Name_________________________________________________
Common Core Algebra: Midterm Review
Date__________________________________________
I. Expressions/Equations/Inequalities: Show all work on loose-leaf. Transfer answers under each
question.
1) Solve for y: 2(3y-4)=10
7) Which value of x is in the solution set of the
inequality  3x  5  12 ?
(1) -8
(2) -6
(3) -3
2) Solve for x:
3
( x  2)  6( x  12)
4
8) Solve for x: 3ax  b  c
3) Solve for x:
5
6
( x  )  20
3
25
9) Solve for h: A 
(4) 0
1
h(b1  b2 )
2
4) Name the smallest integer value for x:
2x  5  17
10) Solve for h: A  r 2 h
5) Given 3x+ax-5>10, determine the smallest
integer value of x when a=2?
11) Find the product of (3x  6) and (5x 2  2 x  7) .
6) Given 5m+mn+1>11, determine the largest
integer value of n when m=-2.
12) If A= 3x 3  5 x 2  6 x  3 and B=  4 x 2  5 x  7 ;
find each of the following:
a) A+B
b) A-B
13) Simplify and express as a trinomial:
5( x  3) 2  6( x  2)
14 ) 14) Which statement is not always true?
1) The sum of two rational numbers is rational.
2) The product of two irrational numbers is
rational.
3) The sum of a rational number and an
irrational number is irrational.
4) The product of a nonzero rational number
and an irrational number is irrational.
II. Word Problems
15) The Ambrose family has two children whose
ages can be represented by consecutive odd
integers. If the sum of their ages is 37, which of the
following equations could be used to find the age of
the youngest child?
(1) x+x+1=37
(2) x(x+1)=37
(3) x+x+2=37
(4) x(x+2)=37
17) Jonathan has been on a diet since January 2013.
So far, he has been losing weight at a steady rate.
Based on monthly weigh-ins, his weight, w, can be
modeled by the function w=-3m+205 where m is
the number of months after January 2013.
a) How much did Jonathan weigh at the start of the
diet?
b) How much weight has Jonathan been losing each
month?
c) How many months did it take Jonathan to lose 45
pounds?
16) The length of a rectangular sandbox is 4 more
than twice the width, w. Write an equation that
shows the perimeter of the playground is 98 feet.
Solve the equation to determine the length of the
sandbox.
Write an equation that shows the area of the
sandbox is equal to 510 square feet.
18) Alex makes ceramic bowls to sell at a monthly
craft fair in a nearby city. Every month, she spends
$50 on materials for the bowls from a local art
store. At the fair, she sells each completed bowl for
a total of $25 including tax. Which equation
expresses Alex’s profit as a function as a function of
the number of bowls that she sells in one month?
(1) p(x)=50x+125
(2) p(x)=15x+25
(3) p(x)=25
(4) p(x)=25x-50
III. Graphs of Equations/Inequalities & Systems
19) What is the solution to the system of linear
equations: y  x  4 and y  2 x  1 ?
(1) (-1,3)
(2) (0,4)
(3) (1,-1)
(4) (-3,3)
20) Which point is in the solution set to the system
1
of inequalities y  2 x  1 and y  x  5 ?
2
(1) (-3,10)
(2) (8,2)
(3) (-2,1)
(4) (4,1)
x y 5
21) Which system of equations would have the same solution as the system:
3 x  2 y  10
(1)
3x  2 y  5
x  y  10
(2)
 3x  3 y  5
3 x  2 y  10
(3)
 3 x  3 y  15
3 x  2 y  10
(4)
2x  2 y  5
3 x  2 y  10
22) Graph the following system on the coordinate plane below and state an
ordered pair in the solution set.
x  3 y  15
x4
IV. Statistics
23) The accompanying box-and-whisker plot
represents the scores earned on a science test.
24) Which statistic would indicate that a linear
function would not be a good fit to model a data set?
Explain your response.
1)
2)
3)
4)
Answer each of the following questions about the
box plot shown above:
Minimum=
Range=
st
1 quartile=
Median=
Interquartile Range=
rd
3 Quartile=
Maximum=
Percentage of scores between 75-85
Explain:
25) Since 1990, fireworks usage nationwide has
grown, as shown in the accompanying table, where t
represents the number of years since 1990, and p
represents the fireworks usage per year, in millions of
pounds.
Number of
years since
1990
0
2
4
6
7
8
9
11
Fireworks
usage per
year, in
millions of
pounds
67.6
88.8
119.0
120.1
132.5
118.3
159.2
161.6
Create the residual plot using the table in question
#25 on the set of axes given below.
Residual
-5.2
-0.4
13.4
-1.8
2.4
-20.0
12.7
-1.3
Find the equation of the linear regression model for
this set of data, round values to the nearest hundredth.
V. Functions
26) If the function h(x) represents the number of
full hours that it takes a person to assemble x sets
of tires in a factory, which would be an appropriate
domain for the function?
(1) Set of real numbers
(2) Set of negative integers
(3) Set of integers
(4) Set of non-negative integers
27)