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A new comedian is building a fan base. The table shows the number of people who attended his shows in the first, second, third and fourth months of his career. Which graph could represent the data shown in the table?
A.
B.
C.
D.
Correct Answer D.
2.
A hiker climbs up a steep bank and then rests for a minute. He then walks up a small hill and finally across a flat plateau. What sketch of a graph could represent the elevation of the hiker?
A.
B.
C.
Any of the graphs could represent the situation, depending on the hiker's speed.
Correct Answer A.
3.
In the diagram below, what is the relationship between the number of triangles and the perimeter of the figure they form?
Which of the following represents the above relationship?
A.
The perimeter, P, is equal to the length of the base of one triangle muliplies by the number of triangles in the figure, n, plus the length of another side. The equation of the perimeter is P=4n+7.
B.
The perimeter, P, is equal to the length of the base of one triangle multiplied by the number of triangles in the figure, n, plus two times the length of another side. The equation for the perimeter is P=4n+14.
C.
The perimeter, P, is equal to the length of the sideof one triangle multiplied by the number of triangles in the figure, n, plus the length of the base. The equation for the perimeter is P=7n+4.
D.
The perimeter, P, is equal to the length of the sideof one triangle multiplied by the number of triangles in the figure, n, plus two times the length of the base. The equation for the perimeter is P=7n+8.
Correct Answer B. The perimeter, P, is equal to the length of the base of one triangle multiplied by the number of triangles in the figure, n, plus two times the length of another side. The equation for the perimeter is P=4n+14.
Explanation The correct answer is "The perimeter, P, is equal to the length of the base of one triangle multiplied by the number of triangles in the figure, n, plus two times the length of another side. The equation for the perimeter is P=4n+14." This is because the equation correctly represents the relationship between the number of triangles and the perimeter of the figure. The equation states that the perimeter is equal to the length of the base of one triangle multiplied by the number of triangles, n, plus two times the length of another side. This accurately describes how the perimeter is determined based on the number of triangles in the figure.
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4.
The table shows the relationship between the number of sports teams a person belongs to and the amount of free time the person has per week.
Is the above relationship a linear function?
A.
Yes
B.
No
Correct Answer A. Yes
Explanation The relationship between the number of sports teams a person belongs to and the amount of free time they have per week is a linear function. This means that as the number of sports teams increases, the amount of free time decreases or vice versa, and the relationship can be represented by a straight line on a graph.
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5.
What is the graph for the above relationship?
A.
B.
C.
D.
Correct Answer A.
6.
The ordered pairs (1, 36), (2, 49), (3, 64), (4, 81), and (5, 100) represent a function. What is a rule that represents this function?
A.
B.
C.
D.
Correct Answer D.
Explanation The rule that represents this function is y = x^2. This can be determined by observing that the second element in each ordered pair is the square of the first element.
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7.
What is the graph of the function rule?
A.
B.
C.
D.
Correct Answer B.
8.
Write a function rule for the situation. Is the graph continuous or discrete?
A movie store sells DVDs for $14 each. What is the cost, C, of n DVDs?
A.
C=14+n ; continuous
B.
C=14n ; discrete
C.
C=14+n ; discrete
D.
C=14n ; continuous
Correct Answer B. C=14n ; discrete
Explanation The function rule for the situation is C=14n, where C represents the cost of n DVDs. This means that the cost of the DVDs is directly proportional to the number of DVDs purchased. The graph of this function would be discrete because the number of DVDs purchased can only be a whole number, resulting in discrete points on the graph.
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9.
What is the graph of each function rule?
A.
B.
C.
D.
Correct Answer D.
10.
What is the graph of each function rule?
A.
B.
C.
D.
Correct Answer D.
11.
A snail travels at a rate of 2.15 feet per minute.
Write a rule to describe the function
How far will the snail travel in 6 minutes?
A.
B.
C.
D.
Correct Answer C.
Explanation The snail will travel 12.9 feet in 6 minutes. This can be calculated by multiplying the rate of 2.15 feet per minute by the time of 6 minutes.
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12.
A tomato plant in Steve's gardeb was 11 centimeters tall when it was first planted. Since then, it has grown approximately 0.7 centimeters per day.
Write a rule to describe the function.
After how many days will the tomato plant be 18.7 centimeters tall?
A.
B.
C.
D.
Correct Answer C.
Explanation The rule to describe the function is that the tomato plant grows approximately 0.7 centimeters per day. To find out after how many days the tomato plant will be 18.7 centimeters tall, we can subtract the initial height of 11 centimeters from the target height of 18.7 centimeters. Then, we divide this difference by the growth rate of 0.7 centimeters per day. This gives us the number of days it will take for the tomato plant to reach 18.7 centimeters tall, which is approximately 12 days.
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13.
Identify the mapping diagram that represents the relation and determine wheter the relation is a function.
A.
B.
C.
D.
Correct Answer D.
14.
The function j(x)=27x represents the number of jumping jacks j(x) you can do in x minutes. How many jumping jacks can you do in 15 minutes?
A.
142
B.
405
C.
1
D.
212
Correct Answer B. 405
Explanation The given function states that the number of jumping jacks you can do in x minutes is equal to 27 times x. To find out how many jumping jacks can be done in 15 minutes, we substitute x with 15 in the function. Therefore, j(15) = 27 * 15 = 405. So, the correct answer is 405.
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15.
You have 8 cups of flour. It takes 1 cup to make 24 cookies. The function c(f)=24f represents the number of cookies, c, that can be made with f cups of flour. What domain and range are reasonable for the function? What is the graph of the function?
A.
B.
C.
D.
Correct Answer D.
Explanation The domain of the function represents the possible input values, which in this case is the number of cups of flour. Since we have 8 cups of flour, a reasonable domain would be any non-negative number less than or equal to 8. Therefore, the domain is [0, 8].
The range of the function represents the possible output values, which in this case is the number of cookies. Since it takes 1 cup of flour to make 24 cookies, a reasonable range would be any non-negative multiple of 24. Therefore, the range is [0, infinity).
The graph of the function would be a straight line with a positive slope, passing through the origin (0,0) and extending indefinitely in the positive y-direction.
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16.
Describe the pattern in each sequence. What are the next two terms of each sequence?
7, 9, 11, 13, ...
A.
Subtract 2 from the previous term: 11, 9
B.
Multiply the previous term by 2: 26, 52
C.
Add 2 to the previous term: 15, 17
D.
Multiply the previous term by 2: 15, 52
Correct Answer C. Add 2 to the previous term: 15, 17
17.
Describe the pattern in each sequence. What are the next two terms of each sequence?
1, 2, 4, 8, ...
A.
Add 1 to the previous term: 7, 6
B.
Multiply the previous term by 2: 16, 32
C.
Subtract 1 from the previous term: 16, 32
D.
Multiply the previous term by -2: -16, 32
Correct Answer B. Multiply the previous term by 2: 16, 32
Explanation The pattern in the given sequence is that each term is obtained by multiplying the previous term by 2. Therefore, to find the next two terms, we multiply the previous term (8) by 2. This gives us 16 as the next term, and multiplying 16 by 2 gives us 32 as the term after that.
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18.
Tell whether the sequence is arithmetic. If it is, what is the common difference?
4, 9, 15, 22, ...
A.
Yes; 6
B.
Yes; 4
C.
Yes; 5
D.
No
Correct Answer D. No
Explanation The sequence is not arithmetic because there is no consistent difference between consecutive terms. The difference between the first two terms is 5, the difference between the second and third terms is 6, and the difference between the third and fourth terms is 7. Since the differences are not the same, the sequence is not arithmetic.
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19.
Tell whether the sequence is arithmetic. If it is, what is the common difference?
-10, -10.5, -11, -11.5, ...
A.
Yes; 1.1
B.
Yes; -0.5
C.
Yes; -20.5
D.
No
Correct Answer B. Yes; -0.5
Explanation The given sequence is arithmetic because there is a common difference between each term. The common difference is -0.5, as each term is obtained by subtracting 0.5 from the previous term.
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20.
Suppose your buisness has a special checking account used just for paying the phone bill. The balance is $740.00 this month. Next month the balance will be $707.60, after that it will be $675.20, and on the third month the balance will be $642.80. Write a rule to represent the balance in the account as an arithmetic sequence. How many months can you pay your phone bill without depositing any more money in the account?
A.
B.
C.
D.
Correct Answer B.
Explanation The rule to represent the balance in the account as an arithmetic sequence is: each month, the balance decreases by $32.40. To find out how many months you can pay your phone bill without depositing any more money, you need to divide the initial balance of $740.00 by the decrease amount of $32.40. This gives you approximately 22.84 months. Since you cannot have a fraction of a month, you can pay your phone bill for 22 months without depositing any more money.
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21.
An employee recieves a weekly salary of $280 and 3% commission on all sales.
The function rule f(d) that gives weekly earnings in terms of d dollars in sales is:
f(d)=280+0.03d
a) Find the emplyee's earnings for a week with $600 total sales.
b) What are the employee's total sales for a week which her earnings were $670.
A.
A) $298 b)$13000
B.
A) $298 b) $300.10
C.
A) $10666.67 b) $13000
D.
A) $10666.67 b) $300.01
Correct Answer A. A) $298 b)$13000
Explanation For part a), to find the employee's earnings for a week with $600 total sales, we can substitute d = 600 into the function rule f(d) = 280 + 0.03d. So, f(600) = 280 + 0.03(600) = $298.
For part b), to find the employee's total sales for a week when her earnings were $670, we need to solve the equation 670 = 280 + 0.03d for d. Subtracting 280 from both sides gives 390 = 0.03d. Dividing both sides by 0.03 gives d = 13000.
Therefore, the employee's earnings for a week with $600 total sales is $298, and her total sales for a week when her earnings were $670 is $13000.
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22.
Identify the domain and range of the relation.
A.
Domain: -9,-4,1,3 range: -10,3,5,14
B.
Domain: -9,3,5 range: -10,-4,1,14
C.
Domain: -10,3,5,14 range: -9,-4,1,3
D.
Domain: -10,-4,1,14 range: -9,3,5
Correct Answer B. Domain: -9,3,5 range: -10,-4,1,14
Explanation The given correct answer states that the domain of the relation is -9, 3, and 5, while the range is -10, -4, 1, and 14. This means that the relation consists of the values -9, 3, and 5 as inputs, and the values -10, -4, 1, and 14 as outputs.
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23.
Is the relation a function?
A.
Yes, it is a function
B.
No, it is not a function
Correct Answer B. No, it is not a function
Explanation The given answer states that the relation is not a function. This means that there exists at least one element in the domain that is associated with more than one element in the range. In a function, each element in the domain should be associated with only one element in the range. Therefore, if the given relation violates this condition, it is not a function.
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24.
Is the relation a function? (Use the vertical line test)
A.
Yes, it is a function
B.
No, it is not a function
Correct Answer B. No, it is not a function
Explanation The relation is not a function because it fails the vertical line test. This means that there exists at least one vertical line that intersects the graph of the relation at more than one point. In a function, each input (x-value) should correspond to only one output (y-value), but in this case, there are multiple y-values for at least one x-value, violating the definition of a function.
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25.
Find the range of
for the domain {-1, 0, 4, 6}.
A.
{-5, -3, -9}
B.
{1, 0, -4, -6}
C.
{-1, 0, 4, 6}
D.
{-1, -3, -11, -15}
Correct Answer D. {-1, -3, -11, -15}
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