Math1090 Midterm 1
Name ___________________________________
Fall, 2015
uid: ___________________
Instructions:
• Please show all of your work as partial credit will be given where appropriate,
and there may be no credit given for problems where there is no work shown.
•
All answers should be completely simplified, unless otherwise stated.
•
You may use a scientific calculator that has been checked and approved
by your instructor. No other electronics are allowed on this exam. Make sure
all cell phones are put away and out of sight. If you have a cell phone out at
any point, for any reason, you will receive a zero on this exam.
•
You must show us your U of U student ID card when finished with the exam.
•
The exam key will be posted on Canvas by noon.
•
You may ask for scratch paper. You may use NO other scratch paper. Please
transfer all finished work onto the proper page in the test for us to grade
there. We will not grade the work on the scratch page.
•
You are allowed to use one 4x6 inch note card with notes for your reference
during the exam.
(This exam totals 105 points, but the total percentage will be calculated out of 100
points to build in a cushion of extra credit to account for simple arithmetic errors.)
STUDENT—PLEASE DO NOT WRITE BELOW THIS LINE. THIS TABLE IS TO BE USED FOR
GRADING.
Problem Score
1&2
3
4&5
6
7
8
Total
Percentage:
1. (10 pts) Solve the equation
x5 1 x−1
= 
.
x2 3 2x4
Solution: _____________________________
2. (10 pts) Solve this inequality and graph the solutions on the real number line
5x−4≤3 2−x 
Answer 2: ______________________________
<--------------------------------------------------------------------------------------------------->
3.
For the system of inequalities.
2y− x≤5
x y≤7
y≥2
(a) (10 pts) Graph the solution set and label the corners (vertices).
(b) (5 pts) Maximize the objective function
f =5x−6y
with the constraints in (a).
Point where max occurs: ____________________________
Max value of f: ______________________
4. (10 pts) Write an equation of the line that goes through the point (2, -3) and is
perpendicular to x5y=15 . (Put answer in slope-intercept form.)
line: __________________________________________
5. (10 pts) Solve the system of equations.
−2x y=11
5x2y=−5
point of intersection: ________________________
p=4q200 and the demand
6. (10 pts) If the supply function for a product is
p=−3q410
function is
, what is the equilibrium point?
Equilibrium point: __________________________
(write answer as ordered pair, (q,p))
7. The selling price for a text book is $50 and the total cost is given by
C  x =18x8,000 where x is the number of textbooks.
(a) (5 pts) Find the revenue function, R x  .
R x  = ___________________________________
(b) (5 pts) Find the value of
C 20 . Describe the meaning of this number.
C 20 = ____________________
Description: ____________________________________________________________________
_______________________________________________________________________________
(c) (5 pts) How many textbooks need to be sold in order to break even?
(d) (5 pts) What is the marginal profit?
# textbooks: ________________________
Marginal profit = _____________________