Please answer all questions completely and show all of your
work. Be sure to write neatly so that your solution may be read as you intended
it to be read. Partial credit will be awarded. Calculators may be used on the
exam to check an answer. All answers must be exact and fully simplified ; decimal
approximations will not receive full credit. Cross out any work that you do not
wish to be graded and please place a box around your final answer so that it may
be found easily.
1. Find the solutions of
(10 points)
However, x
= 2 is not in the domain and there is no solution.
2. De termine the equation with the information that is given.
Your answer must be written in slope- intercept form .
(a) Passing through the points (3, 5), (1,
11) (5 points)
(b) Through the point (3,-2)
and perpendicular to the line x -3y+6
= 0 (5 points) First, find the slope of the given line
So, the slope of the line perpendicular to this is m = -3.
Therefore, the slope of our line is:
3. Solve the fol lowing linear equation for x:
(10 points)
4. Factor the following trinomials (be sure to check your
answer):
(a) x2
- 9x + 14 (5 points)
x2
- 9x + 14 = (x - a)(x
- b).
Now, we must have ab = 4 so
the possible combinations of a and b
are 1, 14 and 2,
7. Now, 2 + 7 = 9 so a
= 2 and b = 7 is the desired factorization. Thus, x2
- 9x
- 14 = (x
- 2)(x
- 7).
(b)
10y2
+ 11y - 8 (5 points)
10y2
+ 11y - 8 = (cy
- a)(dy
+ b).
Now there are two possible combinations for c and d
since cd = 10. They are 1,
10 and 2, 5. We’ll make c = 2, d =
5 our first guess. Then 10y2
+ 11y - 8 = (2y
- a)(5y
+ b).
Next, we check our possibilities for a and b.
Thus the factorization is 10y2+ 11y - 8 = (2y
- 1)(5y
+ 8). Next we check our answer to be sure that we are
correct.
5. For a given car traveling at a specified speed, the force
needed to keep the car from skidding on a curve varies inversely as the radius
of the curve. For a 2000-pound car traveling at 30 miles per hour, a force of
240 pounds is needed to prevent skidding on a curve of radius 500 feet.
(a) What is the variation equation (be sure to actually write
down the final equation)?
(5 points)
The variation equation is given by F
= 
. Now, we use the
given information to find the value of k . So,
Therefore, the variation equation is
(b) What force (to the nearest pound) is needed to prevent
skidding if the curve radius is 700 feet? (2 points)
(c) If a force of 410 pounds is needed to prevent skidding, what
is the curve’s radius (to the nearest foot)? (3 points)
6. Find the solution(s) of the equation x2
+ 3x = 5x
+ 7 by using the quadratic formula (be sure to check
your answer). (10 points)
7. Solve the following system of equations using the substitution method . (10
points)
Therefore, the solution is x = 2, y = 2.
8.
(a) Sketch the graph of f(x) =
by plotting the points with x-values x = 0, 1, 4, 9, 16. (5 points)
(b) Is the function f(x) =symmetric
about the origin or the y-axis? (3 points)
There is no symmetry.
(c) Using the graph from part (a), use transformations to sketch
the graph of g(x) =
. (7 points)
9. Determine the distance between the points
. (10 points)
10. Find the solutions of
.
(10 points)
We first let choose the “ positive ” equation.
Now, by substituting x = 3 into the original equation we see
that it is indeed a solution of the equation. Next we explore the “ negative ”
solution.
Again, by substituting x = 
into
the original equation we see that it is indeed a solution of the equation.
Therefore, the solutions are x = 3, x =
.
