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The graph below best represents which of the following relationships between temperature and time?
A.
Oven temperature while a cake is baking
B.
Temperature of water that is heated on a stove, removed, and then allowed to cool
C.
Temperature of a container of hot tea after placing several cubes of ice in it
D.
Room temperature of a gym after the air conditioner is turned on
Correct Answer B. Temperature of water that is heated on a stove, removed, and then allowed to cool
Explanation The graph best represents the relationship between temperature and time when water is heated on a stove, removed from the heat source, and then allowed to cool. This is because initially, the temperature of the water will increase as it is heated, but once it is removed from the stove, the temperature will start to decrease gradually over time as the water cools down. The graph would show a rise in temperature followed by a decline as time passes.
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2.
Which graph best represents the inequality x + 2y < -14?
A.
Graph F
B.
Graph G
C.
Graph H
D.
Graph J
Correct Answer C. Graph H
Explanation Graph H represents the inequality x + 2y < -14. This is because in Graph H, the shaded region is below the line x + 2y = -14. Any point in this shaded region will satisfy the inequality x + 2y < -14.
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3.
Which equation best describes the relationship between x and y in the given ordered pairs?
(-4, -11), (-1, -2), (2, 7), and (5, 16)
A.
Y = 1/3x + 1
B.
Y = 1/3x - 1
C.
Y = 3x - 1
D.
Y = 3x + 1
Correct Answer D. Y = 3x + 1
Explanation The equation y = 3x + 1 best describes the relationship between x and y in the given ordered pairs. This can be determined by observing that the y-values increase by 3 for every 1 increase in the x-values. Additionally, the y-intercept is 1, which matches the given ordered pair (0, 1).
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4.
Which of the following sets does not represent a function?
Explanation The set {(-1, 2), (1, 1), (1, -1), (2, 1), (4, 2)} does not represent a function because it has multiple values of y for the same value of x. In this set, both (1, 1) and (1, -1) have the same x-value of 1 but different y-values. In a function, each x-value should have only one corresponding y-value.
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5.
A community-service organization is selling $10 tickets to a fund-raiser for the local children's hosiptal. The money raised from ticket sales will be odnated ot hte Children's hospital. Which best describes the dependent quantity in this situation?
A.
The number of tickets sold is dependent on the amount of the donation
B.
The price of each ticket is dependent on the number of tickets sold
C.
The amount of the donation is dependent on the number of tickets sold.
D.
The price of each ticket is dependent on the amount of the donation.
Correct Answer C. The amount of the donation is dependent on the number of tickets sold.
Explanation The amount of the donation is dependent on the number of tickets sold because the more tickets that are sold, the higher the total amount of money raised for the children's hospital.
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6.
The graph below represents which type of parent function?
A.
Exponential
B.
Absolute value
C.
Linear
D.
Qudratic
Correct Answer C. Linear
Explanation The graph represents a straight line, which is characteristic of a linear parent function. Linear functions have a constant rate of change and can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.
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7.
If (-3.5, y) is a solution to the equation 2x - 5y = 10, what is the value of y?
A.
-3.4
B.
13.75
C.
-0.6
D.
-3.75
Correct Answer A. -3.4
Explanation The given equation is 2x - 5y = 10. To find the value of y, we substitute x = -3.5 into the equation. This gives us 2(-3.5) - 5y = 10. Simplifying this equation, we get -7 - 5y = 10. Rearranging the equation, we have -5y = 10 + 7. Combining like terms, we get -5y = 17. Dividing both sides by -5, we find y = -3.4. Therefore, the value of y is -3.4.
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8.
Which expression is equivalent to
(2/3)(3x - 15y) + (9y - 11x)
A.
-9x - y
B.
11x - 21y
C.
10x - 4y
D.
-9x - 26y
Correct Answer A. -9x - y
Explanation The given expression can be simplified by distributing the 2/3 to both terms inside the first parentheses. This results in (2/3)(3x) - (2/3)(15y), which simplifies to 2x - 10y. Then, we can combine like terms by adding (9y - 11x) to 2x - 10y. This gives us 2x - 10y + 9y - 11x, which simplifies to -9x - y.
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9.
Which inequality best represents the domain of the function shown on the graph?
A.
-3
B.
-3 < x < 6
C.
-1 < x < 5
D.
-1
Correct Answer B. -3 < x < 6
Explanation The graph of the function shows that the values of x start at -3 and end at 6, but do not include these values. Therefore, the correct inequality to represent the domain of the function is -3 < x < 6.
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10.
The squares below are arranged in a sequence to show a pattern.
The table below shows the perimeter of each figure formed by the squares in the five patterns stages. Each side of a square represents 1 unit. If this pattern were to continue, which expression could be used to determine the perimeter of the figure at stage n?
A.
N^2 + 7
B.
2(n^2 + 3)
C.
4(n + 1)
D.
-2(n - 1) + 8n
Correct Answer C. 4(n + 1)
Explanation The correct answer is 4(n + 1). In each stage, the figure formed by the squares is a square with side length n+1. The perimeter of a square is calculated by multiplying the side length by 4. Therefore, the expression 4(n + 1) can be used to determine the perimeter of the figure at stage n.
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11.
A small business purchased a van to handle its delivery orders. The graph below shows the value of this van over a period of time. Which of the following best describes this situation?
A.
The van was purchased for $1,600.
B.
The van decreases in value by $1,600 per year.
C.
The van increases in value by $1,600 per year.
D.
The van has no value after 5 years.
Correct Answer B. The van decreases in value by $1,600 per year.
Explanation The graph shows a consistent downward trend, indicating that the value of the van is decreasing over time. The fact that the van was purchased for $1,600 suggests that its initial value was higher, but it has been depreciating at a rate of $1,600 per year. Therefore, the best description for this situation is that the van decreases in value by $1,600 per year.
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12.
What is the rate of change of the graph below?
Question 8. Multiple choice question
Do not grade
Copy Reorder
A.
3.5
B.
1.67
C.
0.6
D.
-1.67
Correct Answer C. 0.6
13.
What is the y-intercept of the function f(x) = 3(x - 2)?
A.
3
B.
1
C.
-2
D.
-6
Correct Answer D. -6
Explanation The y-intercept of a function is the value of y when x is equal to 0. In this case, the function is f(x) = 3(x - 2). To find the y-intercept, we substitute x = 0 into the function: f(0) = 3(0 - 2) = 3(-2) = -6. Therefore, the y-intercept of the function is -6.
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14.
If the slope of the function y = −3.5x + 12.8 is changed to 1.5, which of the following best describes the
graph of the new function?
A.
The graph of the new function intercepts the y-axis at the same point as the original function.
B.
The graph of the new function intercepts the x-axis at the same point as the original function.
C.
The graph of the new function has a negative slope.
D.
The graph of the new function has a positive x-intercept.
Correct Answer A. The graph of the new function intercepts the y-axis at the same point as the original function.
Explanation When the slope of the function y = -3.5x + 12.8 is changed to 1.5, the only change that occurs is in the slope of the line. The y-intercept remains the same at 12.8. Therefore, the graph of the new function will still intercept the y-axis at the same point as the original function.
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15.
If y varies directly with x and y is 14 when x is 6, which of the following represents this situation?
A.
Y = 20x
B.
Y = (7/3)x
C.
Y = 8x
D.
Y = (3/7)x
Correct Answer B. Y = (7/3)x
Explanation In this situation, y varies directly with x, meaning that as x increases, y also increases proportionally. The equation y = (7/3)x represents this relationship because it shows that y is equal to 7/3 times x. This means that for every increase of 1 in x, y will increase by 7/3. Given that y is 14 when x is 6, plugging these values into the equation y = (7/3)x will give us 14 = (7/3)(6), which is true. Therefore, y = (7/3)x represents the given situation.
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16.
A school district held a meeting for all its physical education teachers. The number of women attending was 5 more than twice the number of men attending. A total of 53 teachers attended the meeting. Which system of equations could be used to find w, the number of women, and m, the number of men, at this meeting?
A.
M = 2x + 5
w + m = 53
B.
2w + m = 5
w + m = 53
C.
W = m + 5
w + m = 53
D.
W = 2m + 5
w + m = 53
Correct Answer D. W = 2m + 5
w + m = 53
Explanation The correct answer is w = 2m + 5 and w + m = 53. This system of equations can be used to find the number of women and men at the meeting. The equation w = 2m + 5 represents the number of women attending the meeting, which is 5 more than twice the number of men attending. The equation w + m = 53 represents the total number of teachers attending the meeting, which is 53. By solving these equations simultaneously, we can determine the values of w and m.
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17.
Victor purchased motor oil for $2 a bottle and car wax for $4 a bottle. The inequality 2x + 4y < 16 can be used to determine the number of bottles of motor oil, x, and the number of bottles of car wax, y, Victor purchased for less thatn $16, not including tax. Which of the following ordered pairs best prepresents a reasonable combination of bottles of motor oil and car wax that Victor could have purchased?
A.
(4, 2)
B.
(2, 3)
C.
(5, 2)
D.
(3, 2)
Correct Answer D. (3, 2)
Explanation The inequality 2x + 4y < 16 represents the total cost of the motor oil and car wax purchased by Victor, which should be less than $16. In order to find a reasonable combination of bottles of motor oil and car wax, we need to substitute the values of x and y from the given ordered pairs and check if the inequality holds true.
For the ordered pair (4, 2), the total cost would be 2(4) + 4(2) = 20, which is greater than 16.
For the ordered pair (2, 3), the total cost would be 2(2) + 4(3) = 16, which is equal to 16.
For the ordered pair (5, 2), the total cost would be 2(5) + 4(2) = 18, which is greater than 16.
For the ordered pair (3, 2), the total cost would be 2(3) + 4(2) = 14, which is less than 16.
Therefore, the ordered pair (3, 2) represents a reasonable combination of bottles of motor oil and car wax that Victor could have purchased.
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18.
An oyster provides approximately 17 calories and a shrimp provides approsimately 26 calories. Jay wants to consume no more than 300 calories eating oysters and shrimp. Which inequality best represents the number of oysters, x, and the number of shrimp, y, that Jay can eat and stay within this limit?
A.
(17 + 26)(x + y) > 300
B.
(17 + x) + (26 + y) > 300
C.
(17 + 26)(x + y)
D.
17x + 26y
Correct Answer D. 17x + 26y
Explanation The inequality that best represents the number of oysters, x, and the number of shrimp, y, that Jay can eat and stay within the limit of 300 calories is 17x + 26y. This is because the total number of calories consumed from oysters (17x) and shrimp (26y) should be less than or equal to 300 in order for Jay to stay within the limit.
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19.
The graph of a system of linear equations is shown below.
Which of the following is the solution to this sytem of linear equations?
A.
(0, 4)
B.
(8, 1)
C.
(0, -3)
D.
10, 2)
Correct Answer D. 10, 2)
Explanation The solution to a system of linear equations is the point where the lines representing the equations intersect. In this case, the point (10, 2) is the only one that lies on both lines. Therefore, it is the solution to the system of linear equations.
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20.
The Future Teachers of America club sold cookies for $0.25 each and cupcakes for $0.50 each to raise money to attend the state convention. if the club raised $24.75 from selling cookies and cupcakes during lunchtime, which of the following is a reasonable combination of the number of cupcakes and cookes that were sold?
A.
24 cookies and 51 cupcakes
B.
50 cookies and 25 cupcakes
C.
51 cookies and 24 cupcakes
D.
35 cookies and 30 cupcakes
Correct Answer C. 51 cookies and 24 cupcakes
Explanation The combination of 51 cookies and 24 cupcakes is a reasonable choice because it would result in a total revenue of $24.75. Since each cookie is sold for $0.25 and each cupcake is sold for $0.50, the revenue from selling 51 cookies would be $12.75 (51 * $0.25 = $12.75) and the revenue from selling 24 cupcakes would be $12.00 (24 * $0.50 = $12.00). Therefore, the total revenue would be $12.75 + $12.00 = $24.75.
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21.
What are the roots and vertex of the graph shown below?
A.
(-4, 0), (2, 0), and (-1, -9)
B.
(0, -4), (2, 0), and (0, -8)
C.
(0, -4), (2, 0), and (-1, -9)
D.
(-1, 9), (0, -8)
Correct Answer A. (-4, 0), (2, 0), and (-1, -9)
22.
The graph below shows the height of a baseball from the time it is thrown from the top of a building to the time it hits the ground. How much time elapses while the baseball is 80 meters or more above the ground?
A.
1 second
B.
9 seconds
C.
7 seconds
D.
6 seconds
Correct Answer D. 6 seconds
Explanation The graph shows that the baseball is at a height of 80 meters or more above the ground for a total of 6 seconds.
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23.
The graph of the function is shown below. If the graph of the original function is shifted 5 units up, which of the following equations best represents the resulting graph?
A.
Y=x^2+5
B.
Y=x^2+2
C.
Y=x^2-2
D.
Y=x^2-8
Correct Answer B. Y=x^2+2
Explanation The graph of the original function is a parabola that opens upwards. Shifting the graph 5 units up means that the y-coordinate of every point on the graph is increased by 5. Therefore, the equation that represents the resulting graph is y = x^2 + 5. The given answer, y = x^2 + 2, is incorrect because it represents a shift of 2 units up, not 5 units up.
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24.
Which of the following expressions is equivalent to ?
(answer A)
(answer B)
(answer C)
(answer D)
A.
Answer A
B.
Answer B
C.
Answer C
D.
Answer D
Correct Answer D. Answer D
25.
What is the effect on the graph of the equation when the equation is changed to ?
A.
The graph of y=-4x^2 opens downward and is wider than the graph of y = 1/2x^2
B.
The graph of y = -4x^2 opens upward and is wider than the graph of y=1/2x^2
C.
The graph of y = -4x^2 opens upward and is narrower than the graph of y=1/2x^2
D.
The graph of y=-4x^2 opens downward and is narrower than the graph of y=1/2x^2
Correct Answer D. The graph of y=-4x^2 opens downward and is narrower than the graph of y=1/2x^2
Explanation The given answer states that the graph of y = -4x^2 opens downward, which means it is a concave down parabola. It also states that the graph is narrower than the graph of y = 1/2x^2, indicating that the coefficient -4 causes the graph to be more compressed horizontally compared to the graph with a coefficient of 1/2.
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