AP CALCULUS SUMMER REVIEW

Name: ______

This packet should be completed, to the best of your ability, by the first day of school. I have posted helpful recourses on our class Edmodo page, in order to assist you with the completion of the packet. Please note; all of the material in the packet was covered in Pre-Calculus, there are no excuses. This packet will be collected on the first day of class and will count as your first TEST grade for the year.

Functions

Graphing

Match the equation with its graph.

  1. ABC
  2. DEF
  3. GHJ
  4. KLM
  5. NPQ

Slopes and Equations

  1. What is the slope of the line through M(2, -3) and N(4, -1)?
  1. Write the equation of the line through M(2, -3) and N(4, -1) in slope-intercept form.
  1. Write the equation of the line through M(2, -3) and N(4, -1) in point-slope form.
  1. Write the equation of the line through M(2, -3) and N(4, -1) in standard form.
  1. Write the equation of the line through (4, 5) and parallel to y -6=2(x+5).
  1. Write the equation of the line through (4, 5) and perpendicular to y -6=2(x+5).
  1. 3x - y=5 and y - 6 = a(x+6) are perpendicular, find a.
  1. Use the table at the right to answer the following:
  2. Write a prediction equation for the data.
  1. What does slope mean in your equation?
  1. Predict what grade comes from studying

45 minutes?

  1. How long would you need to study for a 100?

Relations, Functions, and Their Graphs

State the domain and range for the following. Find when f(x)=0. Graph the function.

Is the following function an odd-function, an even-function or neither.

  1. Use the piecewise function at right to answer the following:

a. f(-2)

b. f(0)

c. f(4)

d. state the domain and range of f

e. graph f

  1. Write a piecewise function for the graph.

Exponential Functions

Graph the following functions. State the domain and range for each. Find any zeros.

  1. Write equations for the following graphs. (Each has base e.) Window is [-5,5] by [-5,5]

A. B.C.

Transformations

In each exercise the function h(x) is given.

(i)Identify its parent function,

(ii)Describe the transformation(s) needed to go from the parent function to h(x),

(iii)Determine the domain and range, and

(iv)draw the graph of both.

(i)

(ii)

(iii)

(i)

(ii)

(iii)

(i)

(ii)

(iii)

(i)

(ii)

(iii)

(i)

(ii)

(iii)

The graph at right is the graph of f(x). Draw the graphs of the h(x).


Solving Equations and Inequalities

Solve algebraically.


  1. A farmer wants to make 2 pens with 800 ft of fencing. The pens will share a common side. What are the dimensions of one pen that maximize the fence?
  1. A gardener wants to pen in a garden using her house as one side. The garden is to be 200 sq ft. How much fence is needed if the gardener is trying to minimize the fence?
  1. An open top box is formed by cutting the same size square out of each corner of a rectangular piece of material. If the sheet is 8m by 10m. What is the maximum volume possible?

Trig

Find the exact value of the given expression.

  1. Given the terminal point
  2. Given the terminal point
  3. Knowing cosx=and the terminal point is in the fourth quadrant find sinx.
  1. Knowing cotx=and the terminal point is in the third quadrant find secx.

State the amplitude, period, phase shift, and vertical shift for each function. Draw the graph by hand and then check it with a graphing calculator.

amplitude:

period:

phase shift:

vertical shift:

amplitude:

period:

phase shift:

vertical shift:

amplitude:

period:

phase shift:

vertical shift:

Multiple Choice

Without a Calculator

  1. Which of the following is undefined at x=2?
  2. What is the equation of the line through (2,6) and perpendicular to 2x +3y=7?
  3. Which of the following graphs is symmetric to the origin?
  4. If and find h(x) if h(x)=
  5. The function has the maximum value of
  6. -2
  7. 2
  8. 3
  9. The zero for is between
  10. -2 and -1
  11. -1 and 0
  12. 0 and 1
  13. 1 and 2

Calculator Permitted

  1. The prediction equation of C(x)= .2x + 4 for a taxi ride where C is the cost and x is in tenths of a mile. What is the predict cost of a 3 mile ride?
  2. $4.23
  3. $4.60
  4. $6
  5. $10
  6. Which of the following equations is symmetric to the y-axis?
  7. The function has how many zero(s)?
  8. 0
  9. 1
  10. 2
  11. 3
  12. 4
  13. The inverse of is
  14. If f(x) is an odd function, which of the following must be true?
  15. f(x) = f(-x)
  16. f(x) = -f(x)
  17. f(-x) = -f(x)
  18. f-1(x) = f(x)
  19. f-1(x) = f(-x)

Open Ended (Extra Credit)

Please complete on separate sheet of paper and attach

Without a Calculator

  1. Let ,
  2. find the rate of change from x=3 to x=6
  3. find the rate of change from x=4 to x=4.1
  4. find the rate of change from x to x+h
  5. Given the graphs of f(x)=and g(x)= find
  6. f(g(0))
  7. g(f(-1))
  8. f-1(1)
  9. For what value of x is g(f(x)) a maximum?
  10. show that
  11. graph f(x) and f-1(x)
  12. find f(ln 4)

Calculator Permitted

  1. Solve the equation
  2. Solve
  3. Solve
  4. How is the solution to the original equation related to the solution of the inequalities?
  5. Given the function
  6. when is the function increasing? decreasing?
  7. when is the function at a maximum? minimum?
  8. How are the answers to parts a and b related?