Download 1. What is the value of x in the equation ? 1.

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Midterm Review
Name: ____________________________________
1.
3.
What is the value of x in the equation
1. -16
3. -4
2. 16
4. 4
?
The gas tank in a car holds a total of 16 gallons of gas. The car
travels 75 miles on 4 gallons of gas. If the gas tank is full at the
beginning of a trip, which graph represents the rate of change in
the amount of gas in the tank?
-------------2.
1.
3.
2.
4.
The box-and-whisker plot below represents a set of grades in a
college statistics class.
Which interval contains exactly 50% of the grades?
1. 63–88
3. 75–81
2. 63–95
4. 75–88
-------------4.
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Which relation represents a function?
1.
2.
3.
4.
{(0,3), (2,4), (0,6)}
{(−7,5), (−7,1), (−10,3), (−4,3)}
{(2,0), (6,2), (6,−2)}
{(−6,5), (−3,2), (1,2), (6,5)}
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5.
What is the slope of the line whose equation is 3x - 4y - 16 = 0?
1.
2.
3. 3
4. -4
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6.
8.
What are the coordinates of the vertex and the equation of the
axis of symmetry of the parabola shown in the graph below?
Which inequality is represented in the accompanying graph?
1. -3 ≤ x < 4
3. -3 < x < 4
2. -3 ≤ x ≤ 4
4. -3 < x ≤ 4
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9.
Find the turning point and the axis of symmetry for the
1.
2.
3.
4.
(0,2) and y = 2
(0,2) and x = 2
(–2,6) and y = –2
(–2,6) and x = –2
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quadratic equation y = x2 − 4x + 8.
1. (2, 4) and y = 2
2. (2, 4) and x = 2
3. (4, 8) and x = 4
4. (−2, 20) and x = −2
-------------10.
Solve for x:
7.
At a wedding, there are 456 people spread out amongst 45
tables. There are no empty seats. The reception hall has tables
that sit 12 people or 8 people. Write a system of equations that
can be used to find the number of each type of table the
restaurant has.
1. 12
3. 40/3
2. 30
4. 3/40
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11.
Which value of x is in the solution set of the inequality −2(x −
5) < 4?
1.
2.
1. 0
3. 3
2. 2
4. 5
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3.
4.
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12.
14.
Which graph does not represent a function?
Which graph represents a function?
1.
3.
2.
1.
3.
2.
4.
4.
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-------------13.
A student correctly graphed the parabola shown below to
solve a given quadratic equation.
15.
The relation {(1, 10), (0, -2), (6, -5)} is a function. Which of the
ordered pairs below could be added to this relation and it
would still be a function?
1. (1, -2)
3. (-7, -5)
2. (0, 4)
4. (6, -8)
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What are the roots of the quadratic equation associated with
this graph?
1.
2.
3.
4.
−6 and 3
−6 and 0
−3 and 2
−2 and 3
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16.
18.
Debbie solved the linear equation 3(x + 4) − 2 = 16 as follows:
The manufacturer of Ron’s car recommends that the tire
pressure be at least 26 pounds per square inch and less than 35
pounds per square inch. Which graph below best shows the
inequality that represents the recommended tire pressure?
1.
2.
3.
4.
-------------19.
She made an error between lines:
1. 1 and 2
3. 3 and 4
2. 2 and 3
4. 4 and 5
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17.
Write an equation of the line whose slope is 2 and whose yintercept is -3.
1.
2.
3.
4.
y = -3x + 2
y = 2x - 3
2y = -3x
-3y = 2x
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Multiply: (x - 3)(x + 2)
1. x2 - x - 6
2. x2 - x + 6
3. x2 + x - 6
4. 2x - 1
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20.
22.
This year the seniors at South Fayette High School and
Alex earned scores of 60, 74, 82, 87, 87, and 94 on his first six
Chartiers Valley High School planned trips to Kennywood
algebra tests. What is the relationship between the measures of
Park. South Fayette High School rented and completely filled 8 central tendency of these scores?
vans and 5 busses with 240 students. Chartiers Valley High
1. median < mode < mean
School rented and completely filled 4 vans and 7 busses with
2. mean < mode < median
228 students. Write a system of equations that would help you
3. mode < median < mean
find the number of students on a van and a bus.
4. mean < median < mode
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1.
23.
The graph of which inequality is shown in the accompanying
diagram?
2.
3.
4.
-------------21.
If the formula for the perimeter of a rectangle is P = 2l + 2w,
then w can be expressed as
1. y >
x+1
2. y ≥
x+1
3. y <
x+1
4. y ≤
x+1
1.
2.
3.
4.
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24.
26.
The temperature in the pool at Yasmin’s house is 68°. She is
having a swim party tomorrow, so her dad turned on the pool
heater, which heats the water 2° each hour. Which function
describes the temperature of the pool water over time?
Which interval describes the solution set shown in the number
line below?
1.
2.
3.
4.
f(x) = 16x + 68
f(x) = 2x + 68
f(x) = 2 + 68
f(x) = 68
1.
2.
3.
4.
-------------25.
What are the vertex and the axis of symmetry of the parabola
shown in the diagram below?
(2,5)
{x|2 ≤ x ≤ 5}
(2,5]
[2,5]
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27.
If x = 2a - b 2 , then a equals
1.
2.
3.
4. x + b 2
--------------
1.
2.
3.
4.
The vertex is
The vertex is
The vertex is
The vertex is
(-2,-3), and the axis
(-2,-3), and the axis
(-3,-2), and the axis
(-3,-2), and the axis
of symmetry is
of symmetry is
of symmetry is
of symmetry is
x = -2.
y = -2.
y = -2.
x = -2.
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28.
31.
Which is an equation of the line of symmetry for the parabola
in the accompanying diagram?
Solve for x: 8x + 9 = 5x + 6
1. −1
2. 1
3. 5
4. −3 /13
-------------32.
1. x = 2
3. x = 3
2. x = 4
4. y = 3
Alexandra purchases two doughnuts and three cookies at a
doughnut shop and is charged $3.30. Briana purchases five
doughnuts and two cookies at the same shop for $4.95. All the
doughnuts have the same price and all the cookies have the
same price. Find the cost of one doughnut and the cost of one
cookie.
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29.
Which of the following relations is not a function?
1. {(1, 6), (5, 6), (1, -3), (-2, 4)}
2. {(1, 6), (2, 6), (-3, 6), (7, 6)}
3. {(9, 0), (8, -4), (-4, 6), (1, 0)}
4. {(-11, 2), (2, -11)}
-------------30.
The cost of one doughnut is $
The cost of one cookie is $
.
.
-------------33.
A movie theater recorded the number of tickets sold daily for a
popular movie during the month of June. The box-and-whisker
plot shown below represents the data for the number of tickets
sold, in hundreds.
The expression (x2 - 5x - 2) - (-6x2 - 7x - 3) is equivalent to
1. 7x2 - 12x - 5
2. 7x2 - 2x + 1
Which conclusion can be made using this plot?
3. 7x2 + 2x + 1
4. 7x2 + 2x - 5
--------------
1.
2.
3.
4.
The second quartile is 600.
The mean of the attendance is 400.
The range of the attendance is 300 to 600.
Twenty-five percent of the attendance is between 300
and 400.
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34.
37.
Solve for x: 4(2x - 1) = 2x + 35
Solve the following system of equations for x:
1. 3.9
3. 6
2. 6.5
4. 39
2x + y = 4
x − 2y = 7
--------------
1. 2
3. 5
2. 3
4. 7
35.
--------------
Which number is in the solution set of the inequality 5x + 3 >
38?
38.
1. 5
3. 7
What is the solution of 3(2m − 1) ≤ 4m + 7?
2. 6
4. 8
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1. m ≤ 5
3. m ≤ 4
2. m ≥ 5
4. m ≥ 4
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36.
The graph of which inequality is shown in the diagram?
39.
Written in set-builder notation, S = {1, 3, 5, 7, 9} is
1.
2.
3.
4.
{x|1 < x < 9, where x is
{x|1 ≤ x ≤ 9, where x is
{x|1 < x < 9, where x is
{x|1 ≤ x ≤ 9, where x is
a prime number}
a prime number}
an odd integer}
an odd integer}
-------------40.
1. y >
x+1
2. y ≥
x+1
3. y <
x+1
4. y ≤
x+1
Which graph represents the solution set for 2x - 4 ≤ 8 and x + 5
≥ 7?
1.
2.
--------------
3.
4.
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41.
43.
The graph below is represented best by which of the
equations?
The values of 11 houses on Washington St. are shown in the
table below.
1.
2.
3.
Find the mean value of these houses in dollars.
4.
--------------
Answer: $
42.
Find the median value of these houses in dollars.
Solve the following system of equations for x:
Answer: $
4x + y = 11
x+y=2
1. −1
3. 3
State which measure of central tendency, the mean or the
median, best represents the values of these 11 houses.
2. 2
4. 27
Answer:
--------------
-------------44.
Find the sum of 3x2 + 5x - 1 and x2 - 2x - 7.
1. 2x2 - 7x - 6
2. -2x2 - 7x + 6
3. 4x2 - 3x + 8
4. 4x2 + 3x - 8
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45.
48.
The diagram below represents a relation.
Which equation is represented by the graph below?
List the ordered pairs in the relation and tell whether or not the
relation is also a function.
1. {(1, 4), (2, 4), (3, 5)}; the relation is a function
2. {(1, 4), (2, 4), (2, 6), (3, 5)}; the relation is not a function
3. {(1, 4), (2, 4), (2, 6), (3, 5)}; the relation is a function
4. {(1, 4), (2, 4), (3, 5)}; the relation is not a function
-------------46.
1.
2.
3.
4.
The graph below is the graph of what type of function?
2y + x = 10
y – 2x = –5
–2y = 10x – 4
2y = –4x – 10
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49.
Margo describes a set using the set builder notation {x|-11 ≤ x ≤
1}. How could she describe the same set in interval notation?
1. Linear
3. Absolute value
2. Exponential
4. Quadratic
--------------
1. (-11,1)
3. [-11,1]
2. [-11,1)
4. (-11,1]
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47.
Graphically find the roots of the equation y = x2 + 4x − 32.
1.
2.
3.
4.
x = −8, only
x = 8 and −4
x = −8 and 4
x = −8 and −4
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50.
Which coordinate point is in the solution set for the system of inequalities shown in the accompanying graph?
1. (3,1)
3. (1,-1)
2. (2,2)
4. (0,1)
--------------
51.
Charles and Chastity solved a system of equations. Is either of them correct? Explain your reasoning.
-------------52.
Solve the following system of equations for x:
5x + y = 19
2x + y = 1
1. -11
3. 3
2. 6
4. 18
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53.
55.
The expression (x − 4)2 is equivalent to
Two health clubs offer different membership plans. The
accompanying graph represents the total cost of belonging to
Club A and Club B for one year.
1. x2 − 16
2. x2 + 16
3. x2 − 8x + 16
4. x2 + 8x + 16
-------------54.
If x and y are defined as indicated by the accompanying table,
which equation correctly represents the relationship between x
and y?
(a) If the yearly cost includes a membership fee plus a monthly
charge, the membership fee for Club A is $
1. y = x + 2
3. y = 2x + 3
2. y = 2x + 2
4. y = 2x - 3
--------------
.
(b) The number of the month when the total cost is the same for
both clubs is
.
(c) The total cost for Club A when both plans are the same is $
.
(d) The monthly charge for Club B is $
.
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56.
During a Marathon, Bob averaged a rate of 5 mph, Gary averaged a rate of 3 mph, and Carla averaged a rate of 7 mph. Which line
in the following graph represents Bob’s run?
1. Line A
2. Line B
3. Line C
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57.
In order to be admitted for a certain ride at an amusement park, a child must be greater than or equal to 36 inches tall and less
than 48 inches tall. Which graph represents these conditions?
1.
2.
3.
4.
-------------58.
Express as a trinomial: (2x − 3)(x + 7)
1. 2x2 + 11x − 21
2. 2x2 − 11x − 21
3. 2x2 − 11x + 21
4. 2x2 + 11x + 21
-------------59.
Solve the following system of equations algebraically and check:
3x - 5y = -6
2x - 3y = -5
Answer: x =
and y =
--------------
60.
What is the value of x in the equation 4(2x + 1) = 27 + 3(2x − 5)?
1. 21
2. 9
3. 7
4. 4
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