Name:
Math 140: College Algebra
Midterm Exam - SAMPLE
INSTRUCTIONS: Show all work. Answers without work will NOT receive full credit.
Clearly indicate your final answers. The maximum possible score is 80 points.
Question 1 (10 pts). Find the distance between the given points P1 and P2 .
P1 = (6, 1)
P2 = (−1, 5)
Question 2 (10 pts). Find the real solutions, if any, of the following equation. Use the quadratic formula.
3x(x + 2) = 2
Question 3 (10 pts). Write the slope-intercept form of the equation of the line that has a slope of 6 and
that contains the point (−1, 5).
Question 4. Answer the questions about the following function:
f (x) = 3x2 + 3x + 7
(a) (5 points) What is f (−4)? Simplify completely.
(b) (5 points) What is f (x + h)? Simplify completely.
Question 5 (10 pts). Find all points having an x-coordinate of 4 whose distance from the point (−4, 2) is
10. Give your answer as one or more ordered pairs.
Question 6. Suppose that f (x) =
2x
4
and g(x) =
.
−9
x+3
x2
f
(a) (5 points) Find the function ( )(x). Simplify completely.
g
(b) (5 points) What is the domain of
f
?
g
1
n(n + 1).
2
How many consecutive integers, starting with 1, must be added to get a sum of 210? (For full credit, you
must use principles from this course - not trial and error!)
Question 7 (10 pts). The sum of the consecutive integers 1, 2, 3, . . . , n is given by the formula
Question 8. A sprinkler company installs irrigation systems. To track monthly costs C and revenues R,
they use the following functions, where x is the number of systems they install.
R(x) = 8x2 + 12x + 4
C(x) = 7x2 + 20x − 12
(a) (5 points) Find the monthy profit function P (x) = R(x) − C(x) by subtracting cost from revenue.
(b) (5 points) Find the number of sprinkler installations that result in a zero monthly profit (a break-even
point).