Q. Which of the following can be inferred about the author's perspective on education and inequality?
A.
Education is the sole solution to inequality.
B.
Access to quality education can reduce inequality.
C.
Inequality in education is a myth.
D.
All educational systems are equally effective.
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Solution
The passage indicates that access to quality education is a significant factor in reducing inequality.
Correct Answer:
B
— Access to quality education can reduce inequality.
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Q. Which of the following can be inferred about the author's perspective on the impact of education on social inequalities?
A.
Education has no significant impact on reducing inequalities.
B.
Education is a key factor in addressing social inequalities.
C.
Education exacerbates existing inequalities.
D.
Education is only beneficial for the wealthy.
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Solution
The passage suggests that education plays a crucial role in mitigating social inequalities, highlighting its importance.
Correct Answer:
B
— Education is a key factor in addressing social inequalities.
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Q. Which of the following can be inferred about the author's perspective on wealth distribution? (2023)
A.
Wealth should be evenly distributed among all citizens.
B.
Wealth concentration is beneficial for innovation.
C.
Wealth distribution should be based on merit.
D.
Wealth inequality leads to social unrest.
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Solution
The passage suggests that wealth inequality can lead to social tensions and unrest.
Correct Answer:
D
— Wealth inequality leads to social unrest.
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Q. Which of the following can be inferred about the relationship between economic policies and social inequalities from the passage? (2023)
A.
Economic policies have no impact on social inequalities.
B.
Economic policies can exacerbate social inequalities if not designed inclusively.
C.
All economic policies inherently reduce social inequalities.
D.
Social inequalities are independent of economic policies.
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Solution
The passage suggests that economic policies must be inclusive to prevent the widening of social inequalities.
Correct Answer:
B
— Economic policies can exacerbate social inequalities if not designed inclusively.
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Q. Which of the following can be inferred about the relationship between education and social inequality from the passage? (2023)
A.
Education exacerbates social inequality.
B.
Higher education levels correlate with reduced social inequality.
C.
Education has no effect on social inequality.
D.
Social inequality is solely determined by educational attainment.
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Solution
The passage suggests that increased access to education can lead to a decrease in social inequality, highlighting its importance.
Correct Answer:
B
— Higher education levels correlate with reduced social inequality.
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Q. Which of the following can be the lengths of the sides of a triangle?
A.
2, 3, 5
B.
4, 4, 8
C.
5, 5, 10
D.
6, 8, 10
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Solution
The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. Only 6, 8, and 10 satisfy this condition.
Correct Answer:
D
— 6, 8, 10
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Q. Which of the following describes a consistent system of linear equations?
A.
It has no solutions.
B.
It has exactly one solution.
C.
It has infinitely many solutions.
D.
It can have either one or infinitely many solutions.
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Solution
A consistent system can either have one solution or infinitely many solutions.
Correct Answer:
D
— It can have either one or infinitely many solutions.
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Q. Which of the following describes a dependent system of linear equations?
A.
The equations have no solutions.
B.
The equations have exactly one solution.
C.
The equations have infinitely many solutions.
D.
The equations are parallel.
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Solution
Dependent systems have infinitely many solutions as they represent the same line.
Correct Answer:
C
— The equations have infinitely many solutions.
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Q. Which of the following describes a polynomial function?
A.
A function that can be expressed as a sum of powers of x with constant coefficients.
B.
A function that includes variables in the denominator.
C.
A function that has a variable exponent.
D.
A function that is defined only for integer values of x.
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Solution
A polynomial function is defined as a function that can be expressed as a sum of powers of x with constant coefficients.
Correct Answer:
A
— A function that can be expressed as a sum of powers of x with constant coefficients.
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Q. Which of the following describes a polynomial that is not a function?
A.
A polynomial with a degree of 0.
B.
A polynomial with a degree of 1.
C.
A polynomial that includes a variable in the denominator.
D.
A polynomial with complex coefficients.
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Solution
A polynomial that includes a variable in the denominator is not a polynomial function.
Correct Answer:
C
— A polynomial that includes a variable in the denominator.
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Q. Which of the following describes a polynomial that is not a polynomial function?
A.
x^2 + 3x - 5
B.
1/x + 2
C.
3x^3 - 4x + 1
D.
2x^4 + x^2
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Solution
The expression 1/x + 2 is not a polynomial function because it contains a term with a negative exponent.
Correct Answer:
B
— 1/x + 2
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Q. Which of the following describes the end behavior of the graph of a cubic function?
A.
Both ends rise.
B.
Both ends fall.
C.
One end rises and the other falls.
D.
The graph is constant.
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Solution
A cubic function has one end rising and the other falling, characteristic of odd-degree polynomials.
Correct Answer:
C
— One end rises and the other falls.
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Q. Which of the following describes the end behavior of the polynomial P(x) = -2x^4 + 3x^3 - x + 5?
A.
Both ends go up.
B.
Both ends go down.
C.
Left goes down, right goes up.
D.
Left goes up, right goes down.
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Solution
Since the leading coefficient is negative and the degree is even, both ends of the polynomial go down.
Correct Answer:
B
— Both ends go down.
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Q. Which of the following describes the graphical representation of the equation y = 3x + 1? (2023)
A.
A horizontal line.
B.
A vertical line.
C.
A line with a slope of 3.
D.
A line with a slope of -3.
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Solution
The equation is in slope-intercept form, where the slope is 3, indicating the line rises steeply.
Correct Answer:
C
— A line with a slope of 3.
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Q. Which of the following describes the range of the function f(x) = x^2?
A.
All real numbers.
B.
All positive real numbers.
C.
All non-negative real numbers.
D.
All integers.
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Solution
The range of f(x) = x^2 is all non-negative real numbers since the output of the function is always zero or positive.
Correct Answer:
C
— All non-negative real numbers.
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Q. Which of the following describes the term 'leading coefficient' in a polynomial?
A.
The coefficient of the term with the highest degree.
B.
The coefficient of the term with the lowest degree.
C.
The sum of all coefficients in the polynomial.
D.
The product of all coefficients in the polynomial.
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Solution
The leading coefficient is defined as the coefficient of the term with the highest degree in the polynomial.
Correct Answer:
A
— The coefficient of the term with the highest degree.
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Q. Which of the following equations has no solution in modular arithmetic?
A.
2x ≡ 4 (mod 6)
B.
3x ≡ 9 (mod 6)
C.
5x ≡ 10 (mod 6)
D.
4x ≡ 8 (mod 6)
Show solution
Solution
3x ≡ 9 (mod 6) has no solution because 3 and 6 are not coprime, and 9 is not divisible by the gcd(3, 6).
Correct Answer:
B
— 3x ≡ 9 (mod 6)
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Q. Which of the following equations is true in modular arithmetic?
A.
5 ≡ 10 (mod 5)
B.
6 ≡ 12 (mod 6)
C.
7 ≡ 14 (mod 7)
D.
8 ≡ 15 (mod 8)
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Solution
8 ≡ 15 (mod 8) is false; the correct answer is 5 ≡ 10 (mod 5) is true.
Correct Answer:
D
— 8 ≡ 15 (mod 8)
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Q. Which of the following equations represents a circle with a center at (0, 0) and a radius of 5?
A.
x^2 + y^2 = 5
B.
x^2 + y^2 = 25
C.
x^2 - y^2 = 25
D.
x^2 + y^2 = 10
Show solution
Solution
The standard equation of a circle with center (0, 0) and radius r is x^2 + y^2 = r^2. Here, r = 5, so r^2 = 25.
Correct Answer:
B
— x^2 + y^2 = 25
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Q. Which of the following equations represents a circle with a center at (3, -2) and a radius of 5?
A.
(x - 3)² + (y + 2)² = 25
B.
(x + 3)² + (y - 2)² = 25
C.
(x - 3)² + (y - 2)² = 25
D.
(x + 3)² + (y + 2)² = 25
Show solution
Solution
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Correct Answer:
A
— (x - 3)² + (y + 2)² = 25
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Q. Which of the following equations represents a line parallel to the line represented by 2x + 3y = 6?
A.
2x + 3y = 12
B.
3x + 2y = 6
C.
x - 2y = 4
D.
4x + 6y = 18
Show solution
Solution
Parallel lines have the same slope. The equation 2x + 3y = 12 has the same slope as 2x + 3y = 6.
Correct Answer:
A
— 2x + 3y = 12
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Q. Which of the following equations represents a line parallel to y = -3x + 4?
A.
y = -3x + 1
B.
y = 3x - 4
C.
y = -x + 2
D.
y = 2x + 3
Show solution
Solution
Parallel lines have the same slope. The slope of y = -3x + 4 is -3, so any line with the same slope, like y = -3x + 1, is parallel.
Correct Answer:
A
— y = -3x + 1
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Q. Which of the following equations represents a valid modular arithmetic statement?
A.
5x ≡ 10 (mod 5)
B.
6x ≡ 12 (mod 6)
C.
7x ≡ 14 (mod 7)
D.
8x ≡ 16 (mod 8)
Show solution
Solution
All options are valid, but 5x ≡ 10 (mod 5) simplifies to 0 ≡ 0, which is trivially true.
Correct Answer:
A
— 5x ≡ 10 (mod 5)
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Q. Which of the following expressions is equivalent to (2^3)^2?
A.
2^5
B.
2^6
C.
2^9
D.
2^1
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Solution
Using the power of a power property, (a^m)^n = a^(m*n), we get 2^(3*2) = 2^6.
Correct Answer:
B
— 2^6
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Q. Which of the following expressions is equivalent to (x + 2)(x - 3)?
A.
x^2 - x - 6
B.
x^2 + x - 6
C.
x^2 - 5x - 6
D.
x^2 - x + 6
Show solution
Solution
Expanding (x + 2)(x - 3) gives x^2 - 3x + 2x - 6 = x^2 - x - 6.
Correct Answer:
A
— x^2 - x - 6
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Q. Which of the following expressions is equivalent to (x^3 * y^2)^2?
A.
x^6 * y^4
B.
x^5 * y^2
C.
x^3 * y^6
D.
x^2 * y^2
Show solution
Solution
Using the power of a product rule, (x^3 * y^2)^2 = x^(3*2) * y^(2*2) = x^6 * y^4.
Correct Answer:
A
— x^6 * y^4
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Q. Which of the following expressions is equivalent to 2(x + 3) - 4?
A.
2x + 6 - 4
B.
2x + 2
C.
2x + 10
D.
2x - 2
Show solution
Solution
Distributing 2 gives 2x + 6, and then subtracting 4 results in 2x + 2.
Correct Answer:
A
— 2x + 6 - 4
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Q. Which of the following expressions is equivalent to 2(x + 3)?
A.
2x + 3
B.
2x + 6
C.
x + 6
D.
2x + 9
Show solution
Solution
Distributing 2 gives 2 * x + 2 * 3 = 2x + 6.
Correct Answer:
B
— 2x + 6
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Q. Which of the following expressions is equivalent to 3(x + 4) - 2(x - 1)?
A.
x + 14
B.
x + 10
C.
x + 12
D.
x + 16
Show solution
Solution
Distributing gives 3x + 12 - 2x + 2 = x + 14.
Correct Answer:
A
— x + 14
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Q. Which of the following expressions is equivalent to 3(x + 4)?
A.
3x + 12
B.
3x + 4
C.
x + 12
D.
3x + 7
Show solution
Solution
Distributing 3 gives 3x + 12, which is the equivalent expression.
Correct Answer:
A
— 3x + 12
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