.14)r^2h

Question 24

VECTORS
Equivalent
magnitude
adding and subtracting are the same

Answer 24

Having the same direction and magnitude

use pythag. theorem

Question 25

INEQUALITIES
when does the sign change
dotted v. solid line
shading
 (absolute value)

Answer 25

when you divide/multiply by a negative #
= has solid, not = has dotted
when shading pick the origin of possible (not on the line) and insert that into the inequality . If the statement is true that side is shaded.

|x| < 12

Question 26

Height equations

Answer 26

h = -16t^2 + h{0}  dropped
h = -16t^2 + v{0}t + h{0}  thrown

Question 27

Permutation formula

Answer 27

5! = 54321

(n!)/(n-r)!

Question 28

Probability

Answer 28

#fav. outcome/#total poss. outcomes
Independent Events - past roll doesn't affect the next roll
Dependent Events - past roll does affect the next roll

Question 29

Distance
Speed
Time

Answer 29

D = SxT
S = D/T
T = D/S

Question 30

GCF

LCM

Answer 30

GCF 20, 80, 300 = 20

LCM 5, 20, 60 = 60

Question 31

Complex numbers

Answer 31

z = a +bi
|z| =  √(a^2 + b^2) modulus, hypotenuse, distance from origin to point

Question 32

LINES
|| x-axis
|| y-axis
|| y=mx+b
Perpendicular y=mx+b
Standard
Point slope

Answer 32

x=5
y=5
m
-1/m
y = mx+b 
y - y{1} = m(x - x{1})

Question 33

ANGLES
Vertical
Complementary
Supplementary
Corresponding
Alternate Exterior
Alternate Interior

Answer 33

angles directly opposite each other - congruent
next to each other and add to = 90 deg.
next to each other and add to = 180 deg.
|| cut by transv. same angle created on both || lines - congruent
|| cut by transv. 1 corresp. angle and the vertical of the other angle on the outside - supplementary
|| cut by transv. 1 corresp. angle and the vertical of the other angle on the inside - supplementary

Question 34

Congruent Triangles

Answer 34

1) SAS
2)SSS
3)ASA
3/4 are the same
4)AAS
5)RHS
right triangle only

Question 35

Similar Triangles

Answer 35

1) AA
2) sss
3)sAs
AB/A^1B^1 = BC/B^1C^1 = CA/C^1A^1

Question 36

Radians

Answer 36

2(3.14) radians = 360 deg
(3.14) rad. = 180 deg
1 rad. = 180deg/(3.14) = 57.3deg

Question 37

Cosine Law

Sine Law

Answer 37

c^2 = a^2 + b^2 - 2abCosC
b^2 = a^2 + c^2 - 2acCosB
a^2 = b^2 + c^2 - 2bcCosA

a/SinA = b/SinB = c/SinC

Question 38

QUADRANTS

Are Sin, Cos, Tan +/-

Answer 38

All Students Take Calculus
Quad 1 = all +
Quad 2 = Sin +
Quad 3 = Tan +
Quad 4 = Cos +

Question 39

Periodic Functions
Amplitude
Period
phase shift
vertical shift

Answer 39

y = Asin(Bx + C) + D
A = distance from sinusodial axis (x-axis) to peak
Period = 2(3.14)/B
phase shift = -C/B
vertical shift = D