Name:
Recitation Instructor:
Recitation Day and Time:
College Algebra – FINAL EXAM FORM A- Part 1 - July 30, 2009
Page 1 Page 2
25 pts
28 pts
Page 3
22 pts
Directions: You will find 11 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(x2 + 1) + 3(x − 3) = 5(x − 7) + 2(2x2 − 2)
2. (6 points) Solve: 2x3 − 3x2 − 200x = −300
3. (8 points) Solve for x and check your work:
4. (6 points) Solve: 5x − 3 < 3(x + 9)
3x − 15
x−1
=
6x + 19
2x + 5
5. (8 points) Solve and check your answers: |x − 4| = 7 − 2x
6. (8 points) Solve: (x − 4)(x + 5) ≤ 0
7. (12 points) Given the functions f (x) = x2 + 5x and g(x) = 3x + 1:
(a) Find (f + g)(x) and simplify completely.
(b) Find (f g)(x) and simplify completely.
(c) Find (f ◦ g)(x) and simplify completely.
8. (5 points) Given the points (1, 5) and (4, 3), find the equation of the line connecting the two points.
Write answer in slope-intercept form.
9. (6 points) The profit for a certain product can be described by P (x) = −.02x2 + 20x − 1500, where
P (x) is in dollars and x is the number of units produced and sold. What is the maximum possible
profit, and how many units must be sold to achieve maximum profit?
10. (6 points) A rectangular garden has a perimeter of 610 feet. The width is one-fourth of the length.
What are the dimensions of the garden, and what is the area of the garden? Please define any
variables used and show all your work using algebra.
11. (5 points) Write an equation for a function that has the shape of y = x3 , but shifted left 4 units.
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 FORM A - Part 2 - July 31, 2009
Page 4 Page 5 Page 6/7 TOTAL (both days)
18 pts
23 pts
34 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.
12. (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) On what x-interval(s) is f (x) increasing? Refer to your graph in your explanation.
13. (8 points) Find a rational function with a horizontal asymptote at y = 2, zeros at x = 3 and x = 4,
and vertical asymptotes (poles) at x = −1 and x = 1. (You need not multiply anything out in the
numerator or denominator of your function.)
14. (a) (5 points) Solve: log2 (10 + 3x) = 4
(b) (4 points) Write the augmented matrix determined by the following system:
2x + 3y = 7
x + 6y = −1
2 2
(c) (4 points) Using your calculator, find the inverse of the matrix A =
.
1 6
(d) (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 inverse of the function r(x) = x3 + 7.
16. (6 points) Almonds cost $8.50/lb, while raisins cost $4.50/lb. How much of each type is required
to make a blend of 8 pounds that costs $7.00/lb? You must define any variables used and show all
your work using algebra.
17. (8 points)
(a) Given f (x) = ln (x − 4), find f (5).
(b) Does the graph of f (x) have a vertical asymptote? If so, what is it?
18. (6 points) Condense into√a single logarithmic expression using properties of logarithms:
5 log(x) + log(z) − log( w). (Here, x,z, and w are all positive.)
19. (6 points) Suppose that in a certain town, there were 30 teachers in the year 1950, and 40 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 1950.)
(b) How many teachers were there in the town in 1975? (Here, t = 0 corresponds to the year
1950.)
20. Consider the polynomial f (x) = x3 + 8x2 + 22x + 20.
(a) (4 points) List all possible rational zeros of f (x).
(b) (4 points) Given that x = −2 is a zero of f (x), find the other zeros, both real and complex,
of f (x). You must show your work.
Pledge: On my honor, as a student, I have neither given nor received unauthorized aid on this examination.
Signature:
Date: