AP Calculus Review

Hit the slopes

100

A quadratic function can be used to model the path of a ball if thrown up in the air in a vertical trajectory. What is the slope of the tangent line for this function when the ball reaches its maximum height?

slope is zero

200

The equation of a circle is given as  x² + y² = 36 .  Find the equation of the normal line when x = 6 ?

y = 0

300

The equation of a circle is given as  x² + y² = 49 .  Find the equation of the tangent line when x = -7 ?

x = -7

400

Find the slope of the secant line passing thru the points (-5, f(-5)) and (-2, f(-2)) for the cubic function 

f(x)=-1/3(x+2)^3-1

slope is -3

500

Find the equation of the tangent line for the function below at the point 

(pi, f(pi))    

f(x)=Sin(x) 

y = -x + pi 

Take it to the limit

100

Use the function below to answer the following: Determine the concavity of f(x).

f(x) = x^2 – 2x -15

concave up

200

Use the discriminant to determine the number of solutions and type of solutions for the equation

4x^2-3x+7=0.

discriminant: -103 no real solutions two imaginary solutions

300

Find the coordinates for the point of inflection of the function below:

f(x)=x^3+x^2-6x-13

P.O.I. at

(-1/3, -295/27)

400

Find the interval where the following function is concave down:

f(x)=x^4-x^2

(-root2(6)/6 ,root2(6)/6)

500

Alexander’s catapult will launch an object. The equation below describes the height of the object. h(t)= -4.9t^2+22t+1 What is the maximum height of the object in meters?

25.7 meters

Don't drink and derive

100

Find the inverse if f(x)= (2x-3)/4

f^-1(x)=(4x+3)/2

200

Given f(x) = 2x^2-x-4 and g(x) = x+6: Find ( f/g ) (-2).

3/2

300

Given f(x) = 2x^2-x-4 and g(x) = x+6: Find (g o f)(x).

2x^2-x+2

400

A person’s weight on the moon is approximately one sixth of the weight on Earth. If a person’s weight on Earth is represented by the variable w, then the function that represents the weight on the moon in terms of the weight on Earth can be given as f(w) = 1/6 w. Find the inverse of the function f(w).

f^-1(w)=6w

500

Derive the following function:

f(x)=sin(x)^2+cos(x)^2

f'(x)=0

I sine and you cosine

100

Evaluate the logarithm: Log₅ (1)

0

200

Solve for x: 2 = x – 5ln(e)

x=7

300

A typical beehive contains 20,000 insects. The population can increase in size by a factor of 2.5 every 6 weeks. In theory, after how many weeks will the population of bees increase to 76,293,945?

After 54 weeks

400

Suzanne wants to invest $20,000 in an account for 25 years at an interest rate of 2.75% compounded continuously. Find the accumulated amount in the account at the end of 25 years.

$39,774.75

500

Write the following from least to greatest:

Log₇(343), Log₂(64), Log₅(1), e^-2, Log(Log(10¹⁰) 

Log₅(1), e^-2, Log(Log(10¹⁰), Log₇(343), Log₂(64)

You Can't Touch This

100

Given the function  f(x) below, find 

lim_(x->-7^-) f(x)

f(x) = (x+1)(x-2)^2(x+3)

limit is 1944

200

Given the function below, find its asymptotes:

f(x)=1/(x^2-36)

x=6 and x=-6

300

Given the rational function, f(x) = (x^2-x-6)/(x^2-9), find the vertical asymptotes

x=-3

400

Given the rational function, f(x) = (x^2-x-6)/(x^2-9), find the horizontal asymptote.

y=1

500

Using the function: f(x)=(x^4-x^3+6)/x^2, find the oblique or non-linear asymptote.

y=x^2-x