Stuff You Must Know Cold

Question 1

Formula for Area of a Circle

Answer 1

A=πr^2

Question 2

Formula for Circumference of a Circle

Answer 2

C=2πr

Question 3

Area of a Rectangle

Answer 3

A=bh

Question 4

Area of a Triangle

Answer 4

A=1/2bh

Question 5

Area of a Trapezoid

Answer 5

A=1/2(b1 + b2)h

Question 6

Volume of a Cone

Answer 6

V=1/3πr^2h

Question 7

Factor a^2-b^2

Answer 7

(a+b)(a-b) Difference of Squares

Question 8

a^3-b^3

Answer 8

(a-b)(a^2+ab+b^2) Difference of Cubes, same, different always positive

Question 9

a^3+b^3

Answer 9

(a+b)(a^2-ab+b^2) Sum of Cubes

Question 10

What does this function look like? 1/x

Answer 10

VA@0, Opposite Origin, HA@0

Question 11

What does f(x)=1/x^2 look like?

Answer 11

VA@0, HA@0, Reflection across y-axis

Question 12

What does f(x)=e^x look like?

Answer 12

HA@0, (0,1), goes through (1, 2….)

Question 13

What does f(x)=ln(x) look like?

Answer 13

Opposite e^x, (1,0)

Question 14

What f(x)=sin(x) look like?

Answer 14

Starts at (0,0), (pi/2,1)

Question 15

What does f(x)=cox(x) look like?

Answer 15

Starts at (0,1), (pi/2,0)

Question 16

What does f(x)=/a^2-x^2 look like?

Answer 16

Semi Circle, starts at (a,0), up to (0,a), then (-a,0)

Question 17

Rewrite cot(x)

Answer 17

1/tan(x)

Question 18

Rewrite sec(x)

Answer 18

1/cos(x)

Question 19

Rewrite csc(x)

Answer 19

1/sin(x)

Question 20

What can 1+tan^2x substitute?

Answer 20

sec^2x

Question 21

What can 1+cot^2x substitute?

Answer 21

csc^2x

Question 22

What can tan(x) also be?

Answer 22

sin(x)/cos(x)

Question 23

What can cot(x) also be?

Answer 23

cos(x)/sin(x)

Question 24

What does ln(e)= to?

Answer 24

1

Question 25

x^ax^b

Answer 25

Addition of Exponents x^a+b

Question 26

x^a/x^b

Answer 26

Subtraction of Exponents x^a-b

Question 27

(x^a)^b

Answer 27

Power to Power is Multiplication x^ab

Question 28

x^-a

Answer 28

1/x^a

Question 29

x^1/a

Answer 29

^a/x

Question 30

x^0

Answer 30

1

Question 31

ln(a) + ln(b)=

Answer 31

ln(ab)

Question 32

ln(a) - ln(b)=

Answer 32

ln(a/b)

Question 33

aln(b)=

Answer 33

lnb^a

Question 34

What does the graph look like if f(x) does not exist?

Answer 34

Discontinuous, there is a hole at f(x)

Question 35

What does the graph look like if lim of x to a f(x) does not exist?

Answer 35

Discontinuous, two different lines at different y values

Question 36

What does the graph look like of f(a) does NOT equal lim x to a f(x)?

Answer 36

Discontinuous, a dot filled above the hole in the function.

Question 37

What is the definition of a derivative?

Answer 37

lim of h to 0 f(x+h) - f(x) over h

Question 38

What is the product rule?

Answer 38

"Right d-left plus left d-right"

Question 39

What is the quotient rule?

Answer 39

"low d-high minus high d-low over low squared"

Question 40

What is the chain rule?

Answer 40

f'(g(x)xg'(x) Ex.sin(x^2)= cos(x^2)2x

Question 41

derivative of sinx

Answer 41

cosx

Question 42

derivative of cosx

Answer 42

-sinx

Question 43

derivative of tanx

Answer 43

sec^2x

Question 44

derivative of cotx

Answer 44

-csc^2x

Question 45

derivative of secx

Answer 45

secx tanx

Question 46

derivative of cscx

Answer 46

-cscx cotx

Question 47

A function is increasing if...

Answer 47

f'(x) is positive

Question 48

A function is decreasing if...

Answer 48

f'(x) is negative

Question 49

A function is CCU if...

Answer 49

f''(x) is positive

Question 50

A function is CCD if...

Answer 50

f''(x) is negative

Question 51

A function has a maximum if...

Answer 51

f'(x) changes from + to -

Question 52

A function has a minimum if...

Answer 52

f'(x) changes from - to +

Question 53

A function has a point of inflection if...

Answer 53

f''(x) changes sign