Q. What is the maximum slope of the function f(x) = -x^2 + 4x?
Solution
f'(x) = -2x + 4. Setting f'(x) = 0 gives x = 2. The maximum slope occurs at x = 2, f'(2) = 2.
Correct Answer: A — 4
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Q. What is the maximum value of f(x) = -x^2 + 4x?
Solution
The vertex form gives the maximum at x = -b/(2a) = 4/2 = 2, f(2) = -2^2 + 4*2 = 4.
Correct Answer: A — 4
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Q. What is the maximum value of the function f(x) = -x^2 + 4x + 1?
Solution
The vertex occurs at x = -b/(2a) = 4/(-2) = 2. f(2) = -2^2 + 4*2 + 1 = 6.
Correct Answer: B — 6
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Q. What is the maximum value of the quadratic function f(x) = -x^2 + 4x + 1?
Solution
The vertex form gives the maximum value at x = 2, f(2) = 5.
Correct Answer: A — 5
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Q. What is the maximum value of the quadratic function f(x) = -x^2 + 6x - 8?
Solution
The vertex form gives the maximum value at x = 3, f(3) = -3^2 + 6*3 - 8 = 4.
Correct Answer: C — 4
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Q. What is the mean of the data set: 2, 4, 6, 8, 10?
Solution
Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.
Correct Answer: C — 6
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Q. What is the mean of the data set: 5, 10, 15, 20, 25?
Solution
Mean = (5 + 10 + 15 + 20 + 25) / 5 = 75 / 5 = 15.
Correct Answer: B — 15
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Q. What is the mean of the first five prime numbers?
Solution
Mean = (2 + 3 + 5 + 7 + 11) / 5 = 28 / 5 = 5.6.
Correct Answer: B — 6
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Q. What is the mean of the following data set: 2, 4, 6, 8, 10?
Solution
Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.
Correct Answer: C — 6
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Q. What is the mean of the following data set: 5, 10, 15, 20, 25?
Solution
Mean = (5 + 10 + 15 + 20 + 25) / 5 = 75 / 5 = 15
Correct Answer: B — 15
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Q. What is the mean of the following data: 2, 4, 6, 8, 10?
Solution
Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.
Correct Answer: B — 6
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Q. What is the mean of the following numbers: 1, 1, 1, 1, 1?
Solution
Mean = (1 + 1 + 1 + 1 + 1) / 5 = 5 / 5 = 1.
Correct Answer: A — 1
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Q. What is the mean of the following numbers: 2, 4, 6, 8, 10, 12?
Solution
Mean = (2 + 4 + 6 + 8 + 10 + 12) / 6 = 42 / 6 = 7.
Correct Answer: C — 8
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Q. What is the mean of the following numbers: 2, 4, 6, 8, 10?
Solution
Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.
Correct Answer: B — 6
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Q. What is the mean of the following numbers: 4, 8, 12, 16, 20?
Solution
Mean = (4 + 8 + 12 + 16 + 20) / 5 = 60 / 5 = 12.
Correct Answer: B — 12
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Q. What is the mean of the following numbers: 4, 8, 12, 16?
Solution
Mean = (4 + 8 + 12 + 16) / 4 = 40 / 4 = 10.
Correct Answer: B — 10
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Q. What is the median of the data set {7, 3, 5, 9, 1}?
Solution
First, arrange the data: {1, 3, 5, 7, 9}. The median is the middle value, which is 5.
Correct Answer: A — 5
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Q. What is the median of the following data set: 1, 3, 3, 6, 7, 8, 9?
Solution
Median = 6 (middle value of the ordered set).
Correct Answer: B — 6
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Q. What is the median of the following data set: 3, 1, 4, 2, 5?
Solution
Sorted data: 1, 2, 3, 4, 5. Median = 3 (middle value).
Correct Answer: B — 3
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Q. What is the median of the following data set: 3, 5, 7, 9, 11, 13, 15?
Solution
Median = 9 (middle value).
Correct Answer: C — 9
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Q. What is the median of the following numbers: 1, 3, 3, 6, 7, 8, 9?
Solution
Median = 6 (middle value of the ordered set).
Correct Answer: B — 6
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Q. What is the median of the following numbers: 12, 15, 14, 10, 18?
Solution
Arranging the numbers: 10, 12, 14, 15, 18. Median = 14.
Correct Answer: B — 14
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Q. What is the median of the following numbers: 3, 1, 4, 2, 5?
Solution
Arranging in order: 1, 2, 3, 4, 5. Median = 3.
Correct Answer: B — 3
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Q. What is the median of the following numbers: 3, 7, 8, 12, 14?
Solution
Median = 8 (middle value in ordered list).
Correct Answer: B — 8
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Q. What is the median of the following numbers: 7, 9, 12, 15, 18, 20?
Solution
Median = (12 + 15) / 2 = 27 / 2 = 13.5.
Correct Answer: A — 12
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Q. What is the middle term in the expansion of (x + 2)^8?
-
A.
128
-
B.
112
-
C.
256
-
D.
64
Solution
The middle term is T(5) = C(8,4) * (2)^4 = 70 * 16 = 1120.
Correct Answer: A — 128
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Q. What is the midpoint of the line segment joining the points (1, 2) and (3, 4)?
-
A.
(2, 3)
-
B.
(1, 2)
-
C.
(3, 4)
-
D.
(4, 6)
Solution
Midpoint = ((1+3)/2, (2+4)/2) = (2, 3).
Correct Answer: A — (2, 3)
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Q. What is the midpoint of the line segment joining the points (2, 3) and (4, 7)?
-
A.
(3, 5)
-
B.
(2, 5)
-
C.
(4, 3)
-
D.
(5, 7)
Solution
Midpoint = ((2+4)/2, (3+7)/2) = (3, 5).
Correct Answer: A — (3, 5)
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Q. What is the minimum value of the function f(x) = 2x^2 - 8x + 10?
Solution
The vertex form gives the minimum at x = 2. f(2) = 2(2^2) - 8(2) + 10 = 6.
Correct Answer: B — 4
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Q. What is the minimum value of the function f(x) = x^2 - 4x + 5?
Solution
The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4(2) + 5 = 1.
Correct Answer: A — 1
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