Math to memorize

Question 1

|A| < B

Answer 1

-B < A < B

Question 2

|A| > B

Answer 2

A < -B ; A > B

Question 3

( A + B )( A - B )

Answer 3

= A² - B²

Question 4

( A + B )²

Answer 4

= A² + 2AB + B²

Question 5

( A - B )²

Answer 5

= A² - 2AB + B²

Question 6

( A + B )³

Answer 6

= A³ + 3A²B + 3AB² + B³

Question 7

( A - B )³

Answer 7

= A³ - 3A²B + 3AB² - B³

Question 8

A³ + B³

Answer 8

= ( A + B )( A² - AB + B² )

Question 9

A³ - B³

Answer 9

= ( A - B )( A² + AB + B² )

Question 10

What gives you the discriminant?

Answer 10

= b² - 4ac

Question 11

If the discriminant is greater than zero…

Answer 11

…there are two distinct real roots.

Question 12

If the discriminant equals zero…

Answer 12

…one real zero.

Question 13

If the discriminant is less than zero…

Answer 13

…there are two complex roots.

Question 14

What does the rational root theorem say?

Answer 14

If f(x) is a polynomial with integer coefficients with rational zeros, then they must be of the form +-p/q, where p is all the factors of the constant coefficient and q is all the factors of the leading coefficient.

Question 15

y = log (x)

Answer 15

x = 10^y

Question 16

log (x) = [base change]

Answer 16

ln (x) / ln (10)

Question 17

log (10^x) =

Answer 17

= x

Question 18

10^log (x) =

Answer 18

= x

Question 19

Formula to find radians from degrees

Answer 19

= pi/180 (degrees)

Question 20

Formula to find degrees from radians

Answer 20

= 180/pi (radians)

Question 21

sin ø =

Answer 21

= y/r

Question 22

cos ø =

Answer 22

= x/r

Question 23

tan ø =

Answer 23

= (sin ø / cos ø) = y/x

Question 24

cot ø =

Answer 24

= ( 1 / tan ø ) = ( cos ø / sin ø ) = x/y

Question 25

sec ø =

Answer 25

= ( 1 / cos ø ) = r/x

Question 26

csc ø =

Answer 26

= (1 / sin ø) = r/y

Question 27

x = r _____ø

Answer 27

cos

Question 28

y = r _____ø

Answer 28

sin

Question 29

prove: cos²ø + sin²ø = 1

Answer 29

given: x² + y² = r² x = r cosø y = r sinø then: r²cos²ø + r²sin²ø = r²