Equations to Remember

Question 1

PEMDAS

Answer 1

Order of operations:
Parentheses
Exponents
Multiplication/Division together left to right
Addition/Subtraction together left to right

Question 2

Percent Formula

Answer 2

Part = Percent x Whole

Question 3

Percent Increase

Answer 3

Percent Increase = (Amount of Increase/Original Whole) x 100%

Question 4

Percent Decrease

Answer 4

Percent Decrease = (Amount of Decrease/Original Whole) x 100%

Question 5

Average

Answer 5

Average = Sum of Terms / Number of Terms

Question 6

Sum from Average

Answer 6

Sum = (Average) x (Number of Terms)

Question 7

Ratio

Answer 7

Ratio = of/to

Question 8

Probability

Answer 8

Probability = (Number of favorable outcomes)/(Total number of possible outcomes)

Question 9

Area of a Triangle

Answer 9

Area = 1/2(Base)(Height)

Question 10

Pythagorean Theorem

Answer 10

a^2 + b^2 = c^2

a and b are legs and c is the hypotenuse

Question 11

Special Right Triangles

Answer 11

3:4:5 and 5:12:13
30-60-90 degrees and 45-45-90 degrees
1, root of 3, 2 and 1, 1, root of 2 are the side ratios

Question 12

Perimeter of Rectangle

Answer 12

Perimeter = 2(length + width)

Question 13

Area of a Rectangle

Answer 13

Area = (length)(width)

Question 14

Area of a Square

Answer 14

Area = (side)^2

Question 15

Area of a Parellelogram

Answer 15

Area = (base)(height)

Question 16

Area of a Trapezoid

Answer 16

Area = (average of parallel sides)(height)

Question 17

Circumference of a Circle

Answer 17

Circumference = 2pi(r), r is radius
Circumference = pi(d), d is diameter

Question 18

Area of a Circle

Answer 18

Area = pi(r^2)

Question 19

Slope of a Line

Answer 19

Slope = rise/run = (change in y)/(change in x)

Question 20

Simple Interest

Answer 20

Interest = (principal) x (interest rate as a decimal) x (time in years or fraction of a year)

Question 21

Compound Interest

Answer 21

(Final Balance) = (Principal) x (1+ (interest rate)/c)^(time)(c)
C = number of times compounded annually

Question 22

Use Original Average and New Average to figure out what was added or deleted

Answer 22

Number Added = (new sum) - (original sum)

Number Deleted = (original sum) - (new sum)

Question 23

Average Rate

Answer 23

Average A per B = (Total A)/(Total B)

Question 24

Combined Work

Answer 24

1/r + 1/s = 1/t
r and s are # of hours it takes each to do the same work individually
t is the # of hours it takes them to do the same work together

Question 25

Group Problem with Both/Neither

Answer 25

Group 1 + Group 2 + Neither - Both = Total

Question 26

Permutation (when arranging a smaller group from within a larger group and order matters)

Answer 26

nPk = n!/(n-k)!
n = # in larger group
k = # you're arranging

Question 27

Combination (order doesn’t matter)

Answer 27

nCk = n!/(k!(n-k)!)
n = # in large group
k = # you're choosing

Question 28

Multiply/Divide Exponents Powers

Answer 28

(x^a) x (x^b) = x^(a+b)

x^c)/(x^d) = x^(c-d

Question 29

Exponent Raised to an Exponent

Answer 29

(x^a)^b = x^(ab)

Question 30

Linear Equation

Answer 30

y = mx + b, m is slope and b is y-intercept

x + y = c

Question 31

Length of an Arc

Answer 31

Length of an Arc = n/360 x 2pi(r)

n is angle of center of circle

Question 32

Area of a Sector

Answer 32

Area of Sector = n/360 x pi(r^2)

n is angle of center of circle

Question 33

Volume of a Rectangular Solid

Answer 33

Volume = length x width x height

Question 34

Surface Area of a Rectangular Solid

Answer 34

Surface Area = 2(lw) + 2(wh) + 2(lh)
l = length
w = width
h = height

Question 35

Volume of a Cylinder

Answer 35

Volume = area of the base x height = pi(r^2)h

Question 36

Surface Area of a Cylinder

Answer 36

Surface Area = 2pi(r^2) + 2pi(r)(h)

Question 37

Standard Deviation

Answer 37

1. Find the average of the list of numbers.
2. Subtract each item in the list from the average.
3. Square the differences.
4. Find the average of the squared differences.
5. Take the positive square root of the average.