Q. In the context of the passage, which of the following best describes a 'discontinuity'?
A.
A point where a function is not defined.
B.
A point where a function has a vertical tangent.
C.
A point where the function's limit does not exist.
D.
A point where the function is continuous.
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Solution
A discontinuity occurs at points where the function is not defined, leading to breaks in the graph.
Correct Answer: A — A point where a function is not defined.
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Q. In the context of the passage, which of the following statements about exponential functions is true?
A.
They always cross the x-axis.
B.
They have a constant rate of change.
C.
They grow or decay at a rate proportional to their value.
D.
They are linear functions.
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Solution
Exponential functions grow or decay at a rate that is proportional to their current value, which is a defining characteristic.
Correct Answer: C — They grow or decay at a rate proportional to their value.
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Q. In the context of the passage, which of the following statements best summarizes the author's view on inequalities?
A.
Inequalities are a natural part of society.
B.
Inequalities can be eliminated through policy changes.
C.
Inequalities are primarily economic in nature.
D.
Inequalities are often overlooked in discussions of social justice.
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Solution
The author argues that policy changes can address systemic inequalities, suggesting that they are not inevitable.
Correct Answer: B — Inequalities can be eliminated through policy changes.
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Q. In the equation 3x + 4y = 12, what is the value of y when x = 0?
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Solution
Substituting x = 0 gives 4y = 12, thus y = 3.
Correct Answer: C — 4
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Q. In the equation 4x + 5y = 20, what is the value of y when x = 0?
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Solution
Setting x = 0 in the equation gives 5y = 20, leading to y = 4.
Correct Answer: C — 5
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Q. In the equation 5x - 2y = 10, what is the value of y when x = 0?
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Solution
Substituting x = 0 into the equation gives -2y = 10, leading to y = -5.
Correct Answer: B — 5
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Q. In the expansion of (2 + 3x)^5, what is the coefficient of x^2?
A.
90
B.
180
C.
270
D.
360
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Solution
The coefficient of x^2 is given by 5C2 * (3^2) * (2^3) = 10 * 9 * 8 = 720.
Correct Answer: B — 180
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Q. In the expansion of (2x - 3)^6, what is the term containing x^4?
A.
-540x^4
B.
540x^4
C.
-810x^4
D.
810x^4
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Solution
The term containing x^4 is given by 6C4 * (2^4) * (-3)^2 = 15 * 16 * 9 = -2160.
Correct Answer: A — -540x^4
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Q. In the expansion of (2x - 3y)^5, what is the sign of the term containing x^3y^2?
A.
Positive
B.
Negative
C.
Zero
D.
Indeterminate
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Solution
The term containing x^3y^2 will have a negative sign due to the -3y factor raised to an even power.
Correct Answer: B — Negative
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Q. In the expansion of (a + b)^6, which term will contain a^2b^4?
A.
The 3rd term
B.
The 4th term
C.
The 5th term
D.
The 6th term
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Solution
The term containing a^2b^4 corresponds to C(6,2) * a^2 * b^4, which is the 4th term in the expansion.
Correct Answer: B — The 4th term
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Q. In the expansion of (a + b)^n, which of the following represents the general term?
A.
nCk * a^(n-k) * b^k
B.
nCk * a^k * b^(n-k)
C.
nCk * a^(k) * b^(k)
D.
nCk * a^(n+k) * b^(n-k)
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Solution
The general term in the expansion of (a + b)^n is given by nCk * a^(n-k) * b^k.
Correct Answer: A — nCk * a^(n-k) * b^k
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Q. In the expansion of (a - b)^n, how does the sign of the terms alternate?
A.
All terms are positive.
B.
All terms are negative.
C.
The signs alternate starting with positive.
D.
The signs alternate starting with negative.
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Solution
In the expansion of (a - b)^n, the signs alternate starting with negative due to the negative sign in front of b.
Correct Answer: D — The signs alternate starting with negative.
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Q. In the expression 4x^2 + 8x + 4, what is the common factor?
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Solution
The common factor in all terms is 4, so the expression can be factored as 4(x^2 + 2x + 1).
Correct Answer: B — 4
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Q. In the expression 4x^2 - 12x + 9, what is the value of the discriminant?
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Solution
The discriminant is b^2 - 4ac = (-12)^2 - 4(4)(9) = 0.
Correct Answer: A — 0
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Q. In the expression 4x^2 - 12x + 9, what is the vertex of the parabola?
A.
(1.5, -1.5)
B.
(1.5, 0)
C.
(1.5, 1.5)
D.
(3, 0)
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Solution
The vertex can be found using the formula x = -b/(2a), which gives x = 1.5. Substituting back gives the y-coordinate.
Correct Answer: A — (1.5, -1.5)
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Q. In the expression log_a(b) + log_a(c), what can it be simplified to?
A.
log_a(bc)
B.
log_a(b/c)
C.
log_a(b-c)
D.
log_a(b+c)
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Solution
The property of logarithms states that the sum of logarithms with the same base is equal to the logarithm of the product, thus log_a(b) + log_a(c) = log_a(bc).
Correct Answer: A — log_a(bc)
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Q. In the function f(x) = |x|, what is the nature of the graph?
A.
It is a straight line.
B.
It is a parabola.
C.
It is a V-shape.
D.
It is a circle.
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Solution
The graph of f(x) = |x| forms a V-shape, reflecting the absolute value function.
Correct Answer: C — It is a V-shape.
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Q. In the function f(x) = |x|, what is the output when x is negative?
A.
The output is negative.
B.
The output is zero.
C.
The output is positive.
D.
The output is undefined.
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Solution
The absolute value function |x| outputs the positive value of x, regardless of whether x is negative or positive.
Correct Answer: C — The output is positive.
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Q. In the function f(x) = |x|, what is the value of f(-3)?
A.
-3
B.
0
C.
3
D.
Undefined
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Solution
The absolute value function returns the non-negative value of x, so f(-3) = 3.
Correct Answer: C — 3
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Q. In the passage, the author suggests that addressing inequalities requires a multifaceted approach. Which of the following best exemplifies this idea?
A.
Focusing solely on economic reforms.
B.
Combining policy changes with cultural shifts.
C.
Implementing educational programs only.
D.
Ignoring historical contexts.
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Solution
The author advocates for a combination of policy changes and cultural shifts to effectively address inequalities.
Correct Answer: B — Combining policy changes with cultural shifts.
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Q. In the passage, the author suggests that economic inequality is linked to which of the following?
A.
Cultural differences.
B.
Political instability.
C.
Educational disparities.
D.
Technological advancements.
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Solution
The author discusses how educational disparities contribute to economic inequality.
Correct Answer: C — Educational disparities.
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Q. In the passage, the author uses the term 'systemic inequalities' to refer to:
A.
Inequalities that are caused by individual actions.
B.
Inequalities that are embedded in societal structures.
C.
Inequalities that are temporary and can be resolved.
D.
Inequalities that are only economic in nature.
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Solution
The term 'systemic inequalities' indicates that these inequalities are deeply rooted in the structures of society.
Correct Answer: B — Inequalities that are embedded in societal structures.
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Q. In the passage, the phrase 'level the playing field' most likely means:
A.
To create equal opportunities for all.
B.
To eliminate competition.
C.
To increase the stakes in a game.
D.
To ensure fairness in sports.
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Solution
The phrase 'level the playing field' refers to creating equal opportunities for all individuals, particularly in the context of addressing inequalities.
Correct Answer: A — To create equal opportunities for all.
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Q. In the passage, the term 'systemic inequalities' most likely refers to:
A.
Inequalities that are random and unconnected.
B.
Inequalities that are embedded in societal structures.
C.
Inequalities that can be easily resolved.
D.
Inequalities that only affect a small population.
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Solution
The term 'systemic inequalities' indicates that these disparities are deeply rooted in the fabric of society.
Correct Answer: B — Inequalities that are embedded in societal structures.
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Q. In the passage, the term 'systemic inequality' is best understood to mean:
A.
Inequality that arises from individual actions.
B.
Inequality that is embedded in societal structures.
C.
Inequality that is temporary and can be resolved.
D.
Inequality that affects only a small segment of the population.
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Solution
The term 'systemic inequality' refers to inequalities that are deeply rooted in the structures and systems of society.
Correct Answer: B — Inequality that is embedded in societal structures.
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Q. In the polynomial 4x^3 - 2x^2 + x - 5, what is the coefficient of x^2?
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Solution
The coefficient of x^2 in the polynomial 4x^3 - 2x^2 + x - 5 is -2.
Correct Answer: B — -2
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Q. In the polynomial f(x) = 2x^3 - 3x^2 + x - 5, what is the coefficient of x^2?
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Solution
The coefficient of x^2 in the polynomial f(x) = 2x^3 - 3x^2 + x - 5 is -3.
Correct Answer: B — -3
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Q. In the polynomial f(x) = 2x^4 - 3x^3 + x - 5, what is the coefficient of x^3?
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Solution
The coefficient of x^3 in the polynomial f(x) = 2x^4 - 3x^3 + x - 5 is -3.
Correct Answer: A — -3
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Q. In the polynomial h(x) = 4x^3 - 2x^2 + 3, what is the constant term?
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Solution
The constant term in the polynomial h(x) = 4x^3 - 2x^2 + 3 is 3.
Correct Answer: C — 3
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Q. In the polynomial k(x) = 2x^4 - 3x^3 + 0x^2 + 5, what is the term with the highest degree?
A.
2x^4
B.
-3x^3
C.
0x^2
D.
5
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Solution
The term with the highest degree in the polynomial k(x) is 2x^4, as it has the highest exponent.
Correct Answer: A — 2x^4
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