Q. Which of the following statements is true regarding the expression 2^(x+y)?
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A.
It can be expressed as 2^x + 2^y.
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B.
It can be expressed as 2^x * 2^y.
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C.
It is always greater than 1.
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D.
It is equal to x + y.
Solution
The property of exponents states that a^(m+n) = a^m * a^n.
Correct Answer:
B
— It can be expressed as 2^x * 2^y.
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Q. Which of the following statements is true regarding the function f(x) = x^2?
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A.
It is a linear function.
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B.
It is a quadratic function.
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C.
It is a constant function.
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D.
It is an exponential function.
Solution
The function f(x) = x^2 is a quadratic function because it can be expressed in the form ax^2 + bx + c.
Correct Answer:
B
— It is a quadratic function.
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Q. Which of the following statements is true regarding the graph of a linear equation?
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A.
It can be a curve.
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B.
It is always a straight line.
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C.
It can have multiple slopes.
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D.
It can intersect the x-axis at multiple points.
Solution
The graph of a linear equation is always a straight line.
Correct Answer:
B
— It is always a straight line.
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Q. Which of the following statements is true regarding the graph of a quadratic function?
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A.
It is always a straight line.
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B.
It can open upwards or downwards.
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C.
It has no intercepts.
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D.
It is always increasing.
Solution
The graph of a quadratic function is a parabola that can open upwards (if a > 0) or downwards (if a < 0).
Correct Answer:
B
— It can open upwards or downwards.
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Q. Which of the following statements is true regarding the graph of the equation 3x + 4y = 12? (2023)
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A.
It intersects the x-axis at (4, 0).
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B.
It intersects the y-axis at (0, 3).
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C.
It has a positive slope.
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D.
It is a vertical line.
Solution
Setting y = 0 gives x = 4, indicating that the graph intersects the x-axis at (4, 0).
Correct Answer:
A
— It intersects the x-axis at (4, 0).
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Q. Which of the following statements is true regarding the graph of the equation 5x + 2y = 10?
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A.
It is a vertical line.
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B.
It is a horizontal line.
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C.
It has a positive slope.
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D.
It has a negative slope.
Solution
Rearranging the equation to y = -5/2x + 5 shows that the slope is negative.
Correct Answer:
D
— It has a negative slope.
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Q. Which of the following statements is true regarding the graph of the equation y = mx + b?
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A.
The graph is always a circle.
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B.
The slope m indicates the steepness of the line.
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C.
The y-intercept b is always negative.
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D.
The graph can never be horizontal.
Solution
In the equation y = mx + b, m represents the slope, which indicates how steep the line is.
Correct Answer:
B
— The slope m indicates the steepness of the line.
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Q. Which of the following statements is true regarding the graph of the equation y = 2x + 1?
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A.
It is a vertical line.
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B.
It has a positive slope.
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C.
It intersects the y-axis at -1.
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D.
It has a negative slope.
Solution
The equation y = 2x + 1 has a positive slope of 2 and intersects the y-axis at 1.
Correct Answer:
B
— It has a positive slope.
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Q. Which of the following statements is true regarding the inverse of a function?
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A.
The inverse of a function is always a function.
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B.
The inverse of a function is defined only for linear functions.
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C.
The graph of a function and its inverse are symmetric about the line y = x.
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D.
The inverse of a function can never be found.
Solution
The graph of a function and its inverse are symmetric about the line y = x, which is a key property of inverse functions.
Correct Answer:
C
— The graph of a function and its inverse are symmetric about the line y = x.
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Q. Which of the following statements is true regarding the solutions of the equation 5x + 2y = 10?
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A.
It has no solutions.
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B.
It has one solution.
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C.
It has infinitely many solutions.
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D.
It has two solutions.
Solution
This linear equation represents a line, which has infinitely many solutions.
Correct Answer:
B
— It has one solution.
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Q. Which of the following statements is true regarding the vertical line test for functions?
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A.
A vertical line can intersect a graph at more than one point for it to be a function.
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B.
A vertical line can intersect a graph at only one point for it to be a function.
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C.
A vertical line test is irrelevant for determining functions.
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D.
All graphs pass the vertical line test.
Solution
For a graph to represent a function, any vertical line drawn must intersect the graph at most once.
Correct Answer:
B
— A vertical line can intersect a graph at only one point for it to be a function.
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Q. Which of the following terms best describes a polynomial with more than one variable?
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A.
Univariate polynomial
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B.
Multivariate polynomial
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C.
Constant polynomial
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D.
Linear polynomial
Solution
A polynomial that contains more than one variable is referred to as a multivariate polynomial.
Correct Answer:
B
— Multivariate polynomial
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Q. Which of the following terms is NOT a polynomial?
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A.
5x^2 + 3x - 7
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B.
2x^3 - 4x + 1
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C.
3/x + 2
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D.
x^4 + 2x^2 + 1
Solution
The term 3/x is not a polynomial because it contains a negative exponent when rewritten as 3x^(-1).
Correct Answer:
C
— 3/x + 2
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Q. Which of the following terms is used to describe a polynomial with exactly one term?
-
A.
Binomial
-
B.
Trinomial
-
C.
Monomial
-
D.
Polynomial
Solution
A polynomial with exactly one term is called a monomial.
Correct Answer:
C
— Monomial
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Q. Which of the following transformations would result in a vertical shift of the graph of the function f(x)?
-
A.
f(x) + k
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B.
f(x + k)
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C.
kf(x)
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D.
f(kx)
Solution
Adding a constant k to the function f(x) results in a vertical shift of the graph.
Correct Answer:
A
— f(x) + k
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Q. Which of the following transformations would result in a vertical shift of the graph of the function f(x) = x^2?
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A.
f(x) = x^2 + 3
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B.
f(x) = 3x^2
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C.
f(x) = x^2 - 3
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D.
f(x) = 2x^2
Solution
Adding a constant to the function, such as f(x) = x^2 + 3, results in a vertical shift upwards.
Correct Answer:
A
— f(x) = x^2 + 3
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Q. Which of the following words best captures the author's attitude towards the current state of inequality?
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A.
Pessimistic.
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B.
Indifferent.
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C.
Concerned.
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D.
Skeptical.
Solution
The author expresses concern about the persistence and impact of inequality in society.
Correct Answer:
C
— Concerned.
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Q. Which of the following words best captures the author's view on the urgency of addressing inequalities?
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A.
Critical.
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B.
Optional.
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C.
Negligible.
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D.
Controversial.
Solution
The author emphasizes the critical nature of addressing inequalities, suggesting it is an urgent issue.
Correct Answer:
A
— Critical.
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Q. Which of the following words from the passage is closest in meaning to 'perpetuate'?
-
A.
End
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B.
Continue
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C.
Diminish
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D.
Challenge
Solution
In the context of the passage, 'perpetuate' means to continue, as it refers to the ongoing nature of inequalities.
Correct Answer:
B
— Continue
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