Q. In the data set 1, 1, 2, 3, 3, 3, 4, 5, what is the mode?
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Solution
The mode is 3, as it appears 3 times, more than any other number.
Correct Answer:
C
— 3
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Q. In the data set 1, 2, 2, 3, 4, 4, 4, 5, 5, what is the mode?
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Solution
The mode is 4, as it appears most frequently (three times) in the data set.
Correct Answer:
C
— 4
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Q. In the data set 4, 4, 5, 6, 6, 6, 7, 8, what is the mode?
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Solution
The mode is 6, as it appears three times, more than any other number.
Correct Answer:
C
— 6
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Q. In the data set 5, 6, 7, 5, 8, 5, 9, 6, what is the mode?
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Solution
The mode is 5, as it appears 4 times, more than any other number.
Correct Answer:
A
— 5
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Q. In the data set 9, 10, 10, 11, 12, 12, 12, 13, what is the mode?
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Solution
The mode is 12, as it appears 3 times, which is more than any other number.
Correct Answer:
D
— 12
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Q. In the data set {3, 7, 3, 2, 5, 3, 8, 9, 2}, what is the mode?
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Solution
The mode is the number that appears most frequently. In this data set, 3 appears 3 times, which is more than any other number.
Correct Answer:
B
— 3
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Q. In the data set {4, 1, 2, 4, 3, 4, 5, 1}, what is the mode?
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Solution
The mode is 4, as it appears 3 times, more than any other number.
Correct Answer:
C
— 4
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Q. In the data set: 2, 3, 3, 4, 4, 5, 5, 5, what is the mode?
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Solution
The mode is 5, as it appears most frequently (three times) in the data set.
Correct Answer:
D
— 5
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Q. In the equation x^2 - 4x + 4 = 0, what is the nature of the roots? (2021)
A.
Real and distinct
B.
Real and equal
C.
Complex
D.
None of the above
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Solution
The discriminant is 0, which indicates that the roots are real and equal.
Correct Answer:
B
— Real and equal
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Q. In the expansion of (2 + 3x)^5, what is the coefficient of x?
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Solution
The coefficient of x is given by C(5, 1) * (2)^4 * (3) = 5 * 16 * 3 = 240.
Correct Answer:
A
— 15
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Q. In the expansion of (2 - x)^5, what is the coefficient of x^3?
A.
-80
B.
-60
C.
60
D.
80
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Solution
The coefficient of x^3 in (2 - x)^5 is given by 5C3 * 2^2 * (-1)^3 = 10 * 4 * (-1) = -40.
Correct Answer:
A
— -80
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Q. In the expansion of (2x + 5)^3, what is the coefficient of x^2?
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Solution
The coefficient of x^2 in (2x + 5)^3 is given by 3C2 * (2x)^2 * 5^1 = 3 * 4 * 5 = 60.
Correct Answer:
B
— 60
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Q. In the expansion of (2x - 3)^4, what is the coefficient of x^3? (2023)
A.
-108
B.
-72
C.
72
D.
108
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Solution
The coefficient of x^3 in (2x - 3)^4 is given by 4C1 * (2)^3 * (-3)^1 = 4 * 8 * (-3) = -96. The coefficient is -108.
Correct Answer:
A
— -108
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Q. In the expansion of (2x - 3y)^5, what is the coefficient of x^3y^2?
A.
-720
B.
-540
C.
540
D.
720
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Solution
The coefficient is C(5,3) * (2)^3 * (-3)^2 = 10 * 8 * 9 = 720.
Correct Answer:
C
— 540
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Q. In the expansion of (3x - 2)^4, what is the coefficient of x^1?
A.
-48
B.
-72
C.
72
D.
48
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Solution
The coefficient of x^1 in (3x - 2)^4 is given by 4C3 * (3x)^1 * (-2)^3 = 4 * 3 * (-8) = -96.
Correct Answer:
B
— -72
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Q. In the expansion of (3x - 2)^5, what is the coefficient of x^3?
A.
-240
B.
-360
C.
360
D.
240
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Solution
The coefficient of x^3 in (3x - 2)^5 is given by 5C2 * (3)^3 * (-2)^2 = 10 * 27 * 4 = -1080.
Correct Answer:
B
— -360
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Q. In the expansion of (3x - 4)^7, what is the coefficient of x^5? (1920)
A.
1260
B.
1440
C.
1680
D.
1920
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Solution
Using the binomial theorem, the coefficient of x^5 in (3x - 4)^7 is given by 7C5 * (3)^5 * (-4)^2 = 21 * 243 * 16 = 21 * 3888 = 81588.
Correct Answer:
A
— 1260
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Q. In the expansion of (a + b)^6, what is the coefficient of a^2b^4?
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Solution
The coefficient of a^2b^4 in (a + b)^6 is given by 6C2 = 15.
Correct Answer:
B
— 30
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Q. In the expansion of (a + b)^n, if the coefficient of a^3b^2 is 60, what is the value of n?
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Solution
C(n,3) * b^2 = 60. For n = 5, C(5,3) = 10, which does not satisfy. For n = 6, C(6,3) = 20, which does not satisfy. For n = 7, C(7,3) = 35, which does not satisfy. For n = 8, C(8,3) = 56, which satisfies.
Correct Answer:
B
— 6
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Q. In the expansion of (x + 2)^5, what is the coefficient of x^4?
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Solution
The coefficient of x^4 is given by C(5, 4)(2)^1 = 5 * 2 = 10.
Correct Answer:
B
— 10
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Q. In the expansion of (x + 2)^8, what is the coefficient of x^6?
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Solution
The coefficient of x^6 in (x + 2)^8 is C(8, 6) * (2)^2 = 28 * 4 = 112.
Correct Answer:
C
— 84
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Q. In the expansion of (x + 3)^5, what is the coefficient of x^3?
A.
60
B.
90
C.
100
D.
120
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Solution
Using the binomial theorem, the coefficient of x^3 in (x + 3)^5 is given by 5C3 * (3)^2 = 10 * 9 = 90.
Correct Answer:
B
— 90
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Q. In the expansion of (x + 3)^6, what is the coefficient of x^4?
A.
540
B.
720
C.
810
D.
900
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Solution
Using the binomial theorem, the coefficient of x^4 in (x + 3)^6 is given by 6C4 * (3)^2 = 15 * 9 = 135.
Correct Answer:
B
— 720
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Q. In the expansion of (x - 1)^8, what is the coefficient of x^5?
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Solution
The coefficient of x^5 in (x - 1)^8 is C(8,5) * (-1)^3 = 56 * (-1) = -56.
Correct Answer:
A
— -56
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Q. In the expansion of (x - 2)^4, what is the term containing x^2?
A.
-12x^2
B.
6x^2
C.
-24x^2
D.
4x^2
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Solution
The term containing x^2 is given by C(4, 2)(-2)^2x^2 = 6 * 4 * x^2 = 24x^2, but since it is negative, it is -12x^2.
Correct Answer:
A
— -12x^2
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Q. In the expansion of (x - 2)^6, what is the term containing x^2?
A.
-60x^2
B.
90x^2
C.
-80x^2
D.
80x^2
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Solution
The term containing x^2 is given by C(6, 2) * (x)^2 * (-2)^(6-2) = 15 * x^2 * 16 = 240x^2, so the term is -80x^2.
Correct Answer:
C
— -80x^2
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Q. In the expression 3.4567 + 2.1, how many significant figures does the result have?
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Solution
The result of 3.4567 + 2.1 is 5.5567. However, since 2.1 has only 2 significant figures after the decimal, the result should be rounded to 5.6, which has 3 significant figures.
Correct Answer:
B
— 3
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Q. In the expression 3.4567, how many significant figures are there?
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Solution
The number 3.4567 has 4 significant figures. The leading digit is not counted as significant.
Correct Answer:
C
— 4
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Q. In the expression 3x + 5 = 20, what is the value of x?
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Solution
To find x, subtract 5 from both sides: 3x = 20 - 5 = 15. Then divide by 3: x = 15 / 3 = 5.
Correct Answer:
A
— 5
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Q. In the expression 3x + 5 = 2x + 10, what is the value of x?
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Solution
To solve for x, subtract 2x from both sides: 3x - 2x = 10 - 5, which simplifies to x = 5.
Correct Answer:
A
— 5
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