Q. In the equation y = mx + b, what does 'm' represent?
A.
The y-intercept
B.
The slope of the line
C.
The x-intercept
D.
The constant term
Show solution
Solution
'm' represents the slope of the line, indicating how steep the line is.
Correct Answer:
B
— The slope of the line
Learn More →
Q. In the expansion of (1 + x)^n, what is the term containing x^4?
A.
C(n, 4)x^4
B.
C(n, 3)x^4
C.
C(n, 5)x^4
D.
C(n, 2)x^4
Show solution
Solution
The term containing x^4 in the expansion of (1 + x)^n is C(n, 4)x^4.
Correct Answer:
A
— C(n, 4)x^4
Learn More →
Q. In the expansion of (2 + 3x)^5, what is the coefficient of x^2?
A.
90
B.
180
C.
270
D.
360
Show solution
Solution
The coefficient of x^2 is given by 5C2 * (3^2) * (2^3) = 10 * 9 * 8 = 720.
Correct Answer:
B
— 180
Learn More →
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
Show solution
Solution
The term containing x^4 is given by 6C4 * (2^4) * (-3)^2 = 15 * 16 * 9 = -2160.
Correct Answer:
A
— -540x^4
Learn More →
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
Show solution
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
Learn More →
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
Show solution
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
Learn More →
Q. In the expansion of (a + b)^n, if the coefficient of a^2b^3 is 10, what is the value of n?
Show solution
Solution
The coefficient of a^2b^3 in (a + b)^n is given by C(n, 3). Setting C(n, 3) = 10 gives n = 6.
Correct Answer:
B
— 6
Learn More →
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)
Show solution
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
Learn More →
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.
Show solution
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.
Learn More →
Q. In the expression 4x^2 + 8x + 4, what is the common factor?
Show solution
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
Learn More →
Q. In the expression 4x^2 - 12x + 9, what is the value of the discriminant?
Show solution
Solution
The discriminant is b^2 - 4ac = (-12)^2 - 4(4)(9) = 0.
Correct Answer:
A
— 0
Learn More →
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)
Show solution
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)
Learn More →
Q. In the expression 5x^2 - 3x + 2, which term is the constant?
A.
5x^2
B.
-3x
C.
2
D.
None of the above
Show solution
Solution
The constant term is the one without a variable, which is 2.
Correct Answer:
C
— 2
Learn More →
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)
Show solution
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)
Learn More →
Q. In the function f(x) = x^2 - 4, what are the x-intercepts?
A.
2 and -2
B.
4 and -4
C.
0 and 4
D.
None
Show solution
Solution
To find the x-intercepts, set f(x) = 0: x^2 - 4 = 0, which factors to (x - 2)(x + 2) = 0, giving x-intercepts at 2 and -2.
Correct Answer:
A
— 2 and -2
Learn More →
Q. In the function f(x) = |x - 2|, what is the value of f(2)?
A.
0
B.
1
C.
2
D.
Undefined
Show solution
Solution
Substituting x = 2 gives f(2) = |2 - 2| = |0| = 0.
Correct Answer:
A
— 0
Learn More →
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.
Show solution
Solution
The graph of f(x) = |x| forms a V-shape, reflecting the absolute value function.
Correct Answer:
C
— It is a V-shape.
Learn More →
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.
Show solution
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.
Learn More →
Q. In the function f(x) = |x|, what is the value of f(-3)?
A.
-3
B.
0
C.
3
D.
Undefined
Show solution
Solution
The absolute value function returns the non-negative value of x, so f(-3) = 3.
Correct Answer:
C
— 3
Learn More →
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.
Show solution
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.
Learn More →
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.
Show solution
Solution
The author discusses how educational disparities contribute to economic inequality.
Correct Answer:
C
— Educational disparities.
Learn More →
Q. In the passage, the author uses the term 'social mobility' to refer to: (2023)
A.
The ability of individuals to move between social classes.
B.
The increase in wealth among the upper class.
C.
The decline of traditional social structures.
D.
The stability of social hierarchies.
Show solution
Solution
The term 'social mobility' is defined in the passage as the capacity for individuals to change their social class status.
Correct Answer:
A
— The ability of individuals to move between social classes.
Learn More →
Q. In the passage, the author uses the term 'systemic barriers' to refer to what? (2023)
A.
Obstacles that are easily overcome.
B.
Challenges that are inherent in social structures.
C.
Temporary issues faced by individuals.
D.
Personal choices that lead to inequality.
Show solution
Solution
The term 'systemic barriers' refers to deep-rooted challenges within social structures that perpetuate inequality.
Correct Answer:
B
— Challenges that are inherent in social structures.
Learn More →
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.
Show solution
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.
Learn More →
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.
Show solution
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.
Learn More →
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.
Show solution
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.
Learn More →
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.
Show solution
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.
Learn More →
Q. In the polynomial 2x^3 + 3x^2 - x + 5, which term has the highest degree?
A.
2x^3
B.
3x^2
C.
-x
D.
5
Show solution
Solution
The term with the highest degree is 2x^3, as it has the highest exponent of x.
Correct Answer:
A
— 2x^3
Learn More →
Q. In the polynomial 4x^3 - 2x^2 + x - 5, what is the coefficient of x^2?
Show solution
Solution
The coefficient of x^2 in the polynomial 4x^3 - 2x^2 + x - 5 is -2.
Correct Answer:
B
— -2
Learn More →
Q. In the polynomial 5x^4 - 3x^3 + 2x^2 - x + 7, what is the coefficient of the x^2 term?
Show solution
Solution
The coefficient of the x^2 term in the polynomial is 2.
Correct Answer:
C
— 2
Learn More →
Showing 1651 to 1680 of 2503 (84 Pages)
