Math Formulas

Question 0

How do you solve for the nth term?

(each term is equal to the previous term plus d) Arithmetic sequence.

Answer 0

The nth term is tn =t1 +(n−1)d

Question 1

How does an arithmetic sequence work?

Answer 1

Sequence: t1, t1 + d, t1 + 2d, . . .

Question 2

Number of integers from a to b inclusive.

Answer 2

a to b =a-b+1

Question 3

The sum of the first n terms. Of an arithmetic sequence. (each term is equal to the previous term plus d)

Answer 3

Sn=(n/2) · (t1 + tn)

Question 4

What is a geometric sequence ?

Answer 4

each term is equal to the previous term times r

Sequence: t1, t1 ·r, t1 ·r^2, …

Question 5

What is prime factorization?

Answer 5

Ex:

200 = 4 × 50 = 2 × 2 × 2 × 5 × 5

Question 6

How to find the GCF?

Answer 6

Ex:

200 = 2 × 2 × 2 × 5 × 5 60 = 2 × 2 × 3 × 5
GCF(200, 60) = 2 × 2 × 5 = 20

Question 7

How to find the lcm?

Answer 7

check multiples of the largest number
LCM(200, 60): 200 (no), 400 (no), 600 (yes!)

Question 8

How to find the sum of a group of numbers that has an n term.

Answer 8

Sum= average x (number of terms)

Question 9

What is the fundamental counting principal!

Answer 9

If an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N ×M ways. (Extend this for three or more: N1 ×N2 ×N3 …)

Question 10

What is probability?

Answer 10

probability = (number of desired outcomes)➗(number of total outcomes)

Question 11

What is the probability of to DIFFERENT events happening?

Answer 11

P (A and B) = P (A) · P (B), as long as the events are independent (not mutually exclusive).

Mutually Exclusive: Situation where the acceptance of one alternative automatically excludes the other alternatives.

Mutually Inclusive: Situation where one event cannot occur without the other.

Question 12

What is (x+a)•(x+b)?

Answer 12

(x+a)(x+b)=x2 +(b+a)x+ab

FOIL

Question 13

What is the difference of two squares?

DOTS

Answer 13

a2 − b2 = (a + b)(a − b)

Question 14

What is Reverse FOIL

Answer 14

You can use Reverse FOIL to factor a polynomial by thinking about two numbers a and b which add to the number in front of the x, and which multiply to give the constant. For example, to factor x2 + 5x + 6, the numbers add to 5 and multiply to 6, i.e., a = 2 and b = 3, so that x2 + 5x + 6 = (x + 2)(x + 3).

Question 15

What determines which way a Parabola opens up?

Answer 15

y = ax2 + bx + c.

If a > 0, the parabola opens up. If a < 0, the parabola opens down.

Question 16

How to find the distance between two points in a linear function?

Answer 16

(The square root of)

(Xtwo-Xone)^2+(Ytwo-Yone)^2

Question 17

How to find the midpoint between two linear points?

Answer 17

(x1 + x2)/2 , (y1 + y2)/2

(X , Y)

Question 18

What is point slope form and what is it used for?

Answer 18

(y − y1) = m(x − x1)

Question 19

How do you find the total degrees of a polygon?

Answer 19

(N-2)•180

N=number of sides in the polygon

Question 20

How do you find the are of a triangle?

Answer 20

A=((1/2)b)h

Question 21

How do you find the length of the hypotenuse given the other 2 sides?

Answer 21

a^2+b^2=c^2

Question 22

What is the area of a circle?

Answer 22

Area = πr2

Question 23

What is the circumference of a circle?

Answer 23

C=2πr

Question 24

How do you calculate the length of an arc on a circle?

Answer 24

Length Of Arc = (n◦/360◦) · 2πr

Question 25

How do you find the area of a sector of a circle?

Answer 25

Area Of Sector = (n◦/360◦) · πr2

Question 26

What do sides H, Sl, and Ll of a 30-60-90 triangle equal? H= Hypotenuse Sl= short leg Ll= long leg

Answer 26

``` H= 2x Sl= x Ll= x(square root of 3) ```

Question 27

What are the sides of a 45-45-90 triangle?

Answer 27

H=x(the square root of 2) | L=x

Question 28

How to find nth term of an geometric sequence?

Answer 28

N=t1•r^(n-1)

Question 29

How to find the sum of n terms in a geometric sequence.

Answer 29

Sn=(t1/(1-r))•(1-r^n)

Question 30

What is the formula to determine the number of lines created from n points?

Answer 30

n(n-1)/2

Question 31

How many ways can six people fit in six chairs?

Answer 31

6!

Question 32

How many ways can 6 people sit in 3 chairs?

Answer 32

6P3

Question 33

If order doesn't matter then what can you do to determine the number of ways in which an group can be arranged?

Answer 33

nCr

Question 34

What is the exponential growth formula?

Answer 34

original•(1+rate)^number of changes made

Question 35

Exponential decay formula

Answer 35

original•(1-rate)^number of changes made

Question 36

What is the formula for inverse proportions.

Answer 36

xy=k K is the constant of proportionality

Question 37

What is the formula for direct proportions?

Answer 37

y=Kx K is the constant of proportionality

Question 38

Squaring a polynomial

Answer 38

(a+b)^2 = (a+b)(a+b) =a^2+2ab+b^2