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! = 5*4*3*2*1 | (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 ```