Solution:
12. If , then t =
Solution:
==>
==>
==>
==>
13. The sum of the solutions of the equation is equal to:
Solution:
==>
or
or
e) The equation of the horizontal asymptote of the graph of f is y = 1
Solution:
Note: All questions are related to the graph of f(x) (When graphing remember the rule )
From the graph we see that part (d) is false.
8. A wheel on a truck has a diameter of 12/p feet. How far will the truck move if the wheel turns through 840 degrees.
a) 26 feet
b) 28 feet
c) 12 feet
d) 18 feet
e) 9 feet
Solution:
9. The domain of the function is:
a) (-,-1) U (0, ) b) (-1, 1) c) (0, ) d) (-, 0) U (0, )
e) (- , -1) U (1, )
Solution:
==>
________+_________-1______-_______0______-_______1________+________
Thus, the domain is (- , -1) U (1, )
10. If W(t) is the wrapping function, then W(-17p/3) is equal to:
Solution:
11.
16. Given ln 2 = x and ln 3 = y, then =
Solution:
17. The asymptotes of are given by , where n is an integer, then
Solution:
asymptotes of are the zeros of
==>
==>
Therefore A = 4 and B = 3
18. If b, x, y and z are positive real numbers and , then the expression =
solution:
19.
Solution:
Therefore,
Mathcad check:
__________________THE END________________
Mathcad check:
14. Which of the following is true?
a) for any real number x.
Not true if x < 0
b) If , then x = 1.

c) ln x > 0 for x e (0, 1).


d) log(3+3) = (log 3)(log 3).


e) log x is always a positive real number.
ln x < 0 for x e (0, 1).
The log of sums or differences can not be simplified
The range of log x is (- , )
Solution:
Part (b)
==>
15. The supplementary angle of is:
Solution:
=
----------------------------------------
Mathcad check:
2. If , (a > 0, b > 0) has period p and range [-1, 3], then is equal to:
a)
b)
c)
d)
e)
Solution:
range = [-1, 3] ==>
vertical shift = d =
(Midpoint formula)
Thus,
3. In the adjacent figure, the expression w + 2x =
a)
b)
c)
d)
e)
Solution:
==>
Math 002-043-A. Farhat
Major Exam 1 Solution
July 23, 2005
version 3
1. The solution set of
a) { }
b) { }
c) { }
d) { }
e) { }
Solution:
==>
Cross multiply
==>
Divide by 2 and then multiply both side by
==>
==>
Take log of both sides
==>
Use the property
==>
Mathcad returns the answer in terms of the natural log.
(S > 0 ==> right shift)
Your may also rewrite the function in standard form as and then find the values of A, P and S:
==>
(S > 0 ==> right shift)
6. Suppose that the terminal side of an angle q in standard position lies on the line where , then
a) -3
b) 4
c) -4
d) 3
e) 5
Solution:
Choose a value for x, say x = 1 ==> y = -3
==>
7. If , which one of the following is FALSE?
a) The graph of f is decreasing.

b) The range of f (- , 1) .

c) The graph of f has one x-intercept and on y-intercept
d) The graph of f is above the x-axis for x e (1, )
and
==>
==>
==>
==>
Therefore,
4. If , , then the graph of f is below the x-axis on the interval
a)
b)
c)
d)
e)
Solution:
The graph of is the same as the graph of shifted to the right by p /4 and reflected about the x-axis.

As shown in the graph, the interval where the graph is below the x-axis is (p /4, 5p/4)
5. The function has amplitude A, period P and phase shift S. Then,
a) A = 2, P = 2p /3, S = p /3 to the right
b) A = -2, P = 2p /3, S = p /3 to the left

c) A = 2, P = 2p /3, S = p to the right

d) A = 2, P = p /3, S = p to the right

e) A = -2, P = p /3, S = p to the left
Solution: