Q. Which of the following represents the factored form of x^2 - 9?
-
A.
(x - 3)(x + 3)
-
B.
(x - 9)(x + 1)
-
C.
(x + 3)(x + 3)
-
D.
(x - 3)(x - 3)
Solution
x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. Which of the following represents the slope of the line in the equation y = 3x + 2?
Solution
In the slope-intercept form y = mx + b, m represents the slope. Here, m = 3.
Correct Answer:
B
— 3
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Q. Which of the following represents the slope of the line represented by the equation y = mx + b?
Solution
In the equation y = mx + b, 'm' represents the slope of the line.
Correct Answer:
A
— m
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Q. Which of the following sequences cannot be a harmonic progression?
-
A.
1, 1/2, 1/3
-
B.
2, 4, 8
-
C.
3, 1, 1/3
-
D.
5, 10, 15
Solution
The sequence 2, 4, 8 does not have reciprocals that form an arithmetic progression, hence it cannot be a harmonic progression.
Correct Answer:
B
— 2, 4, 8
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Q. Which of the following sequences is a geometric progression?
-
A.
1, 2, 4, 8
-
B.
1, 3, 6, 10
-
C.
2, 4, 8, 16
-
D.
1, 1, 1, 1
Solution
The sequence 2, 4, 8, 16 has a constant ratio of 2, making it a geometric progression.
Correct Answer:
C
— 2, 4, 8, 16
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Q. Which of the following sequences is a harmonic progression?
-
A.
1, 2, 3
-
B.
1, 1/2, 1/3
-
C.
2, 4, 6
-
D.
3, 6, 9
Solution
The sequence 1, 1/2, 1/3 has reciprocals 1, 2, 3 which are in arithmetic progression, thus it is a harmonic progression.
Correct Answer:
B
— 1, 1/2, 1/3
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Q. Which of the following sequences is an arithmetic progression?
-
A.
2, 4, 8, 16
-
B.
1, 3, 5, 7
-
C.
5, 10, 15, 25
-
D.
3, 6, 9, 12
Solution
An arithmetic progression has a constant difference between consecutive terms. The sequence 1, 3, 5, 7 has a common difference of 2.
Correct Answer:
B
— 1, 3, 5, 7
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Q. Which of the following statements about a geometric progression is true?
-
A.
The ratio of consecutive terms is constant.
-
B.
The difference between consecutive terms is constant.
-
C.
The sum of the terms is always positive.
-
D.
The first term is always the largest.
Solution
In a geometric progression, the ratio of consecutive terms is indeed constant, which defines the progression.
Correct Answer:
A
— The ratio of consecutive terms is constant.
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Q. Which of the following statements about an arithmetic progression is true?
-
A.
The sum of any two terms is always even.
-
B.
The difference between any two consecutive terms is constant.
-
C.
The product of any two terms is constant.
-
D.
The terms are always positive.
Solution
In an arithmetic progression, the difference between any two consecutive terms is indeed constant, which defines the sequence.
Correct Answer:
B
— The difference between any two consecutive terms is constant.
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Q. Which of the following statements about exponents is false?
-
A.
a^m * a^n = a^(m+n)
-
B.
a^m / a^n = a^(m-n)
-
C.
a^0 = 0
-
D.
a^(-n) = 1/a^n
Solution
The statement a^0 = 0 is false; in fact, a^0 = 1 for any non-zero a.
Correct Answer:
C
— a^0 = 0
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Q. Which of the following statements about exponents is incorrect?
-
A.
a^(m+n) = a^m * a^n
-
B.
a^(m-n) = a^m / a^n
-
C.
a^m * b^m = (ab)^m
-
D.
a^m + a^n = a^(m+n)
Solution
The statement a^m + a^n = a^(m+n) is incorrect; addition of exponents does not apply in this manner.
Correct Answer:
D
— a^m + a^n = a^(m+n)
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Q. Which of the following statements about geometric progressions is true?
-
A.
The ratio of consecutive terms is constant.
-
B.
The sum of terms is always positive.
-
C.
The first term must be greater than the second.
-
D.
The common ratio can only be an integer.
Solution
In a geometric progression, the ratio of consecutive terms is indeed constant, which defines the progression.
Correct Answer:
A
— The ratio of consecutive terms is constant.
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Q. Which of the following statements about harmonic progression is false?
-
A.
The sum of the terms is finite
-
B.
The terms can be negative
-
C.
The terms can be zero
-
D.
The terms can be fractions
Solution
In a harmonic progression, terms cannot be zero as it would make the reciprocal undefined.
Correct Answer:
C
— The terms can be zero
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Q. Which of the following statements about harmonic progression is true?
-
A.
The sum of the terms is always positive.
-
B.
The terms can be negative.
-
C.
The terms are always integers.
-
D.
The common difference is always positive.
Solution
In a harmonic progression, the terms can be negative as long as their reciprocals form an arithmetic progression.
Correct Answer:
B
— The terms can be negative.
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Q. Which of the following statements about negative exponents is correct?
-
A.
They indicate a reciprocal of the base raised to the positive exponent.
-
B.
They always result in a negative number.
-
C.
They can only be applied to integers.
-
D.
They are not applicable in real number systems.
Solution
Negative exponents indicate the reciprocal of the base raised to the positive exponent.
Correct Answer:
A
— They indicate a reciprocal of the base raised to the positive exponent.
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Q. Which of the following statements about the graph of a function is true if it is continuous everywhere?
-
A.
It has no breaks or holes.
-
B.
It must be a polynomial function.
-
C.
It can only be a linear function.
-
D.
It must have at least one x-intercept.
Solution
A continuous function has no breaks or holes in its graph.
Correct Answer:
A
— It has no breaks or holes.
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Q. Which of the following statements about the graph of a quadratic function is true?
-
A.
It is always a parabola that opens upwards.
-
B.
It can be a straight line.
-
C.
It can intersect the x-axis at three points.
-
D.
It is symmetric about its vertex.
Solution
The graph of a quadratic function is symmetric about its vertex.
Correct Answer:
D
— It is symmetric about its vertex.
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Q. Which of the following statements about the inverse of a function is true?
-
A.
The inverse of a function is always a function.
-
B.
The inverse of a function is symmetric to the original function about the line y = x.
-
C.
The inverse can only exist for polynomial functions.
-
D.
The inverse of a function is always linear.
Solution
The inverse of a function is symmetric to the original function about the line y = x, provided the original function is one-to-one.
Correct Answer:
B
— The inverse of a function is symmetric to the original function about the line y = x.
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Q. Which of the following statements aligns with the author's argument regarding systemic inequalities? (2023)
-
A.
Systemic inequalities are easily resolved.
-
B.
Systemic inequalities require collective action.
-
C.
Systemic inequalities are a myth.
-
D.
Systemic inequalities benefit everyone.
Solution
The author argues that systemic inequalities require collective action to address effectively.
Correct Answer:
B
— Systemic inequalities require collective action.
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Q. Which of the following statements can be logically inferred from the passage?
-
A.
All inequalities are economic.
-
B.
Inequalities can be addressed through collective action.
-
C.
Inequalities are a recent phenomenon.
-
D.
Inequalities affect only certain demographics.
Solution
The passage suggests that collective action is necessary to address inequalities, indicating that they can be tackled through collaborative efforts.
Correct Answer:
B
— Inequalities can be addressed through collective action.
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Q. Which of the following statements is most aligned with the author's argument regarding wealth distribution?
-
A.
Wealth distribution is a personal responsibility.
-
B.
Wealth distribution should be equal for all.
-
C.
Wealth distribution is influenced by systemic factors.
-
D.
Wealth distribution does not affect social mobility.
Solution
The passage discusses how systemic factors influence wealth distribution, aligning with this statement.
Correct Answer:
C
— Wealth distribution is influenced by systemic factors.
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Q. Which of the following statements is true about the equation 4x - 5y = 20?
-
A.
It represents a vertical line.
-
B.
It has a positive slope.
-
C.
It has no x-intercept.
-
D.
It is a horizontal line.
Solution
Rearranging the equation to slope-intercept form gives y = (4/5)x - 4, indicating a positive slope.
Correct Answer:
B
— It has a positive slope.
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Q. Which of the following statements is true about the graph of a function that is periodic?
-
A.
It repeats its values at regular intervals.
-
B.
It is always increasing.
-
C.
It has no maximum or minimum values.
-
D.
It is a straight line.
Solution
A periodic function is characterized by repeating values at regular intervals, such as sine and cosine functions.
Correct Answer:
A
— It repeats its values at regular intervals.
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Q. Which of the following statements is true about the inverse of a function?
-
A.
The inverse of a function is always a function.
-
B.
The inverse of a function is not necessarily a function.
-
C.
The inverse of a function is always linear.
-
D.
The inverse of a function cannot be graphed.
Solution
The inverse of a function is a function only if the original function is one-to-one.
Correct Answer:
B
— The inverse of a function is not necessarily a function.
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Q. Which of the following statements is true about the linear equation 4x - 5y = 20?
-
A.
It has no solutions.
-
B.
It has infinitely many solutions.
-
C.
It has exactly one solution.
-
D.
It is a quadratic equation.
Solution
A linear equation in two variables has exactly one solution unless it is a special case (like parallel lines). Here, it is a standard linear equation.
Correct Answer:
C
— It has exactly one solution.
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Q. Which of the following statements is true about the roots of a polynomial function?
-
A.
A polynomial can have at most as many roots as its degree.
-
B.
All roots of a polynomial are real numbers.
-
C.
A polynomial of degree n has exactly n distinct roots.
-
D.
Roots of a polynomial cannot be complex.
Solution
A polynomial function can have at most as many roots as its degree, but not all roots need to be real.
Correct Answer:
A
— A polynomial can have at most as many roots as its degree.
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Q. Which of the following statements is true regarding an arithmetic progression?
-
A.
The sum of any two terms is constant.
-
B.
The difference between consecutive terms is constant.
-
C.
The product of any two terms is constant.
-
D.
The ratio of any two terms is constant.
Solution
In an arithmetic progression, the difference between consecutive terms is constant, which is the defining property of an AP.
Correct Answer:
B
— The difference between consecutive terms is constant.
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Q. Which of the following statements is true regarding harmonic progression?
-
A.
The sum of the terms is always positive.
-
B.
The terms can be negative.
-
C.
The terms are always integers.
-
D.
The common difference is constant.
Solution
In a harmonic progression, the terms can indeed be negative, as the definition does not restrict the terms to positive values.
Correct Answer:
B
— The terms can be negative.
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Q. Which of the following statements is true regarding harmonic progressions?
-
A.
The sum of the terms is always constant.
-
B.
The product of the terms is always constant.
-
C.
The reciprocals of the terms form an arithmetic progression.
-
D.
The terms are always integers.
Solution
In a harmonic progression, the reciprocals of the terms indeed form an arithmetic progression.
Correct Answer:
C
— The reciprocals of the terms form an arithmetic progression.
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Q. Which of the following statements is true regarding the composition of functions?
-
A.
The composition of two functions is always a function.
-
B.
The composition of two functions is never a function.
-
C.
The composition of two functions can be a function or not, depending on the functions involved.
-
D.
The composition of two functions is always linear.
Solution
The composition of two functions can result in a function or not, depending on the nature of the original functions.
Correct Answer:
C
— The composition of two functions can be a function or not, depending on the functions involved.
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