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ALGEBRA MIDTERM REVIEW SHEET
Exam date:
Wednesday, January 28, 2015 — 8:15 a.m.
Name ______________________
Period _________
Part I: Be sure to show all work or explain if there is no work to show.
1 What is the solution of the system of equations
shown in the graph below? Explain.
[2 points each]
4 If x varies directly (means has a proportional
relationship) as y, and x = 8 when y = 24, what is
the value of x when y = 6?
5 What is the solution to the equation
12 =
2 John has four more nickels than dimes in his
pocket, for a total of $1.25. Write an equation that
could be used to determine the number of dimes, x,
in his pocket.
3 Solve for x:
(
)
1
36x +18
9
6 The graph of y = f(x) is shown below. Find
f(-2). Explain.
7 Given the relation {(8,2), (3,6), (7,5), (k, 4)},
which value of k will result in the relation not being
a function? Explain.
(1) 1
(2) 2
10 Write an equation in slope-intercept form that
passes through the point (3, 5) with slope -4.
(3) 3
(4) 4
8 The scatter plot shown represents a relationship
between x and y.
11 Over which interval is the graph always
decreasing? Write your answer in both set and
interval notation. Explain.
What type of relationship is it? Explain.
(1)
(2)
(3)
(4)
A positive correlation
A negative correlation
a zero correlation
not able to be determined
( ) ( )
12 The equation 3 4x = 4x 3 illustrates which
property? Explain.
9 What is the solution set for the equation shown
below?
|3 – 2x| = 5
13 What is an algebraic expression for 4 less than
the product of 3 and a number x.
14 What is the rate of change for the data in the
table to the right?
x
y
0.5
9.0
1
8.75
1.5
8.5
2
8.25
2.5
8.0
17 Solve the inequality below to determine and
state the smallest possible value for x in the
solution set.
18 What is the range of the function shown to the
right? Show your answer in set and interval
notation. Explain.
15 The third term in an arithmetic sequence is 10
and the fifth term is 26. If the first term is a1, which
is an equation for the nth term of this sequence?
16 Let f be a function such that f(x) = 2x – 4 is
defined on the domain 2 < x < 6. The range of this
function is
(1) 0 < y < 8
(2) 0 < y <
(3) 2 < y < 6
(4)
<y<
19 What is the slope of the line represented by the
equation 4x + 3y = 12?
20 What is the value of the y-intercept for the
graph of 4x – 5y = 40 ?
23 Sam and Jeremy have ages that are consecutive
integers. The sum of their ages is 131. Write an
equation that could be used to find Jeremy’s age, j,
if he is the younger man.
24 What is the solution set to -3 £ 2x -1< 5 ?
21 Which graph does not represent a function?
Explain.
25 Two cyclists start at the same time from
opposite ends of a course that is 45 miles long. One
cyclist is riding at 14 mph and the second cyclist is
riding at 16 mph. How many hours after they begin
will they meet?
22 Write, in interval notation, an expression that
represents the set of all real numbers greater than 2
and less than or equal to 20?
26 A function is graphed on the set of axes below.
Which function is related to the graph? Explain.
27 Which graph shows a line where each value of y
is three more than half of x? Explain.
(1)
(2)
(3)
(4)
28 An electronics store sells DVD players and cordless telephones. The store makes a $75 profit on the sale of
each DVD player (d) and a $30 profit on the sale of each cordless telephone (c). The store wants to make a
profit of at least $255.00 from its sale of DVD players and cordless phones. Write an inequality that represents
the situation.
Part II:
[3 points each]
29 Solve for w, in terms of x and y if:
30 If f (x) = x 2 + 3x -5, find f (-3).
2y + 2w = x
31 The steps used to solve the equation 5(3 – x) = 20 are written out of order on the tiles below. Put the tiles in
logical order and justify each step.
x = -1
-15 + 15 – 5x = 20 - 15
()
()
32 Find f -1 x , the inverse of f x = 3x + 5.
æ 1ö
æ 1ö
ç - ÷ -5x = 5 ç - ÷
è 5ø
è 5ø
( ) ()
-5x = 5
15 – 5x = 20
Part III:
[4 points each]
33 a Determine the solution set of the absolute value inequality |x + 3| < 5.
b Graph the solution set.
c Write the solution set in interval notation.
34 Business students want to predict the average customer tip from an average customer’s restaurant bill. They
have collected data from five customers. The results are listed below.
a Write the linear regression for this data rounding each coefficient
to the nearest hundredth.
Bill ($)
Tip ($)
98.84
14.56
33.46
3.77
63.60
9.81
50.68
8.91
107.34
17.33
b Using your equation from part a, predict the tip that a customer will leave if the bill totals $75.50.
35 Luis spent $55 buying songs and movies at an online store that charges $1.25 for each song and $2.75 for
each movie. He purchased a total of 26 songs and movies combined.
Write a system of equations that represents this situation. Then determine how many songs and how many
movies Luis purchased.
36 Sarah went on a bike ride. The graph below shows the distance, y, in miles, that she had traveled after biking
for x hours.
State the domain and range of the function shown in the graph.
State the interval of time during which Sarah was riding the fastest, and explain how you know.
Part IV:
[6 points each]
37 Solve the system graphically
y = 4x – 1
2x + y = 5
38 On the axes below, graph f(x) = |3x|
If g(x) = f(x) – 2, how is the graph of f(x)
translated to form the graph of g(x)?
If h(x) = f(x – 4), how is the graph of f(x)
translated to form the graph of h(x)?