Math 152
Fall 2015
Name: _____________________________
Instructor: G. Rodriguez
Exam 4
The exam is due Monday, December 7 during the first minute or two of class. I will not accept
any late exams so be on time. If you have to miss that day, or you are concerned about
getting to class late, email the exam to me. (IMPORTANT: The email must be sent before the start of class.
Be sure the email gets delivered!)
You can use your notes and textbook. You can get help from anyone to do these problems
EXCEPT the MLC/ILC tutors or me.
In an attempt to minimize the amount of time required to grade everyone’s exams, they need to
be fairly uniform. For your exam to be accepted for grading, the following guidelines must be
followed:
§
Problems are to be separated by at least one line width.
§
If you do problems in columns, make sure the problems don’t run into each other. I
should see distinct columns.
§
Show sufficient work. Your work must match your answer. Show the work next to the
problem number. No credit will be given for a list of answers.
§
You cannot ‘guess and check’ to solve any of the problems. You must use the methods
taught in class to solve the problems.
§
Circle/box your answer. Include units where appropriate. When doing word problems, the
answer is not complete unless the final answer includes the units. For example, 5 feet.
§
Do the problems in order and put the pages in order.
IMPORTANT: Because this is a take home exam I will grade more strictly!
1) Simplify using the quotient rule.
2) Divide and simplify.
5
5
3
250x 8
27y15
64x10 y 8
4 points
2x 2 y −2
3) Add or subtract as indicated. You may need to simplify to identify like terms.
3
3
4 points
3
54x + x 128
4) Multiply. If possible, simplify any radical expressions that appear in the product.
(
4 points
)(
5−4 2 3 5+ 2
)
5) Rationalize the denominator.
6) Solve.
3
4 points
2x + 4 + 10 = 8
12
3
9x 5 y 7
4 points
4 points
7) Solve.
x = 5 + 4x − 15
4 points
8) Solve.
x −16 + x = 8
5 points
1
9)
The function f (x) = 21x 3 models the number of plant species, f ( x ) , on an island in terms of
the area, x, in square miles, of that island. What is the area of an island that has 105
species of plants?
4 points
10) Subtract. Write imaginary results in the form a + bi.
11) Multiply. Write imaginary results in the form a + bi.
12) Multiply. Write imaginary results in the form a + bi.
13) Divide and simplify to the form a + bi.
(5 + 6i ) − (9 − 7i )
−8 ⋅ −6
(5 − 2i )
2
6 + 5i
2 − 3i
2 points
3 points
3 points
4 points
14) Solve the following equation by using the Square Root Property. If possible, simplify
radicals and rationalize denominators. Express imaginary solutions in the form a + bi.
49x 2 + 36 = 0
4 points
15) Solve the following equation by using the Quadratic Formula. If possible, simplify
radicals. Express imaginary solutions in the form a + bi
2x 2 + 9 = 4x
4 points
16) Graph f (x) = (x − 2) 2 + 3 by finding the vertex, y-intercept, and x-intercept(s), if any. The
graph must include five points.
5 points
17) Graph f (x) = x 2 − 6x − 7 by finding the vertex, y-intercept, and x-intercept(s), if any. The
graph must include five points.
5 points
18) The length of a rectangle is 5 inches longer than the width. If the area is 30 square inches,
find the rectangle’s dimensions. Round to the nearest tenth.
5 points
19) A person standing close to the edge on the top of a 160-foot building throws a baseball
vertically upward. The quadratic function h(t) = −16t 2 + 64t + 160 models the ball's height
above the ground, h(t) , in feet, t seconds after it was thrown.
Note: The following two questions could have been asked in either order. The answer to one does NOT matter for the other.
a)
How many seconds does it take for the ball to reach 200 feet? Round to the nearest
tenth.
4 points
b) After how many seconds does the ball reach its maximum height? What is the
maximum height?
3 points
20) Solve the following equation that is quadratic in form. If at any point in the solution process
both sides of an equation are raised to an even power, a check is required. If possible,
simplify the answer(s).
4 points
3x − 5 x
=2
21) Solve. Graph the solution set and write it using interval notation.
2
4 points
3x +11x ≤ 20
22) Let f (x) = x − 6 and
2
a) Find (g  f )(x) .
g(x) = 5x + 4 .
Simplify result as much as possible.
3 points
b) Find (g  f )(4) .
2 points
()
23) Find BOTH f(g(x)) and g(f(x)) and determine if f x = 5x − 6 and g x =
each other.
()
x+6
are inverses
5
4 points
24) Find the inverse of the following one-to-one function. Use appropriate function notation for
the answer.
f (x) = (x − 2)3 + 5
4 points