AP Calculus Summer Assignment



NEATLY SHOW YOUR WORK ON A SEPARATE SHEET OF PAPER. Please BOX YOUR FINAL ANSWERS.

Evaluate. You should be able to do these without a calculator (unless otherwise stated). You will be expected to work similar problems on a quiz or test without a calculator.

Your answers should be in radian measures.

1.) [pic] 2.) [pic] 3.) [pic] 4.) [pic] 5.) [pic]

Solve for y:

6.) [pic]

Rewrite the following using interval notation

7.) [pic] 8.) [pic] 9.) All real numbers

Find [pic]for the following functions.

10.) [pic] 11.) [pic] 12.)[pic] 13.)[pic]

For each of the functions find the indicated value.

14.) Given [pic] Find [pic]

15.) Given [pic] Find [pic]

16.) Given [pic] Find [pic]

17.)[pic]

Simplify.

18.) [pic] 19.) [pic]

Rewrite the following in simplified form.

20.) [pic] 21.) [pic] 22.) [pic]

Algebraically determine the x and y intercepts. Name the intercepts as points.

23.) [pic] 24.) [pic]

Algebraically determine the domain and range of the following functions. State your answer using interval notation.

25.) [pic] 26.) [pic]

State the EQUATIONS of any horizontal asymptotes and/or vertical asymptotes.

State the domain and range.

27.) [pic] 28.) [pic]

Sketch a graph of the function and find the value of the indicated limits. State whether the function is continuous or discontinuous.

29.) [pic]

30.) [pic]

Rewrite the following as a piecewise function.

31.) [pic] 32.) [pic]

Graphically determine if the following is an even, odd or neither function.

33.) [pic] 34.) [pic]

Use the [pic]test to determine whether the following is an even, odd or neither function. Then state the type of symmetry (y-axis, origin or neither) of the function.

35.) [pic] 36.) [pic]

Use your graphing calculator to find the POINTS of intersection of the graphs.

37.) [pic] 38.) [pic]

True or False

39.) If (1, -2) is a point on a graph that is symmetric with respect to the y-axis, then (-1, -2) is also a point on the graph.

40.) Given a function f(x), if [pic], then a = b.

41.) If f is a function, then f(ax) = af(x).

Find the equation of each line. Answer MUST be in POINT-SLOPE FORM!

42.) point (–2, 4); [pic] 43.) through (–3, 0) and normal to [pic]

(You may need to look up the definition of a normal line.)

Solve for x. You should be able to do these without a calculator. You will be expected to work similar problems on a quiz or test without a calculator.

44.) [pic] where [pic]

45.) [pic] where [pic]

46.) [pic]

47.) [pic]

48.) [pic]

49.) Given [pic]

Find a.) [pic] b.) [pic] c.) [pic] and give domain.

50.) Given [pic]

Find a.) [pic] b.) [pic] and give domain.

51.) Find the area of an equilateral triangle whose sides are 6 cm each.

52.) Find the area of a trapezoid with height 12 in and bases of 6 in and 9 in.

53.) Find the volume of the right circular cylinder with radius 5 in and height 14 in.

54.) Find the lateral surface area of the right circular cylinder with radius 5 in and height 14 in.

Reduce each completely.

55.) [pic] 56.) [pic]

Trig Identities—Match the statement on the left with an equivalent statement from the right.

|57.) [pic] |A. [pic] |

|58.) [pic] |B. [pic] |

|59.) [pic] |C. 1 |

|60.) [pic] |D. [pic] |

|61.) [pic] |E. [pic] |

|62.) [pic] |F. [pic] |

For [pic], where k is a constant, indicate the concavity and increasing/decreasing behavior of the curve in the first quadrant for the following:

|63.) if [pic] |

|64.) if [pic] |

|65.) [pic] |

66.) A student who commutes 27 miles to attend college remembers, after driving a few minutes, that he forgot his term paper that is due. Driving faster than usual, the student returns home, picks up the paper, and once again starts toward school. Sketch a possible graph of the student’s distance from school as a function of time. Sketch a possible graph of the student’s velocity as a function of time.

67.) Suppose a pet owner decides to wash her dog in the laundry tub. She fills the tub with water, puts the dog in the tub and shampoos it, removes the dog from the tub to towel it, then pulls the plug to drain the tub. Let t be the time in minutes and h(t) be the water level in the tub at time t. If the total time for filling, washing, and draining is 40 minutes, sketch a possible graph of [pic]

Use the graph below to graph the transformations.

[pic]

68.) [pic]

69.) [pic]

70.) [pic]

71.) [pic]

Define the following. You might have to do some research.

72.) Average rate of change

73.) Instantaneous rate of change

74.) Extreme value of a function

75.) Critical point of a function

76.) Point of inflection of a function

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(8, 0)

(6, 6)

(5, 4)

(2, 4)

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