Formulas

Question 1

Distance/Work

Answer 1

D/W = RT

Question 2

Slope

Answer 2

(y2 - y1) ÷ (x2 - x1)

Question 3

Probability

Answer 3

= #success ÷ #possible

Question 4

Arc of a circle

Answer 4

arc = portion of the circumference

arc = 2πr * x/360

Question 5

Sector of a circle

Answer 5

Sector = part of the area extending from the center

sector = πr^2 * x/360

Question 6

Inscribed angle of a circle properties

Answer 6

1. Inscribed angle = half the central arc
2. Inscribed angles drawn to same arc have the same measures
3. Inscribed angles of equal arc length have equal measures

Question 7

Volume of a rectangular solid

Answer 7

v = l * w * h

Question 8

Surface area of a rectangular solid

Answer 8

sum of the area of its faces:

2(lw + wh + hl)

Question 9

Volume of a cylinder

Answer 9

πr^2h

Question 10

Surface area of a cylinder

Answer 10

Area of the rectangular band and the two circles

2πrh + 2(πr^2)

Question 11

Line equation

Answer 11

y = mx + b

m = slope
b = y intercept

Question 12

Percent change

Answer 12

[(difference of original-new) ÷ original]*100

OR
original*(1±change) = final

Question 13

What percent is A of B?

Answer 13

(“is/was B” ÷ “of A”)*100

Question 14

Quantity mixutres

Answer 14

When adding values and quantities of two distinct sets/groups

(ratequantity)+(ratequantity) = total cost

Question 15

Converting units

Answer 15

1. determine conversion factor (i.e. 1 year = 35 weeks)
2. Multiply original value by conversion factor - put same units on opposite sides of fraction bar:

• ->65 weeks/yr * 1yr/52 weeks
• -> 65/52
• –> 1.25 years

Question 16

“AND” Probability questions

Answer 16

Questions with 2+ events that happen sequentially - multiply individual probabilities

Question 17

“OR” Probability questions

Answer 17

Questions asking about the probability of one event OR another - add the probabilities of the individual events

Question 18

Weighted average

Answer 18

](weight1value1) + (weight2value2)] ÷ sum of weights

Question 19

Combination problems

Answer 19

Asks for the number of ways in which one or more smaller group/s of elements can be selected from a larger group
—> ORDER DOES NOT MATTER

n! ÷ (s! * k!)

n! = factorial of total group
s! = factorial of selected group
k! = factorial of unselected group

Question 20

Permutation problems

Answer 20

Asks you to determine the number of ways in which a smaller group of elements can be arranged from a larger group

Slotting or

n! ÷ s!

Question 21

Simple interest

Answer 21

Based only on initial deposit

V = P[1*(rt ÷ 100)]

V = value of investment at the end
P = principal investment
r = interest rate
t = time

Question 22

Compound interest

Answer 22

Interest added to the principal investment at regular time intervals.

V = P[1*(r ÷ 100)^t]

V = value of investment at the end
P = principal investment
r = interest rate
t = time

Question 23

Average speed

Answer 23

total distance ÷ total time