Algebra Equations

Question 0

What is the formula for the Quadratic Equation?

Answer 0

ax^2 + bx + c

–> The quadratic equation can be disguised to look like ax^2 = bx

Question 1

What is the equation for Compound Interest?

Answer 1

Compound Interest = P(1+r/n)^nt

• -> P = principal
• -> r = rate (in decimal format)
• -> n = number of times compounded per year (monthly, weekly, daily)
• -> t = number of years

** You can treat compound interest problems like successive interest problems

Question 2

What are the factors for the special product x^2 - y^2?

Answer 2

(x+y)(x-y) = x^2 - y^2

Question 3

What are the factors for the special product x^2 + 2xy + y^2?

Answer 3

(x+y)^2 = (x+y)(x+y) = x^2 + 2xy + y^2

Question 4

What are the factors of the special product x^2 - 2xy + y^2?

Answer 4

(x-y)^2 = (x-y)(x-y) = x^2 - 2xy + y^2

Question 5

What is the equation to find a change in % or change in actual value?

Answer 5

% change = change in value/original value

Question 6

What is the equation for Distance or Work?

Answer 6

D = RxT or W = RxT

–>Distance or Work = Rate x time

Question 7

What equation is used to find the new % or new value?

Answer 7

New % = new value/original value

Question 8

What is the probability equation used when all outcomes are equally likely to occur?

Answer 8

Probability = # of favorable/ # of possible

–> Multiply the probability of two independent events together when trying to find the probability of those favorable events occuring

Question 9

What is the equation for a Permutation and how is it defined?

Answer 9

P(n,r) = n!/(r-n)!

–> where n = total and r = selected items for permutation

–> All possible arrangements of a collection of things, where the order is important.

Question 10

What is the equation to solve for the sum of a data set when given the average?

Answer 10

A x n = S

–> Average x # of terms = sum of terms

Question 11

What is the equation for a Combination and how is it defined?

Answer 11

C(n, r) = n!/[r!(n-r)!]

–> where n = total and r = selected items for combination

–> Possible arrangement of a collection of things, where the order is NOT important.

–> In general C(n, k) = C(n, n-k)

Question 12

What are two ways to calculated a Weighted Average?

Answer 12

Weighted Avg = (weight/sum of weights)(data point) +(weight/sum of weights)(data point) +….

or

Weighted Avg = [(weight)(data point) + (weight)(data point)]/sum of weights

Question 13

What is the special addition rule for the probability of two mutually exclusive events?

Answer 13

P(E or F) when E and F are mutually exclusive is P(E) + P (F)

Question 14

What is the special multiplication rule for the probability of any two independent events, E and F?

Answer 14

P(E and F) = P(E)xP(F)

Question 15

How to calculate the probability of two events occurring, E or F, that are independent of each other?

Answer 15

P(E or F) = P(E) + P(F) - P(E)xP(F)

Question 16

What is the difference between two events being independent or mutually exclusive?

Answer 16

Independent = two events are independent if the occurrence of either event does not alter the probability that the other event occurs.

Mutually Exclusive = two events such that their occurrence togehter (E and F) is impossible- aka no intersection of sets.

Question 17

What is the probability of either of two events, E or F, occuring?

Answer 17

P(E or F) = P(E) + P(F) - F(E and F)