Q. What is the base of the logarithm if log_b(1) = 0?
A.
Any positive number
B.
1
C.
0
D.
Undefined
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Solution
For any base b > 0, log_b(1) = 0, since b^0 = 1.
Correct Answer:
A
— Any positive number
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Q. What is the effect of a vertical stretch on the graph of a function?
A.
It compresses the graph towards the x-axis.
B.
It stretches the graph away from the x-axis.
C.
It shifts the graph to the left.
D.
It shifts the graph to the right.
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Solution
A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, causing the graph to stretch away from the x-axis.
Correct Answer:
B
— It stretches the graph away from the x-axis.
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Q. What is the effect of multiplying a function by a negative constant on its graph?
A.
It reflects the graph across the x-axis.
B.
It reflects the graph across the y-axis.
C.
It shifts the graph to the left.
D.
It stretches the graph vertically.
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Solution
Multiplying a function by a negative constant reflects the graph across the x-axis.
Correct Answer:
A
— It reflects the graph across the x-axis.
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Q. What is the geometric interpretation of the solution to a system of linear equations?
A.
The area enclosed by the lines
B.
The point of intersection of the lines
C.
The distance between the lines
D.
The angle between the lines
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Solution
The solution represents the point where the lines intersect, if they do.
Correct Answer:
B
— The point of intersection of the lines
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Q. What is the geometric interpretation of the solution to a system of linear equations in two variables?
A.
The point where the two lines intersect.
B.
The area enclosed by the lines.
C.
The distance between the lines.
D.
The slope of the lines.
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Solution
The solution to a system of linear equations in two variables is represented by the point where the two lines intersect.
Correct Answer:
A
— The point where the two lines intersect.
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Q. What is the geometric interpretation of the solution to a system of two linear equations?
A.
The area between the lines.
B.
The point of intersection of the lines.
C.
The distance between the lines.
D.
The slope of the lines.
Show solution
Solution
The solution to a system of two linear equations is represented by the point where the two lines intersect.
Correct Answer:
B
— The point of intersection of the lines.
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Q. What is the geometric representation of the equation 3x - 4y = 12?
A.
A point
B.
A line
C.
A plane
D.
A curve
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Solution
Linear equations represent straight lines in a two-dimensional space.
Correct Answer:
B
— A line
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Q. What is the geometric representation of the equation 5x + 2y = 10?
A.
A point
B.
A line
C.
A plane
D.
A curve
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Solution
The equation represents a straight line in a two-dimensional space.
Correct Answer:
B
— A line
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Q. What is the geometric representation of the equation x + 2y = 4?
A.
A point
B.
A line
C.
A plane
D.
A curve
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Solution
The equation x + 2y = 4 represents a straight line in a two-dimensional space.
Correct Answer:
B
— A line
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Q. What is the implication of the author's argument regarding education and inequality?
A.
Education is the sole solution to inequality.
B.
Improving education alone will not suffice to reduce inequality.
C.
Education exacerbates inequality.
D.
Inequality has no relation to education.
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Solution
The author implies that while education is important, it must be accompanied by other measures to effectively reduce inequality.
Correct Answer:
B
— Improving education alone will not suffice to reduce inequality.
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Q. What is the leading coefficient of the polynomial 7x^4 - 3x^3 + 2x - 1?
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Solution
The leading coefficient is the coefficient of the term with the highest degree, which is 7 in this case.
Correct Answer:
A
— 7
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Q. What is the leading coefficient of the polynomial 7x^5 - 2x^3 + 4x - 1?
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Solution
The leading coefficient of a polynomial is the coefficient of the term with the highest degree, which is 7 in this case.
Correct Answer:
A
— 7
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Q. What is the leading coefficient of the polynomial p(x) = -5x^4 + 3x^2 - 2?
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Solution
The leading coefficient of a polynomial is the coefficient of the term with the highest degree, which in this case is -5.
Correct Answer:
A
— -5
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Q. What is the primary argument made by the author regarding economic inequalities?
A.
They are the most significant type of inequality.
B.
They can be addressed through education.
C.
They are often ignored in policy discussions.
D.
They are a result of individual choices.
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Solution
The author emphasizes that economic inequalities are a critical issue that deserves attention in policy discussions.
Correct Answer:
A
— They are the most significant type of inequality.
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Q. What is the primary purpose of logarithms in mathematics?
A.
To simplify multiplication and division
B.
To solve quadratic equations
C.
To calculate derivatives
D.
To find the area of geometric shapes
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Solution
Logarithms are primarily used to simplify multiplication and division into addition and subtraction, making calculations easier.
Correct Answer:
A
— To simplify multiplication and division
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Q. What is the primary purpose of the author's discussion on economic policies in relation to social inequalities? (2023)
A.
To argue that economic policies are ineffective.
B.
To illustrate how economic policies can mitigate social inequalities.
C.
To suggest that economic policies should be ignored.
D.
To claim that social inequalities are unrelated to economic factors.
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Solution
The author discusses economic policies to demonstrate their potential role in reducing social inequalities, advocating for their reform.
Correct Answer:
B
— To illustrate how economic policies can mitigate social inequalities.
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Q. What is the primary purpose of the author's discussion on historical inequalities? (2023)
A.
To highlight the inevitability of social disparities.
B.
To illustrate how past injustices shape current inequalities.
C.
To argue that historical context is irrelevant to current issues.
D.
To suggest that historical inequalities have been completely resolved.
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Solution
The author discusses historical inequalities to show their lasting impact on present-day social structures.
Correct Answer:
B
— To illustrate how past injustices shape current inequalities.
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Q. What is the primary purpose of the examples provided in the passage?
A.
To illustrate the complexity of inequalities.
B.
To distract from the main argument.
C.
To provide historical context.
D.
To suggest solutions to inequalities.
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Solution
The examples serve to illustrate the multifaceted nature of inequalities, reinforcing the author's argument.
Correct Answer:
A
— To illustrate the complexity of inequalities.
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Q. What is the product of the roots of the polynomial P(x) = x^2 - 7x + 10?
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Solution
The product of the roots of a quadratic polynomial ax^2 + bx + c is given by c/a, which is 10/1 = 10.
Correct Answer:
A
— 10
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Q. What is the product of the roots of the quadratic equation 2x² + 3x - 5 = 0?
A.
-2.5
B.
2.5
C.
-1.5
D.
1.5
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Solution
The product of the roots is given by c/a. Here, -5/2 = -2.5.
Correct Answer:
A
— -2.5
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Q. What is the relationship between the first term and the common ratio if the sum of an infinite GP converges?
A.
The first term must be zero.
B.
The common ratio must be less than one in absolute value.
C.
The first term must be greater than the common ratio.
D.
The common ratio must be greater than one.
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Solution
For the sum of an infinite GP to converge, the common ratio must be less than one in absolute value.
Correct Answer:
B
— The common ratio must be less than one in absolute value.
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Q. What is the relationship between the harmonic mean and the terms of a harmonic progression?
A.
It is the average of the terms.
B.
It is the reciprocal of the arithmetic mean of the reciprocals.
C.
It is the sum of the terms.
D.
It is the product of the terms.
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Solution
The harmonic mean of a set of numbers is the reciprocal of the arithmetic mean of their reciprocals.
Correct Answer:
B
— It is the reciprocal of the arithmetic mean of the reciprocals.
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Q. What is the relationship between the terms of a harmonic progression and their reciprocals?
A.
They are in geometric progression.
B.
They are in arithmetic progression.
C.
They are in quadratic progression.
D.
They are in exponential progression.
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Solution
The terms of a harmonic progression are the reciprocals of the terms of an arithmetic progression.
Correct Answer:
B
— They are in arithmetic progression.
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Q. What is the result of (2^3)^2?
A.
2^5
B.
2^6
C.
2^7
D.
2^8
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Solution
Using the power of a power property, (a^m)^n = a^(m*n), we have (2^3)^2 = 2^(3*2) = 2^6.
Correct Answer:
B
— 2^6
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Q. What is the result of 5^2 * 5^(-3)? (2023)
A.
5^1
B.
5^(-1)
C.
5^0
D.
5^(-5)
Show solution
Solution
Using the property of exponents, we combine the exponents: 5^(2 + (-3)) = 5^(-1).
Correct Answer:
B
— 5^(-1)
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Q. What is the result of adding the polynomials (2x^2 + 3x + 4) and (3x^2 - x + 2)?
A.
5x^2 + 2x + 6
B.
5x^2 + 4x + 6
C.
5x^2 + 3x + 6
D.
5x^2 + 3x + 4
Show solution
Solution
When adding the polynomials, combine like terms: (2x^2 + 3x + 4) + (3x^2 - x + 2) = 5x^2 + 2x + 6.
Correct Answer:
B
— 5x^2 + 4x + 6
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Q. What is the result of adding the polynomials (2x^2 + 3x - 4) and (x^2 - 5x + 6)?
A.
3x^2 - 2x + 2
B.
3x^2 - 2x - 2
C.
x^2 - 2x + 2
D.
3x^2 + 2x + 2
Show solution
Solution
When adding the polynomials, combine like terms: (2x^2 + x^2) + (3x - 5x) + (-4 + 6) = 3x^2 - 2x + 2.
Correct Answer:
A
— 3x^2 - 2x + 2
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Q. What is the result of adding the polynomials (3x^2 + 2x + 1) and (4x^2 - x + 5)?
A.
7x^2 + x + 6
B.
7x^2 + 3x + 6
C.
x^2 + x + 6
D.
7x^2 + 2x + 5
Show solution
Solution
Adding the two polynomials gives (3x^2 + 4x^2) + (2x - x) + (1 + 5) = 7x^2 + x + 6.
Correct Answer:
B
— 7x^2 + 3x + 6
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Q. What is the result of adding the polynomials (3x^2 + 2x - 1) and (4x^2 - 3x + 5)?
A.
7x^2 - x + 4
B.
7x^2 - x - 6
C.
x^2 - x + 4
D.
x^2 + 5
Show solution
Solution
Adding the two polynomials gives (3x^2 + 4x^2) + (2x - 3x) + (-1 + 5) = 7x^2 - x + 4.
Correct Answer:
A
— 7x^2 - x + 4
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Q. What is the result of adding the polynomials 2x^2 + 3x + 4 and 4x^2 - x + 1?
A.
6x^2 + 2x + 5
B.
6x^2 + 4x + 5
C.
2x^2 + 4x + 5
D.
8x^2 + 2x + 5
Show solution
Solution
Adding the coefficients of like terms gives 6x^2 + 2x + 5.
Correct Answer:
B
— 6x^2 + 4x + 5
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