Math 112
Test 1 Sp11 ch. 1, 2, sec. 8.1, 8.2, 8.4
Name __________________
Numbers 1- 12 are short answer problems. For the rest of the problems, you are expected
to show work. Make sure your work is organized and that every step is correct. Even if
your answer is correct, you could loose points if your work has untrue statements in it or
you do not show enough work to lead to your answer. Simplify all answers. If you use
the graphing feature of your calculator to solve a problem, show what you plugged in,
draw a rough sketch of your graph, and show how this led to your final answer.
(5 pts)
1.)
Use the image of a Cartesian grid on the
left and label the following items on it:
a.) the origin
b.) the axis that is usually used as
the x-axis
c.) the axis that is usually used as
the y-axis
d.) each of the four quadrants with
their numbers: I, II, III, and IV
(5 pts)
2.) Classify each of the following numbers by putting a check mark in the box of every
set to which the number belongs. Each row should have more than one box checked.
natural
whole
integers
rational
irrational real
numbers
numbers
numbers
numbers
numbers
-9
7
1.333...  1.3
4
7
5
(2 pts)
3.) Rewrite each of the following numbers as an equivalent number in scientific
notation.
a.) 4,300
____________________________
b.) 0.023
____________________________
(6 pts)
4.) Sets A and B are represented by the following number lines. Graph the indicated sets
on the last two number lines and then write those sets in interval notation. Make sure and
mark your scales by labeling a couple of the tick marks on each number line.
A ∩ B = ___________________
A » B = ____________________
(7 pts)
(2 pts)
5.) Match the graphs to their equations by writing the letter of the corresponding graph
next to the equation.
i.) y = x3 _____
ii.) y = x2 _____
iv.) y = |x| ____
iii.) y = x __
1
v.) y = _____
vi.) y = mx + b, m > 0, b > 0 ____
vii.) y = c, c > 0 ___
x
a.)
b.)
c.)
d.)
e.)
f.)
g.)
h.)
6.) For each of the following, do not evaluate the expression. Instead, just illustrate the
requested property by filling in the right side of the equation.
a.) commutative property
(4 μ 2) μ 3 = ___________________________________
b.) associative property
(4 μ 2) μ 3 = ___________________________________
(3 pts)
7.) Write: “the distance from x to 5 is at least 3” as a mathematical expression involving
absolute value. Do not solve.
__________________________
(2 pts)
8.) Evaluate the slope of the line.
______________
(7 pts)
9.) Use the following graph of f(x) to fill in the blanks. If there is more than one answer,
list all of the answers with a comma in between them. Use interval notation where
appropriate. If an answer cannot be given exactly, estimate it.
a.) f(-2) = ________
b.) f(-4) = ________
c.) f( _______) = -4
d.) the x-intercept(s) of f are:
__________
e.) the y-intercept is _____
f.) domain of f = ___________
g.) range of f = _____________
(6 pts)
(3 pts)
2 x
. Fill in the blanks. Simplify your answers. Use
x3
interval notation where appropriate.
10.) Let g(x) =
5  x and h(x) =
a.) g(-11) = _________________
b.) h(2) = __________________
c.) dom g = _________________
d.) dom h = ___________________
11.) Circle the letters that corresponds with the relations where y is a function of x.
a.)
c.)
b.)
x
1
x
y
-1
y
-1
2
2
0
3
2
4
3
0
3
d.)
(3 pts)
e.)
2
4
3
f.)
12.) A toddler’s mother gets distracted at a display in a store. The toddler begins to run
off giggling along the way. When the toddler is 5 feet away from the mother, she looks
at her child and says, come back. The toddler continues running off at a rate of 3.5
feet/second until the mother threatens to walk the other way (which scares the toddler and
he returns to his mom). During the time that the toddler is running off his distance from
his mother can be described by the equation d(t) = 3.5t + 5 where t is the time in seconds.
a.) Evaluate d(7).
__________
b.) Interpret the meaning of the function value found in part a.
__________________________________________________________
__________________________________________________________
(15 pts)
13.) Perform the indicated operations and simplify the following expressions completely.
There should not be any negative exponents in your final answer. Write your final
answer in the provided blank. Show your work.
5 x 2 y 3
a.)
_________________
2 1
3
xy
 
b.) 5 – 2(3x +1) + 7x
c.)
(10 pts)
3  (5  3) 2
2  3(2)3
__________________
14.) Solve each of the following equations for x. Show your work and write your final
answer(s) in the provided blank
a.)
4x 1 x  3

7
2
6
b.) 6(x + 3) = 2(1 – x)
(4 pts)
__________________
15.) Solve for w:
P = 2w + 2l
____________
___________
_______________
(20 pts)
16.) Solve each of the following inequalities. Show your work. Graph your answer and
write your final answers in the provided blank using interval notation.
a.) 5x + 7 > 22 and 3 – 2x  -7
b.) 10 + 3x > -2 or 5x – 2  13
________________________
______________________
c.) |3 + x| + 2  10
______________________
d.) |3x+2| < 0
_______________________
e.) 5|x – 2|  0
_______________________