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: