AB/BC CALCULUS SUMMER ASSIGNMENT

To be completed by students entering AP calculus AB/BC in the fall of 2008.   Do NOT use a calculator.  Feel free to consult notes, textbooks, friends, etc.

In 1 and 2, find all intercepts, asymptotes and sketch a graph. 

1.                                                                                  2.    

In 3 and 4, find all points of intersection of the graphs .

3.     and                          4.        and    

5.  Find an equation for the line passing through the point  ( 3, -1 ) and perpendicular to the

     line   3x + 2y =3

6.  If    f ( x ) = -x² – 2x  find:

a)  f ( -2 )                                               b)  f ( 3 )                                 c)   f ( 2 + h)

7.  Given     ,  find  f ( x + 1 ) - f ( 1 )  .

8.  If      , find  

9.  If      and         ,  find   f(g(x))

10.  Find the domain  of   

11.   If the point ( -1,1 ) lies on the graph of the equation     , find the value of k.

12.  Given    , find   f ( 1 ) - f ( 5 ).

13.  Solve :    

14.  Solve:   .   Give exact answers in radian form.

15.  Given    ,   find  

16.  Let     f ( x) =          x² + 4   ,      x < 2

                                       3 - 2x  ,      x > 2               Evaluate:

a)  f ( 0 )                                                 b)  f ( 2 )                                 c)  f ( 3 )

17.   A student working for a telemarket company gets paid $5 per hour plus $2.50 for each sale.  Let x

        represent the number of sales the student has in an 8 - hour day.

a)  Write a linear equation giving the day’s salary S in terms of x.

b)  Use the linear equation to calculate the student’s salary of Wednesday if the student makes 24 sales that day.

c)  Use the linear equation to calculate the number of sales per day the student would have to make in order to  earn at least $100 a day.

18.  Find                                                     19.   Find   

20.  Find S₁,S₂, and the sum of the series below

• Find the points that are symmetric to the point (-4, 2)
• Across the x-axis
• Across the y-axis
• Across the origin

• Test to determine whether the following graphs are symmetric with respect to x-axis, y-axis, the origin, or none.
• y=x
• 
• 
• x - y = 4

• Find equations for the vertical and horizontal lines through:
• (1, 3)
• (0, -11)

• Find the equation for the line that passes through point (2, 3) and has slope 2.  Then use the equation to find the line’s intercepts and graph the line.

• Find an equation for the line through the points (2, -1) and (4, 4).  Express it in:
• Point-slope form
• Slope-intercept form
• Standard Form

• Consider the point P(6, 0) and line L: 2x – y = -2
• Find an equation (in slope-intercept form) for the line through P and parallel to L
• Find an equation for the line through P perpendicular to L
• Find the distance from P to L

• Sketch a graph of each equation.  Give the domain and range.
• y = 2x – 3
• 
• y = cos x
• 

28.  Say whether each function even, odd, or neither.

• y = cos x
• y = -cos x
• y = 1 – cos x
• 
• y = x
• 

29.  Write an equation for a circle with center (2, -3) and radius ½ .

30.  Identify the center and radius of the circles:

31.  Find the exact value, in simplified form, of  the sine, cosine, tangent, cosecant, secant, and cotangent of each angle:

32.  Graph each function over the interval  .

33.  Evaluate in radians