Q. What can be inferred about the roots of a cubic function based on its graph?
-
A.
It can have at most two real roots.
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B.
It can have at most three real roots.
-
C.
It can have no real roots.
-
D.
It must have at least one real root.
Solution
A cubic function must have at least one real root due to the Intermediate Value Theorem, as it is a continuous function.
Correct Answer:
D
— It must have at least one real root.
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Q. What can be inferred about the roots of a polynomial function if its graph touches the x-axis at a point?
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A.
The root is a simple root.
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B.
The root is a double root.
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C.
The root is a complex root.
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D.
The root does not exist.
Solution
If a polynomial function touches the x-axis at a point, it indicates that the root at that point is a double root.
Correct Answer:
B
— The root is a double root.
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Q. What can be inferred about the roots of a quadratic function if its graph does not intersect the x-axis?
-
A.
It has two real roots.
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B.
It has one real root.
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C.
It has no real roots.
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D.
It has complex roots only.
Solution
If the graph of a quadratic function does not intersect the x-axis, it indicates that the function has no real roots.
Correct Answer:
C
— It has no real roots.
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Q. What conclusion can be drawn about the author's perspective on individual responsibility in relation to inequalities?
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A.
Individuals have no role in addressing inequalities.
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B.
Individual actions can contribute to systemic change.
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C.
Only collective action can address inequalities.
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D.
Individual responsibility is secondary to government action.
Solution
The author suggests that individual actions can play a significant role in contributing to systemic change regarding inequalities.
Correct Answer:
B
— Individual actions can contribute to systemic change.
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Q. What does the author imply about the future of inequalities if current trends continue?
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A.
Inequalities will likely decrease.
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B.
Inequalities will remain unchanged.
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C.
Inequalities will worsen.
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D.
Inequalities will be resolved through technology.
Solution
The author suggests that without intervention, inequalities are likely to worsen, highlighting the urgency of the issue.
Correct Answer:
C
— Inequalities will worsen.
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Q. What does the author imply about the relationship between privilege and inequality?
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A.
Privilege has no relation to inequality.
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B.
Privilege can shield individuals from the effects of inequality.
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C.
Inequality is a form of privilege.
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D.
All individuals experience privilege equally.
Solution
The author implies that privilege can protect individuals from the impacts of inequality.
Correct Answer:
B
— Privilege can shield individuals from the effects of inequality.
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Q. What does the author imply about the relationship between wealth and access to opportunities?
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A.
Wealth has no impact on access to opportunities.
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B.
Wealth directly correlates with increased access to opportunities.
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C.
Access to opportunities is solely determined by merit.
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D.
Wealth can hinder access to opportunities.
Solution
The author implies that wealth significantly enhances access to various opportunities, perpetuating inequalities.
Correct Answer:
B
— Wealth directly correlates with increased access to opportunities.
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Q. What does the author imply about the role of education in mitigating inequalities? (2023)
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A.
Education alone can solve all inequality issues.
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B.
Education is a critical but insufficient component.
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C.
Education exacerbates existing inequalities.
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D.
Education has no significant impact on social mobility.
Solution
The author implies that while education is essential, it must be part of a broader strategy to effectively reduce inequalities.
Correct Answer:
B
— Education is a critical but insufficient component.
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Q. What does the author suggest about the perception of inequalities in public discourse?
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A.
Inequalities are often exaggerated.
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B.
Inequalities are frequently ignored.
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C.
Inequalities are well understood by the public.
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D.
Inequalities are only a recent concern.
Solution
The author suggests that inequalities are often overlooked in public discussions, indicating a lack of awareness.
Correct Answer:
B
— Inequalities are frequently ignored.
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Q. What does the author suggest as a necessary step for policymakers in addressing social inequalities? (2023)
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A.
To focus solely on economic growth.
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B.
To engage with affected communities.
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C.
To ignore public opinion.
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D.
To prioritize short-term solutions.
Solution
The author advocates for policymakers to engage with communities affected by social inequalities to create effective and relevant solutions.
Correct Answer:
B
— To engage with affected communities.
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Q. What does the author suggest as a potential solution to combat inequalities?
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A.
Increased funding for education.
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B.
Stricter laws against discrimination.
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C.
Community engagement and dialogue.
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D.
All of the above.
Solution
The author suggests that a combination of solutions, including education and community engagement, is necessary.
Correct Answer:
D
— All of the above.
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Q. What does the author suggest as a potential solution to combat social inequalities?
-
A.
Increased funding for education.
-
B.
Stricter laws against discrimination.
-
C.
Community engagement and activism.
-
D.
All of the above.
Solution
The author proposes a multifaceted approach, including education, legal reforms, and community involvement.
Correct Answer:
D
— All of the above.
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Q. What does the author suggest is necessary for meaningful change regarding inequalities?
-
A.
Increased awareness and education.
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B.
A return to traditional values.
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C.
Strict enforcement of laws.
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D.
Isolation of affected communities.
Solution
The author emphasizes the importance of awareness and education as foundational steps towards meaningful change in addressing inequalities.
Correct Answer:
A
— Increased awareness and education.
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Q. What does the passage imply about the importance of understanding graphs in mathematics?
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A.
Graphs are irrelevant to understanding functions.
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B.
Graphs provide a visual representation of functions and their behaviors.
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C.
Graphs can only represent linear functions.
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D.
Graphs are only useful for statistics.
Solution
Understanding graphs is crucial as they visually represent functions and help in analyzing their behaviors.
Correct Answer:
B
— Graphs provide a visual representation of functions and their behaviors.
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Q. What does the term 'asymptote' refer to in the context of graphing functions?
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A.
A point where the function intersects the x-axis.
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B.
A line that the graph approaches but never touches.
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C.
A maximum point on the graph.
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D.
A minimum point on the graph.
Solution
An asymptote is a line that a graph approaches as it heads towards infinity, but does not actually touch.
Correct Answer:
B
— A line that the graph approaches but never touches.
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Q. What does the term 'asymptote' refer to in the context of the passage?
-
A.
A line that a graph approaches but never touches.
-
B.
A point where the function is undefined.
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C.
A maximum or minimum point of the function.
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D.
A point of inflection on the graph.
Solution
An asymptote is a line that a graph approaches as it heads towards infinity, but the graph never actually touches it.
Correct Answer:
A
— A line that a graph approaches but never touches.
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Q. What does the term 'domain' of a function refer to?
-
A.
The set of all possible input values.
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B.
The set of all possible output values.
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C.
The maximum value of the function.
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D.
The slope of the function.
Solution
The domain of a function is the complete set of possible values of the independent variable (input).
Correct Answer:
A
— The set of all possible input values.
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Q. What does the term 'domain' refer to in the context of a function?
-
A.
The set of all possible output values.
-
B.
The set of all possible input values.
-
C.
The maximum value of the function.
-
D.
The minimum value of the function.
Solution
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
Correct Answer:
B
— The set of all possible input values.
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Q. What does the term 'slope' in a linear equation represent?
-
A.
The steepness of the line.
-
B.
The y-intercept of the line.
-
C.
The x-intercept of the line.
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D.
The distance from the origin.
Solution
The slope indicates how steep the line is, representing the rate of change of y with respect to x.
Correct Answer:
A
— The steepness of the line.
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Q. What does the term 'slope' refer to in the context of linear equations?
-
A.
The steepness of the line.
-
B.
The y-intercept of the line.
-
C.
The x-intercept of the line.
-
D.
The distance from the origin.
Solution
The slope of a line indicates its steepness and direction.
Correct Answer:
A
— The steepness of the line.
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Q. What does the vertex of a parabola represent in the context of a quadratic function?
-
A.
The maximum or minimum point of the function.
-
B.
The x-intercept of the function.
-
C.
The y-intercept of the function.
-
D.
The point where the function is undefined.
Solution
The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction it opens.
Correct Answer:
A
— The maximum or minimum point of the function.
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Q. What is the 15th term of an arithmetic progression where the first term is 7 and the common difference is 2? (2023)
Solution
Using the formula for the nth term, the 15th term = 7 + (15-1) * 2 = 7 + 28 = 35.
Correct Answer:
C
— 31
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Q. What is the 4th term of the arithmetic progression where the first term is 10 and the common difference is 5?
Solution
The nth term is given by a + (n-1)d. Here, a = 10, d = 5, and n = 4. So, the 4th term = 10 + (4-1) * 5 = 10 + 15 = 25.
Correct Answer:
A
— 25
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Q. What is the author's perspective on the future of social inequalities?
-
A.
They will inevitably persist.
-
B.
They can be significantly reduced.
-
C.
They are improving on their own.
-
D.
They are a result of individual choices.
Solution
The author expresses a belief that social inequalities can be significantly reduced through concerted efforts.
Correct Answer:
B
— They can be significantly reduced.
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Q. What is the author's stance on the effectiveness of current measures to combat inequalities?
-
A.
Current measures are sufficient and effective.
-
B.
Current measures are inadequate and need improvement.
-
C.
Current measures are irrelevant to the issue.
-
D.
Current measures are only effective in urban areas.
Solution
The author critiques current measures as being insufficient, advocating for more comprehensive solutions.
Correct Answer:
B
— Current measures are inadequate and need improvement.
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Q. What is the author's stance on the relationship between race and social inequalities?
-
A.
Race is a minor factor in social inequalities.
-
B.
Race is a significant factor in perpetuating inequalities.
-
C.
Race and social inequalities are unrelated.
-
D.
Race is the only factor that matters.
Solution
The author highlights race as a significant factor contributing to social inequalities throughout the passage.
Correct Answer:
B
— Race is a significant factor in perpetuating inequalities.
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Q. What is the author's stance on the role of government in addressing inequalities?
-
A.
Governments should take a hands-off approach.
-
B.
Governments have a responsibility to intervene.
-
C.
Governments are the main cause of inequalities.
-
D.
Governments should focus on economic growth only.
Solution
The passage indicates that the author believes governments should actively intervene to address inequalities.
Correct Answer:
B
— Governments have a responsibility to intervene.
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Q. What is the base of the logarithm if log_10(100) = 2?
Solution
The base of the logarithm is 10, as log_10(100) = 2 means 10^2 = 100.
Correct Answer:
B
— 10
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Q. What is the base of the logarithm if log_2(8) = 3?
Solution
Since 8 is 2 raised to the power of 3 (2^3 = 8), the base of the logarithm is 2.
Correct Answer:
A
— 2
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Q. What is the base of the logarithm if log_3(81) = 4?
Solution
Since 81 is 3^4, the base of the logarithm is 3.
Correct Answer:
A
— 3
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