Download Old midterm 1

MATH 116.04
Midterm 2
February 24, 2012
Name
1
2
3
4
Total
•
•
•
•
10
10
10
10
40
Please check that your exam contains 4 problems on 4 pages.
You may use a scientific or graphing calculator.
Please turn all other electronics OFF and put them away for the duration of the exam.
Unless otherwise indicated, you must show your work. The correct answer with no supporting work may result in no credit.
• If you use a guess-and-check method when an algebraic method is available, you may not
receive full credit.
GOOD LUCK!
Math 116.04
1
√
(1) Starting with the graph of f (x) = x, perform the following graphical operations in the
given order:
• Shift down 1.
• Vertical stretch by 2.
• Shift left 2.
• Flip across the y-axis.
For each step, sketch the graph and give the formula for the resulting function.
2
(2) In one month, I make 3 bicycles, and my total costs come to $4300. The next month, I
make 5 bicycles, and my total costs come to $5800.
(a) Assuming my total costs c are a linear function of the number q of bicycles I produce
in a month, find a formula for c(q).
(b) My fixed costs consist only of rent for my workshop. How much am I paying in rent?
Math 116.04
3
(3) The market for computer mice is decribed by the following equations:
• Supply: p − 2q = 1
10
• Demand: p =
q+1
(a) Find the equilibrium market price and quantity.
(b) The government imposes a new tax that adds $0.10 to the price of each mouse. Modify
the equations above to reflect this. (Do not solve this new system.)
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(4) Solve the linear system
3y − z = 2
2x − 2y + z = −4
2x + y = −2