Q. If a cube has a volume of 64 cubic centimeters, what is the length of one side of the cube?
A.
4 cm
B.
8 cm
C.
16 cm
D.
2 cm
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Solution
Volume of a cube = side³. Therefore, side = ∛64 = 4 cm.
Correct Answer:
A
— 4 cm
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Q. If a customer buys two items for $150 each and receives a 10% discount on the total, what is the total amount paid?
A.
$270
B.
$280
C.
$300
D.
$320
Show solution
Solution
Total Price = 2 * 150 = 300. Discount = 10% of 300 = 30. Total Amount Paid = 300 - 30 = $270.
Correct Answer:
A
— $270
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Q. If a customer buys two items priced at $50 and $70 respectively, and receives a total discount of 20% on the total price, what is the amount paid?
A.
$96
B.
$100
C.
$110
D.
$120
Show solution
Solution
Total Price = $50 + $70 = $120. Discount = 20% of $120 = $24. Amount Paid = $120 - $24 = $96.
Correct Answer:
A
— $96
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Q. If a customer buys two items priced at $50 each and receives a 20% discount on the total, how much does he pay?
A.
$80
B.
$70
C.
$90
D.
$60
Show solution
Solution
Total price = 50 + 50 = 100. Discount = 20% of 100 = 20. Final price = 100 - 20 = 80.
Correct Answer:
B
— $70
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Q. If a customer buys two shirts for $50 each and receives a discount of 10% on the total, what is the total amount paid?
A.
$90
B.
$100
C.
$95
D.
$85
Show solution
Solution
Total cost without discount = 2 * $50 = $100. Discount = 10% of $100 = $10. Total amount paid = $100 - $10 = $90.
Correct Answer:
C
— $95
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Q. If a discount of 15% on a product results in a selling price of $85, what was the original price?
A.
$100
B.
$90
C.
$110
D.
$95
Show solution
Solution
Let the original price be x. After a 15% discount, the selling price is x - (0.15 * x) = 0.85x. Setting this equal to $85 gives 0.85x = $85, so x = $85 / 0.85 = $100.
Correct Answer:
A
— $100
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Q. If a function f is defined as f(x) = 3x + 2, what is the value of f(4)?
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Solution
To find f(4), substitute x with 4: f(4) = 3(4) + 2 = 12 + 2 = 14.
Correct Answer:
A
— 14
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Q. If a function f(x) is defined as f(x) = 2x + 3, what is the slope of its graph?
A.
0
B.
2
C.
3
D.
Undefined
Show solution
Solution
In the linear function f(x) = mx + b, 'm' represents the slope, which is 2 in this case.
Correct Answer:
B
— 2
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Q. If a function f(x) is defined as f(x) = 2x + 3, what is the slope of the graph of this function?
A.
0
B.
2
C.
3
D.
Undefined
Show solution
Solution
In the linear function f(x) = 2x + 3, the coefficient of x (which is 2) represents the slope of the graph.
Correct Answer:
B
— 2
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Q. If a function f(x) is defined as f(x) = 2x + 3, what is the slope of the graph?
Show solution
Solution
In the linear function f(x) = mx + b, 'm' represents the slope. Here, the slope is 2.
Correct Answer:
C
— 2
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Q. If a function f(x) is defined as f(x) = 2x + 3, what is the value of f(0)?
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Solution
Substituting x = 0 into the function gives f(0) = 2(0) + 3 = 3.
Correct Answer:
C
— 3
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Q. If a function f(x) is defined as f(x) = 2x + 5, what is the slope of the graph?
A.
0
B.
2
C.
5
D.
Undefined
Show solution
Solution
In the linear function f(x) = mx + b, 'm' represents the slope. Here, m = 2.
Correct Answer:
B
— 2
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Q. If a function f(x) is defined as f(x) = 3x + 2, what is the value of f(4)?
Show solution
Solution
To find f(4), substitute x with 4: f(4) = 3(4) + 2 = 12 + 2 = 14.
Correct Answer:
A
— 14
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Q. If a function f(x) is defined as f(x) = 3x - 5, what is the slope of the graph of this function?
A.
3
B.
-5
C.
0
D.
Undefined
Show solution
Solution
In the linear function f(x) = mx + b, m represents the slope. Here, m = 3, so the slope is 3.
Correct Answer:
A
— 3
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Q. If a function f(x) is defined as f(x) = 3x - 5, what is the slope of the graph?
A.
3
B.
-5
C.
0
D.
Undefined
Show solution
Solution
In the linear function f(x) = mx + b, 'm' represents the slope, which is 3 in this case.
Correct Answer:
A
— 3
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Q. If a function f(x) is defined as f(x) = x^3 - 3x + 2, what can be inferred about its behavior at critical points?
A.
It has no critical points.
B.
It has one local maximum and one local minimum.
C.
It is always increasing.
D.
It is always decreasing.
Show solution
Solution
To find critical points, we take the derivative and set it to zero. The function has one local maximum and one local minimum based on the nature of cubic functions.
Correct Answer:
B
— It has one local maximum and one local minimum.
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Q. If a function f(x) is defined as f(x) = x^3 - 3x, what is the nature of its critical points?
A.
They can be local maxima, local minima, or points of inflection.
B.
They are always local maxima.
C.
They are always local minima.
D.
They do not exist.
Show solution
Solution
Critical points of a function can be local maxima, local minima, or points of inflection, depending on the behavior of the function around those points.
Correct Answer:
A
— They can be local maxima, local minima, or points of inflection.
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Q. If a function is defined as f(x) = 2x + 3, what is the value of f(4)?
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Solution
Substituting x = 4 into the function gives f(4) = 2(4) + 3 = 8 + 3 = 11.
Correct Answer:
B
— 11
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Q. If a function is defined as f(x) = 3x + 2, what is the slope of the line represented by this function?
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Solution
In the linear function f(x) = mx + b, 'm' represents the slope. Here, the slope is 3.
Correct Answer:
A
— 3
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Q. If a function is defined as f(x) = 3x + 2, what is the value of f(4)?
Show solution
Solution
To find f(4), substitute 4 into the function: f(4) = 3(4) + 2 = 12 + 2 = 14.
Correct Answer:
A
— 14
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Q. If a hexagon is regular, what is the relationship between its sides and angles?
A.
All sides are equal, and all angles are equal.
B.
Sides can be of different lengths, but angles are equal.
C.
Sides are equal, but angles can vary.
D.
No specific relationship exists.
Show solution
Solution
In a regular hexagon, all sides are equal in length and all interior angles are equal.
Correct Answer:
A
— All sides are equal, and all angles are equal.
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Q. If a line has the equation 2x - 3y + 6 = 0, what is the y-intercept of the line?
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Solution
To find the y-intercept, set x = 0. The equation becomes -3y + 6 = 0, thus y = 2.
Correct Answer:
B
— 2
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Q. If a line has the equation 3x - 4y + 12 = 0, what is its y-intercept?
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Solution
To find the y-intercept, set x = 0. The equation becomes -4y + 12 = 0, leading to y = 3.
Correct Answer:
A
— 3
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Q. If a line has the equation 3x - 4y = 12, what is the y-intercept of the line?
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Solution
To find the y-intercept, set x = 0. The equation becomes -4y = 12, thus y = -3. The y-intercept is (0, -3).
Correct Answer:
A
— 3
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Q. If a line passes through the points (1, 2) and (3, 6), what is the slope of the line?
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Solution
The slope m is calculated as (6-2)/(3-1) = 4/2 = 2.
Correct Answer:
A
— 2
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Q. If a linear equation is represented in the form Ax + By = C, what does 'C' represent?
A.
The slope of the line
B.
The y-intercept
C.
The x-intercept
D.
The constant term
Show solution
Solution
'C' is the constant term in the equation, representing the value at which the line intersects the axes.
Correct Answer:
D
— The constant term
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Q. If a linear equation is represented in the form Ax + By = C, what does A, B, and C represent?
A.
Constants and variables
B.
Only constants
C.
Only variables
D.
Coefficients and a constant
Show solution
Solution
In the equation Ax + By = C, A and B are coefficients of the variables x and y, while C is a constant.
Correct Answer:
D
— Coefficients and a constant
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Q. If a loan of $5000 is taken at a simple interest rate of 6% per annum, how much interest will be paid after 4 years?
A.
$1200
B.
$1000
C.
$800
D.
$600
Show solution
Solution
Using the simple interest formula, SI = (Principal * Rate * Time) / 100 = (5000 * 6 * 4) / 100 = $1200.
Correct Answer:
B
— $1000
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Q. If a lock has 4 digits, how many different combinations can be formed if digits can be repeated?
A.
10000
B.
9000
C.
8000
D.
7000
Show solution
Solution
Each digit can be any of the 10 digits (0-9). Therefore, the total combinations = 10^4 = 10000.
Correct Answer:
A
— 10000
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Q. If a lock has 4 digits, how many different combinations can be formed using the digits 0-9?
A.
10000
B.
9000
C.
1000
D.
5000
Show solution
Solution
Each digit can be any of the 10 digits (0-9), so the total combinations = 10^4 = 10000.
Correct Answer:
A
— 10000
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