Name:
Recitation Instructor:
Recitation Day and Time:
College Algebra – FINAL EXAM - Part 1 - July 31, 2008
Page 1 Page 2
26 pts
24 pts
Page 3
25 pts
Directions: You will find 10 problems listed below. Please show all your work neatly and box your final
answers. No notes or books are allowed.
1. (5 points) Solve: 4(x + 2) + 3(x − 4) = 5(x − 8).
2. (5 points) Solve by factoring: 2x2 + x − 10 = 0.
3. (8 points) Solve for x and check your work:
4. (8 points) Solve and check your work:
√
1
1
2
−
=
.
x+9 x−9
x−9
5x + 1 = 6.
5. (8 points) Solve and check your answers: |x − 5| = 2x − 9
6. (8 points) Solve: x(x − 3)(x + 5) ≥ 0
7. (8 points) Given the functions f (x) = 4x2 + x and g(x) = x + 2:
(a) Find (f + g)(x) and simplify completely.
(b) Find (f g)(x) and simplify completely.
8. (8 points) Given the points (2, 9) and (4, 5):
(a) Find the slope of the line connecting the two points.
(b) Find the equation of the line connecting the two points. Write answer in slope-intercept form.
9. (8 points) Find an equation of the parabola with vertex at (4, 6), passing through (3, 2). Write
answer in the form y = ax2 + bx + c.
10. (9 points) A rectangular frame has a perimeter of 120 centimeters. The width is twice the length.
What are the dimensions of the frame? Please define any variables used and show all your work
using algebra.
Pledge: On my honor, as a student, I have neither given nor received unauthorized aid on this
examination.
Signature:
Date:
Name:
Recitation Instructor:
Recitation Day and Time:
College Algebra – FINAL EXAM - Part 2 - August 1, 2008
Page 4 Page 5
18 pts
26 pts
Page 6 TOTAL (both days)
31 pts
150 pts
Directions: You will find 9 problems listed below. Please show all your work neatly and box your
final answers. No notes or books are allowed.
11. (a) (5 points) Using your graphing calculator, graph the function f (x) = −x3 − 5x2 + 9x + 45 over
the following intervals: −8 ≤ x ≤ 8 and −75 ≤ y ≤ 75. Find the x-intercepts and relative
extrema, and include these points on your graph.
(b) (5 points) For what x-interval is f (x) increasing? Refer to your graph in your explanation.
12. Consider the polynomial f (x) = 2x3 + 3x2 − 32x − 48.
(a) (4 points) List all possible rational zeros of f (x).
(b) (4 points) Given that x = 4 and x = −4 are zeros of f (x), find the other zero of f (x). You
must show your work.
13. (8 points) Find a polynomial with a single zero at x = −3, a single zero at x = 1, and a single
zero at x = 3. Multiply your answer out completely.
14. (a) (4 points) Write the augmented matrix determined by the following system:
2x + 2y = 1
x + 6y = −1
2 2
(b) (4 points) Using your calculator, find the inverse of the matrix A =
.
1 6
(c) (4 points) Using your answer from part (b), find the solution to the system in (a). Show all
your work!
15. (6 points) Find the vertical asymptotes of the rational function r(x) =
x3
3x − 7
.
− 10x2 + 9x
16. (8 points) Cashews cost $7.50/lb, while raisins cost $4.50/lb. How much of each type is required
to make a blend of 6 pounds that costs $5.00/lb? You must define any variables used and show all
your work using algebra.
17. (8 points)
(a) Given f (x) = ln (x − 6), find f (7).
(b) Does the graph of f (x) have a vertical asymptote? If so, what is it?
18. (7 points) Condense into a single logarithmic expression using properties of logarithms:
√
4 log(x) + log(z) − log( y). (Here, x,y, and z are all positive.)
19. (8 points) Suppose that in a certain town, there were 20 teachers in the year 1940, and 37 teachers
in the year 1960.
(a) Assuming an exponential model of growth, P (t) = P0 ekt , what is the exponential growth rate,
k? (Here, t = 0 corresponds to the year 1940.)
(b) How many teachers were there in the town in 1965? (Here, t = 0 corresponds to the year
1940.)
Pledge: On my honor, as a student, I have neither given nor received unauthorized aid on this examination.
Signature:
Date: