# MATH 211 NIU 04Fall Solution

pg score

Name:

Recitation Instructor: Recitation Day & Time:

Total/200 Page1/40 Page2/40 Page3/40 Page4/40 Page5/40

MATH 100 College Algebra

Final Exam

7:00–8:50pm, Wednesday May 14, 2003

Show All Your Work. Check that you have all five pages.

1. (10 points) Solve the inequality |2x−1| ≥ 5.Graph your solution below.

(Remember to indicate clearly whether end-points are included or excluded).

✲

x−5−4−3−2−1 0 1 2 3 4 5

2. (10 points) Simplify, assuming x, y positive. In the answer only positive rational exponents (no radicals)

should occur.

(a) (xy2)3

x2y3

(b)

3

√x5

√x

3. (10 points)

(a) Find the slope of the line through the points (2,−3) and (0,3).

(b) Give the slope-intercept form of the equation of the straight line through the points in (a).

4. (10 points) Solve the equation 7

x−3

x−1=5

x(x−1).

1

pg score

5. (10 points)

(a) Write 5 ln x−1

3ln y+ 3 ln zas a single logarithm (here x, y, z are positive real numbers).

(b) Express log23 in terms of natural logs, and evaluate it to three decimal places.

6. (10 points) Solve the inequality 2

x≥1. Graph your solution. Check the status of x=−1!

✲

x−5−4−3−2−1 0 1 2 3 4 5

7. (10 points) An account oﬀers an annual interest rate of 3% compounded continuously.

(a) If $10,000 is deposited in the account, what will be the balance after 5 years?

(b) How long does it take for the amount in the account to double?

8. (10 points) Solve the equation √x−3 + 5 = x.

2

## Document Summary

Check that you have all five pages: (10 points) solve the inequality |2x 1| 5. Graph your solution below. (remember to indicate clearly whether end-points are included or excluded). 5 x: (10 points) simplify, assuming x, y positive. In the answer only positive rational exponents (no radicals) should occur. (a) (xy2)3 x2y3. 1 pg score: (10 points) (a) write 5 ln x 1. 2 pg score: (10 points) for the following functions nd the vertical, horizontal and slant asymptotes (give the equation of the asymptote or write n/a if none of that type exists). vertical horizontal slant f (x) = 5x y z = 2. (b) use your calculator to nd the reduced row-echelon form of this matrix. x (c) use (b) to solve, if possible, the system of equations in (a): (10 points) solve. 3x3 5x2 + 2x 1 x2 x 1: (10 points) simplify: x 2 x + 2.