Precalculus Bc/ap Calculus Ab Summer Assignment Worksheet
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4Precalculus BC/AP Calculus AB SUMMER ASSIGNMENT
DUE: First day of class
Do these problems in pencil on NOTEBOOK paper, no graph paper. Show all work to
receive full credit. Work must be neat, orderly and easy to read. Use the TI-89 calculator
when indicated.
I. Calculator Basics (Calculator may be used)
1) Determine which of the following viewing windows, [x min, x max] X [y min, y max] , gives a complete graph for the
indicated equations. Sketch the graph.
2
3x
x 5
3
2
y
x
8x
x 5
f (x)
a)
b)
2
x
1
(i) [-10,10] X [-10,10]
(i)
[-10,10] X [-10,10]
(ii)
[0,10] X [-10,80]
(ii)
[-2,20] X [-20,20]
(iii) [-5,10] X [-10,80]
(iii)
[0,20] X [-5,5]
(iv) [-50,50] X [-100,100]
(iv)
[-5,20] X [-5,5]
2) Sketch the graph and find the largest and smallest y values of each of the following functions on their given
domain intervals.
1
x
2
f (x) 2
x
g(x)
a)
[-4,1]
b)
(-2,2)
2
4 x
2
3x
x 5
f (x)
c)
[2,4]
2
x
1
2
x
9
y
3) Graph
.
x 3
x 3
a) Explain why this graph appears to be a linear function rather than a curve with a vertical asymptote at
.
x 3
x 3
b) Zoom in on the graph around
. Give the viewing window when you first see the empty pixel at
or you notice the graph getting “jagged” around there.
x 3
c) If you had to fill in a y-value when
, what would it be?
4) An open box is to be made from cutting squares of side s from each corner of a piece of cardboard 25” by 30” and
then folding up the sides.
a) Write an expression for the volume, V, of the box in terms of s.
b) Graph of V(s) using your graphing calculator. Identify the domain and range of this graph.
c) What domain and range make sense in this problem situation?
d) Find the value of s that will give the maximum volume of the box.
e) What value(s) of s will give a volume of 1225 cubic inches? Show how you determine this.
II. Cartesian Plane Basics (No calculator)
5) Determine the slope, the length, and the midpoint of the segment with endpoints (1,-2) and (3,2).
5x
ky 3
2x 3y 5
6) For what values of k is
parallel to
? For what values of k are the two lines
perpendicular?
2x 5y 10
7) Plot the line
indicating x- and y-intercepts. Be sure to label your axes to indicate your scale.
x 2y 3
8) Find the distance from point P(1,2) to line L:
.
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