Math Placement Exam Practice Problems Page 2
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1
2(c) [7, ∞)
(c) The profit function, P (x), made from sell-
ing x cups of lemonade.
√
21. If f (x)
=
x + 4, find and simplify
(d) How many cups of lemonade must Russ
f (2 + h)
f (2)
.
sell to break even on his lemonade stand?
h
22. Perform the operations indicated and simplify
2
28. Find the roots of the function f (x) = 3x
+
2
x
4
x
7x
2.
+
.
x
2
x
2
x
2
+ x
6
x
2
+ 4x + 3
29. There are 5 white balls, 8 red balls, 7 yellow
23. Evaluate f (2)
f ( 3) given
balls, and 4 green balls in a container. A ball is
chosen at random. What is the probability a red
3
x
+ 1,
x > 1
ball chosen?
f (x) =
2
2x
3, x ≤ 1
30. Sue has 7 different books to put on a shelf. How
.
many different ways can she arrange the books
on the shelf?
24. Given the points A(4, 5), B( 3, 2), and
C(1, 4), do the following:
31. Jay wants to make a box, with no lid (or top),
(a) Plot points A, B and C.
out of a 10” x 6” rectangular piece of cardboard.
If Jay cuts squares with dimensions x by x out
(b) Find the equation of the horizontal line go-
of each corner of the cardboard, and then folds
ing through the point B.
up the corners to make an open box, find a func-
(c) Find the equation of the vertical line going
tion that represents:
through point C.
(a) The volume of the box.
(d) Find the equation of the line containing
points A and C and write the equation in
(b) The surface area of the box.
piont-slope form.
32. A classroom of 100 students has 65 females, 10
(e) Find an equation of the line that contains
seniors, and 6 females who are seniors. How
piont B but is perpindicular to the line
many students in this classroom are not female
containing points A and C.
and are also not a senior?
25. Graph the inequality 4x + 2y < 10. Does the
33. When making his 6-period class schedule, Mark
point ( 3, 8/3) lie in the solution set?
has 2 options of classes to take for first period,
4 options for second period, 1 option for third
26. Simplify the following expressions
period, 1 option for fourth period, 3 options
2x
for fifth period, and 5 options for sixth period.
(a)
xy + xz + 5x
How many different schedules can Mark possi-
(2.4)(.4)
bly have if he takes one class per period?
(b)
(2.5)(.4) + (.6)(.4) + (1.9)(.4)
34. Suppose and object is moving at 66 feet per sec-
27. Russ set up a lemonade stand where he sold 16
ond. How fast, in miles per hour, would a car
ounce cups of freshly squeezed lemonade for $2
have to travel to keep pace with this object?
per cup. It cost Russ $0.25 in supplies (lemons,
sugar, water, paper cups, and ice) to make each
cup of lemonade, and he spent a total of $52.50
on other necessary supplies (e.g. table, lemon-
ade dispenser, signs). If x is the number of cups
of lemonade that Russ makes and sells on the
day of the lemonade stand, find the following:
(a) The cost function C(x), to make x cups of
lemonade.
(b) The revenue function R(x), generated
from selling x cups of lemonade.
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