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MIDTERM I BENCHMARK REVIEW*
=
7p + 4
1. What is the value of p in the equation shown below?
-3
A -4
B -2
3p + 12
-3
Yp tY
~
l2-
-~
-'-f
2. It costs $12.50 to see a movie at a theater near Jason's house. It costs only $1.95 to rent a OVO from
an online service. A DVO player costs $125. To the nearest whole number, how many movies must
Jason rent instead of going to the theater before he recovers the cost of the DVD player?
=
12.50x
Step 1: Set up an equation .
/.f15x
DVDRental
-!95~
-/. 9Sv:
Step 2: Solve for x by bringing your
x values to one side and your #'s to the
other side.
**Your answer is a decimal. Make sure
lo.SS>c
/o . t.S
you answer the question.**
/!. g_ . .
1. (of..lnl
A 11
@)
c
/;25
/0 . 55
X
Circle the best answer:
110
~@ =Bx-8
3. Find the solution to:
Step 1: Combine like terms on the same side
7x +- Cf
Step 2: Bring your x values to one side and
your constants (#s) to the other side
9
-7x
?c- r
17::::
X
+f
T-f
4. Write each number in scientific notation:
7,080,000
7. 0 ~
B
c
780
7 g X 10
X /0 (:,
8x - 8
.::::
- 7X
Step 3: Divide
A
+;;;s
--~~~~--~~--------
Theater
tJ
0.00781
7'31/t/0- 3
5. Write each number in standard form:
A
4
8.1 X 10
<8 \I DOO
B
7.03
X
10-3
. oo7o3
c
9 .6
X
10-2
.oC10
6. Write an equation to represent each situation:
Step 1: Find your rate/slope
rise
run
Step 2: Find your y-intercept.
look at the graph where the line crosses the v-axis
Step 3: Write your equation in y= mx + b form
];
If
y-=zv-)
Equation of the graph: _ _ _--1-f----..;..-"
_ _ _ __
Equation of the
Step 1: Find your rate/slope
table:._--1t~-_-_l_z_:.x_-_2
_ _~-
y
X
Step 2: Find your y-intercept.
I( your x value is 0, your y value IS THE Y INTERCEPT
X
Step 3: Write your equation in y= mx + b form
1'
+z..
~-if\ l-.
7. State if each relationship shown is proportional or nonproportional:
Hint: y =kx (proportional) y =mx + b (nonproportional)
A
y =ax- a
p
NP
N:P
a.
D y = 12x + 0
C y=lAX
B Y= 7
State if each relationship is linear or nonlinear:
Hint: If x andy are in separate terms and have exponents of 1 =linear
A
y
= ax - 7
B y
= ax2 + 10
C 1Oy
= 3x - 4
NL
L
L
D
i
= 2x +1
NL..
9. Ned has a baseball cards and collected 5 per day. Mark has 40 baseball cards and loses 3 per day. In
how many days will Ned and Mark have the same number of baseball cards?
Ned
Mark
g+S
¥
+3}(:
40- 3x
/
+3x
I
g -+ 8-;c ~ 1-/o
-8
J -g
J;(:=
32
Maggie was comparing prices of two different pool companies to see which company would be best to buy
her new pool from.
Company
Rate
Pools 'R Us
$500 installation
$80 per hr
3 Brothers
$750 installation
$65 per hr
Maggie predicts it will take approximately 10 hours for the pool to be installed. She chooses the
company that is less expensive for the 10 hour job. How much will Maggie spend?
Step 1: Write your expression for both Pools 'R Us and 3 Brothers
Step 2: Rewrite your equation and plug in 10 for x.
Step 3: Bring your x values to one side and your constants (#s) to the other side
Step 2: Solve for x by dividing
3 Brothers
Soo+
oO X
.5 00 f
8'0 (/0)
Soo
+
Ch~a.p~r
oOO
/IJ 13oo 7 ~
75o f hS{!o)
7So f 0So
11oo
Answer: Maggie will spend
11.
Solve for x:
~
8 e/4 X + 2) = X + 29
0X
-1- ~~~~ X -1 ;;q
-;~-
-;~
~X 4 X= 13
-x
-y
Sx::=/3
s
s
12. Circle the graphs that are nonlinear:
0
riot
St-rai
J¥1 t-
Step 1: Distribute your 8.
Step 2: Combine li ke terms on opposite sides .
Step 3: Solve for x by dividing
-F~~·-1~
dj\ -......
13. Sketch a graph that is a not a function:
{ f'a i I s
ve r-1,-ca I
-~I
- - - _L -
14.
I...._,
.........
/,i]e -ks.J. )
~
Solve: 2(x- 3) = 15 + Sx
-
15 -
-
-
v
-t-
c-- .4- ..2_
["--..
EU-Lt,
Step 1: Distribute 2
Step 2: Combine like terms on opposite sides.
Step 3: Solve for x by dividing
aX- fo-
-I
-•
'
'l
I
_o=
i\
ti
X
-
;--
c--
c---1-
-2/ =3x
3 3
-~ s t 3 x- _ _ / 1_7 ~ ;r ) .----------_____,
-o:;x
-_;o
JS
+5x-;;x
I
-2.1= 3-:\'
15. Order the following numbers from least to greatest:
7 x 10-31 7.4 X 10-11 7 X 10-41
Hint: The bigger the negative exponent the smaller the number.
7
X
f0-
3
/
16. Simplify each of the following in terms of positive exponents:
A
4-2
B 85
+ 82
C {7 2 } 3
I
-1(7.
17. Simplify Completely:
A
go
=J
62
3(1 + 1)
B
.::
18. Particle A has 3.4 x tcf atoms. Particle B has 5.3 x tcf atoms. How many atoms do both particles
have combined? (Hint: Exponents must be the same before you add.)
{3Jf
( · 3 Lf
XJo"J + {5.3 X/OS)
X 10 ~)
f
[ 5.
3 X 10 5 )
19. The length of a certain rectangular molecule is 2 x td micrometers. The width of the molecule is
4 x tcf micrometers. What is the area of the molecule expressed in scientific notation?
Hint: A =length x width.
(;; X/D
3
)
(
f k /6b)
(J x <f) (I0 3 X I 0 6)
Ti x;Q!}
20. Mr. & Mrs. Tom save 12% of their monthly income toward retirement. One month they saved
$2,500. That month Mr. Tom earned $10,400. If x represents the amount of income Mrs. Tom made
that month, write an equation to represent this situation.
Mrs. Tom 's income
Let x = Mrs. Tom's income
Equation: .12 (
X +
+ Mr. Tom 's income
\0 1 J..f 0 0
) =$2,500
--
21.
A vendor who sold bread at farmers' markets counted the number of leftover loaves at the
end of each day.
loaves of leftover bread
100
95
90
85
80
75
70
<II
65
>
'11
60
..2 55
...<II 50
> 45
0
40
~
35
<II
30
...J
25
20
15
10
5
0
"'
Sunday
f·1onday
Tuesday
Wednesday
Thursday
Friday
Saturday
Day
Part A: On which day were 80 loaves of bread leftover?
So~rd(f
Part 8: Which day was the least number of loaves leftover?
Part C: What is the difference between the least and greatest # of leftover loaves during the week?
/00 - c{)O
aiJ
22.
A lines passes through the points (0, 3) and (1, 9). What is the equation of this line?
Hint: y,t.-mx + b~
slope
y-intercept
Step 1: Find your slope
J.-.3 - (-()
I
y~
,...
X2-X1
Step 2: Find your y-intercept.
When your x value is 0, your y-value is your y-intercept!
/---;:;;!
!_:}__;
Step 3: Write your answer in y = mx + b form!
Answer:
23.
Function
y~ fox r 3
1is represented by the table: I
Step 1: Find your slope
.1:!y_
; I ~
~ ~ I
1133 2
_'l___
~X
Function 2 is represented by the equation:
Which function has a greater rate of change?
Answer: _
_,_FG_u_n_c_A_'_6Y)
__
1__
-
y = 3x- 5.