AP Calc Accumulative

Question 1

Describe the line and give the slope of:

y = 3?

Answer 1

Horizontal

Slope= 0

Question 2

What is the point slope form of a linear equation?

Answer 2

y₂ - y₁ = m(x₂ -x₁)

Question 3

Describe the line and give the slope of:

x = 4

Answer 3

Vertical Line

Undefined slope

Question 4

What is the slope of any line that is perpendicular to the linear equation with slope m?

Answer 4

-1/m

(the inverse and opposite sign of the parent function)

Question 5

What is the formula for finding the slope of a line?

Answer 5

m= Δy/Δx

or

m= (y₂-y₁)/(x₂-x₁)

Question 6

Does the equation shown represent a function?

x² + y² = 4

Answer 6

No, this equation has term where “y” is raised to an even power. Thus, this equation is not a function, instead it is a circle.

Question 7

If a function is odd the f(-x) =

Answer 7

-f(x)

Question 8

If a function is even then f(-x) =

Answer 8

f(x)

Question 9

What is the domain of f(x) = x / x² - 1

Answer 9

x ≠ ± 1

The denominator of a rational function cannot equal zero.

Question 10

What is the domain of f(x) = ³√x + 1

Answer 10

All real numbers or (-∞ , ∞ ) Any radical function that has an odd index number will have a domain of all real numbers.

Question 11

Identify any horizontal and vertical asymptotes of f(x) = 3x + 1 / 2x² - 2

Answer 11

y = 0

x = 1, -1

the exponent in the denominator is greater than the numerator thus the HA is y = 0

using 1 and -1 for x makes it so the denominator equals 0

Question 12

Identify any horizontal and vertical asymptotes of f(x) = 3x² + 1 / 4x² - 16

Answer 12

y = ¾

x= 2, -2

¾ is the answer because they have the same exponents thus they are taking the fraction of coefficients for the HA

Question 13

Identify any horizontal and vertical asymptotes of f(x) = x⁴ + 1 / x² + 4

Answer 13

NONE

The exponent in the numerator is greater than the denominator, there is no HA

VA: can’t take the square root of a negative number

Question 14

What is the domain of f(x) = x + 1 / x² - 1

Answer 14

x ≠ ± 1

Question 15

y = 3(2)^x is exponential…

Answer 15

Growth

Question 16

y = (¾)^x is exponential…

Answer 16

Decay

Question 17

y = 4(2)^-x is exponential…

Answer 17

Decay

Question 18

y = (½)^-x is exponential…

Answer 18

Growth

Question 19

Write 5³ = 125 in Logarithmic form

Answer 19

Log₅125 = 3

Question 20

Write log₁₆8 = ¾ in exponential form

Answer 20

16^¾ = 8

Question 21

What is the domain of log(x - 4)?

Answer 21

x > 4

Cannot have a log(0) or a log(negative)

Question 22

What is the Change of Base formula?

Answer 22

log_bM = log_aM / log_aB

Question 23

log_b (MN)

Answer 23

= log_bM + log_bN

Question 24

log_b (M / N)

Answer 24

= log_bM - log_bN

Question 25

log_b (M^p)

Answer 25

= plog_bM

Question 26

Definition of

secθ =

cscθ =

cotθ =

Answer 26

secθ = hypotenuse/ adjacent = r/x = 1 / cosθ

cscθ = hypotenuse/ opposite = r/y = 1 / sinθ

cotθ = adjacent / opposite = x/y = 1 / tanθ

Question 27

Fundamental identities: Reciprocal

Answer 27

secθ = 1/cosθ cosθ= 1/ secθ

cscθ = 1/ sinθ sinθ= 1/ cscθ

cotθ = 1/ tanθ tanθ= 1/ cotθ

Question 28

Fundamental identities: Quotient

Answer 28

tanθ = sinθ / cosθ

cotθ = cosθ / sinθ

Question 29

Fundamental identities: Even-Odd

Answer 29

sin (-x) = -sin(x)

cos (-x) = cos(x)

tan (-x) = -tan(x)

csc (-x) = -csc(x)

sec (-x) = sec(x)

cot (-x) = -cot(x)

****Cosine is the only one that comes out positive meaning the reciprocal (sec) comes out positive as well****

Question 30

Fundamental identities: Pythagorean

Answer 30

sin²θ + cos²θ = 1

tan²θ + 1 = sec²θ

1 + cot²θ = csc²θ

Question 31

Evaluate 0 on the Pi Circle:

Answer 31

sinθ = O

cosθ = 1

tanθ = 0

Question 32

Evaluate π/6 on the Pi Circle:

Answer 32

sinθ = ½

cosθ = √3/2

tanθ = 1/√3 or √3/3

Question 33

Evaluate π/4 on the Pi Circle:

Answer 33

sinθ = √2/2

cosθ = √2/2

tanθ = 1

Question 34

Evaluate π/3 on the Pi Circle:

Answer 34

sinθ = √3/2

cosθ = ½

tanθ = √3

Question 35

Evaluate π/2 on the Pi Circle:

Answer 35

sinθ = 1

cosθ = 0

tanθ = UND

Question 36

Evaluate π on the Pi Circle:

Answer 36

sinθ = 0

cosθ = -1

tanθ = 0

Question 37

Distance Formula-

Answer 37

d = √(x₂-x₁)² + (y₂-y₁)²

Question 38

Midpoint Formula-

Answer 38

((x₁ + x₂) /2 , (y₁ + y₂)/ 2)