Download Math 1111 Exam 1

Name:
Date:
Mathematics 1111
Exam 1
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(1) (20 points) Determine whether the following statements are true or false. If the statement
is true, explain why the given statement is true (a proof is not necessary), otherwise provide
a counterexample.
(a)
For real numbers a, b, and c with a 6= 0 the quadratic equation ax2 + bx + c = 0
either has exactly two real solutions or no solutions for x.
(b)
For a positive real number c the interval satisfying the inequality |x| > c is given by
(−c, c).
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(2) (50 points) Solve for x in the following equations. Give exact solutions for each problem.
(a)
9 − |4x + 7| = 5
(b)
2
5
4
−
= 2
x−1 x+1
x −1
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(c)
x2 + 4x − 10 = 0
(d)
x3 − 3x2 − 3x + 9 = 0
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(e)
x−
√
x+1=
x
3
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(3) (10 points) A plumber and his assistant work together to replace the pipes in an old house.
The plumber charges $50 an hour for his own labor and $20 an hour for his assistant’s labor.
The plumber works twice as long as his assistant on this job, and the labor charge on the
final bill is $5400. How long did the plumber and his assistant work on this job?
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(4) (10 points) Phyllis invests $12, 000, a portion earning a simple interest rate of 40% per year
and the rest earning a rate of 10% per year. After 1 year the total interest earned on these
investments was $4200. How much money did she invest at each rate?
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(5) (10 points) Kiran ran from Tortula to Cactus, a distance of 16 miles. She increased her
speed by 2 miles per hour for the 6 mile trip from Cactus to Dry Junction. If the total trip
took 5 hours, then what was her speed from Tortula to Cactus?
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(6) (10 points) The equation 2x + kx − 7 = kx − k + 1 is really a family of equations, because
for each value of k, we get a different equation for the unknown x. The letter k is called a
parameter for this family. What value should we pick for k to make x = 3 a solution for the
resulting equation.