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?
-
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?
-
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 HCF and LCM of two numbers? (2023)
-
A.
HCF is always greater than LCM
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B.
HCF is the product of the numbers
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C.
LCM is always less than the product of the numbers
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D.
HCF * LCM = Product of the numbers
Solution
The correct statement is that HCF * LCM = Product of the numbers.
Correct Answer:
D
— HCF * LCM = Product of the numbers
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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 number '0' in any number system?
-
A.
It is always positive
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B.
It is always negative
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C.
It is neither positive nor negative
-
D.
It is undefined
Solution
Zero is neither positive nor negative in any number system.
Correct Answer:
C
— It is neither positive nor negative
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Q. Which of the following statements is true regarding the number '100' in base 3?
-
A.
It is equal to 9
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B.
It is equal to 10
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C.
It is equal to 12
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D.
It is equal to 27
Solution
'100' in base 3 is calculated as 1*3^2 + 0*3^1 + 0*3^0 = 9.
Correct Answer:
A
— It is equal to 9
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Q. Which of the following statements is true regarding the number 'A' in hexadecimal?
-
A.
A is equal to 10
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B.
A is equal to 11
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C.
A is equal to 12
-
D.
A is equal to 13
Solution
In hexadecimal, 'A' represents the decimal value 10.
Correct Answer:
A
— A is equal to 10
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Q. Which of the following statements is true regarding the number 36?
-
A.
It has exactly 9 factors.
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B.
It is a prime number.
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C.
It is a perfect square.
-
D.
It is a multiple of 10.
Solution
36 is a perfect square as it can be expressed as 6 * 6.
Correct Answer:
C
— It is a perfect square.
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Q. Which of the following statements is true regarding the numbers 8, 12, and 16?
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A.
8 is a multiple of 12
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B.
12 is a factor of 16
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C.
16 is a multiple of 8
-
D.
12 is a multiple of 8
Solution
16 is a multiple of 8, as 16 = 8 * 2.
Correct Answer:
C
— 16 is a multiple of 8
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Q. Which of the following statements is true regarding the points (2, 3), (4, 5), and (6, 7)?
-
A.
They are collinear
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B.
They form a triangle
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C.
They are equidistant
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D.
They lie on different lines
Solution
The slope between any two pairs of these points is the same (1), indicating they are collinear.
Correct Answer:
A
— They are collinear
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Q. Which of the following statements is true regarding the slopes of parallel lines in a coordinate plane?
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A.
They are equal
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B.
They are negative reciprocals
-
C.
They are always zero
-
D.
They are always positive
Solution
Parallel lines have the same slope, hence their slopes are equal.
Correct Answer:
A
— They are equal
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Q. Which of the following statements is true regarding the solutions of the equation 5x + 2y = 10?
-
A.
It has no solutions.
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B.
It has one solution.
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C.
It has infinitely many solutions.
-
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 polygon with all sides and angles equal?
-
A.
Irregular polygon
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B.
Convex polygon
-
C.
Regular polygon
-
D.
Concave polygon
Solution
A polygon with all sides and angles equal is known as a regular polygon.
Correct Answer:
C
— Regular polygon
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Q. Which of the following terms best describes a polynomial with more than one variable?
-
A.
Univariate polynomial
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B.
Multivariate polynomial
-
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 describes a line that touches a circle at exactly one point? (2023)
-
A.
Chord
-
B.
Diameter
-
C.
Tangent
-
D.
Secant
Solution
A line that touches a circle at exactly one point is called a tangent.
Correct Answer:
C
— Tangent
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Q. Which of the following terms is NOT a polynomial?
-
A.
5x^2 + 3x - 7
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B.
2x^3 - 4x + 1
-
C.
3/x + 2
-
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 line that touches a circle at exactly one point?
-
A.
Chord
-
B.
Diameter
-
C.
Tangent
-
D.
Secant
Solution
A tangent is defined as a line that touches a circle at exactly one point.
Correct Answer:
C
— Tangent
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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 terms refers to a line segment that connects two points on a circle?
-
A.
Diameter
-
B.
Chord
-
C.
Tangent
-
D.
Secant
Solution
A chord is defined as a line segment whose endpoints lie on the circle.
Correct Answer:
B
— Chord
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Q. Which of the following terms refers to a partner who is not involved in day-to-day operations but shares in the profits?
-
A.
Active partner
-
B.
Silent partner
-
C.
General partner
-
D.
Equity partner
Solution
A silent partner is one who does not participate in daily operations but is entitled to a share of the profits.
Correct Answer:
B
— Silent partner
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Q. Which of the following terms refers to a polygon with all sides and angles equal?
-
A.
Regular polygon
-
B.
Irregular polygon
-
C.
Convex polygon
-
D.
Concave polygon
Solution
A regular polygon is defined as a polygon where all sides and angles are equal.
Correct Answer:
A
— Regular polygon
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Q. Which of the following terms refers to a polygon with exactly one pair of parallel sides?
-
A.
Trapezoid
-
B.
Parallelogram
-
C.
Rhombus
-
D.
Rectangle
Solution
A trapezoid is defined as a polygon that has exactly one pair of parallel sides.
Correct Answer:
A
— Trapezoid
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Q. Which of the following terms refers to the distribution of profits among partners?
-
A.
Capital contribution
-
B.
Profit sharing
-
C.
Equity distribution
-
D.
Revenue allocation
Solution
Profit sharing refers to the distribution of profits among partners based on the terms outlined in the partnership agreement.
Correct Answer:
B
— Profit sharing
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Q. Which of the following terms refers to the legal document outlining the terms of a partnership?
-
A.
Partnership deed
-
B.
Business charter
-
C.
Operating agreement
-
D.
Corporate bylaws
Solution
The legal document that outlines the terms of a partnership is known as the partnership deed.
Correct Answer:
A
— Partnership deed
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Q. Which of the following terms refers to the middle value in a data set when arranged in ascending order?
-
A.
Mean
-
B.
Mode
-
C.
Median
-
D.
Range
Solution
The median is defined as the middle value in a sorted data set, distinguishing it from mean and mode.
Correct Answer:
C
— Median
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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
-
B.
f(x + k)
-
C.
kf(x)
-
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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