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Adamson U
Applied Mathematics
Practice Quiz (with Answer)

Question:
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What slope of the line passes through points (2, 3) and (6, 7)?
How do you find the area of a triangle using Heron's formula?
Solve the system of equations: 2x + 3y = 6 and 4x - 2y = 8
A company's profit is modeled by the equation P = -x^2 + 10x + 20
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Find the derivative of y = 2x^3 + 3x^2 + 4x + 5
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What is the length of the field?
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A boat is sailing down a river at a speed of 20 km/h
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What is the actual speed of the boat?
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What is the volume of
the cylinder?
10
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A car is traveling at a constant speed of 40 mph
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A cylinder has a volume of 1000 cm^3
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A sample of 100 items has a mean of 10 and a standard deviation of 2
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A sphere has a radius of 4 cm
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A cone has a radius of 5 cm and a height of 8 cm
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Solve the differential equation dy/dx = x^2 + 2x + 1
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What is the area of the
triangle?
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What is the volume of the prism?
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To find the slope of a line that passes through two points, you can use the
formula: slope = (y2 - y1) / (x2 - x1)
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So the slope of the line
that passes through the points (2, 3) and (6, 7) is 1
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To find the area of a triangle using Heron's formula, you first need the
length of all three sides of the triangle
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Then, the area of the triangle is:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
where s = (a + b + c) / 2 is the semiperimeter of the triangle
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To solve the system of equations: 2x + 3y = 6 and 4x - 2y = 8, we can use
either substitution or elimination method
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2x + 3y = 6 => y = (-2/3)x + 2
4x - 2y = 8 => 4x - 2((-2/3)x + 2) = 8

=> 4x + 4/3x = 8
=> x = 3
4
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2x + 3y = 6 => 2x + 3y = 6
4x - 2y = 8 => -4x + 4y = -16
Add the above equations => -2x = -10 => x = 5
Substitute this value of x into any of the equations to find y:
2x + 3y = 6 => 2(5) + 3y = 6 => y = -1
So the solution is x = 5, y = -1

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P = -x^2 + 10x + 20
P = -(x^2 - 10x) - 20
P = -(x^2 - 10x + 25 - 25) - 20
P = -(x - 5)^2 + 5

This is a parabola that opens downward and has a vertex at (5,5) so the maximum
profit is 5
To find the derivative of y = 2x^3 + 3x^2 + 4x + 5, we can use the power rule and
the sum rule
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To find the length of a rectangular field given its area and width, we can use the
formula:
Area = Length * Width
In this case, we know that the area is 420 square meters and the width is 14
meters, so we can solve for the length:
420 = Length * 14
Length = 420 / 14
Length = 30
So the length of the field is 30 meters

7
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Integrating both sides with respect to x:
∫y' dx = ∫(2x + 3) dx
y = x^2 + 3x + C
where C is an arbitrary constant
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8
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62 km/h

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To solve the integral of x^2 + 5x + 6, we can use the power rule for integration
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To find the height of a cylinder given its volume and radius, we can use the
formula:
Volume = πr^2h
In this case, the volume is 1000 cm^3 and the radius is 5 cm, so we can solve for
the height:
1000 = π(5^2)h

1000 = π(25)h
h = 1000/(π * 25)
h = 8/π cm

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Let Z = (X - mean) / standard deviation
We can find P(Z < (6-10)/2) from the standard normal distribution table
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0228
so the probability that a randomly selected item will have a value less than 6 is
2
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To find the surface area of a sphere given its radius, we can use the formula:
Surface area = 4πr^2
In this case, the radius is 4 cm, so we can solve for the surface area:
Surface area = 4π(4^2)
Surface area = 4π(16)
Surface area = 64π cm^2

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To solve the differential equation dy/dx = x^2 + 2x + 1, we can first find the
general solution of the equation by integrating both sides with respect to x
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To find the particular solution, we can use the initial condition and substitute it
into the general solution
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To find the equation of the line that passes through the point (2, 3) and has a
slope of -2, we can use the point-slope form of the equation of a line
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In this case, the point is (2, 3) and the slope is -2, so we can substitute these
values into the point-slope form:
y - 3 = -2(x - 2)
Simplifying:

y = -2x + 2
So the equation of the line that passes through the point (2, 3) and has a slope of 2 is y = -2x + 2

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To find the volume of a rectangular prism given its length, width, and height,
we can use the formula:
Volume = Length * Width * Height
In this case, the length is 12 cm, the width is 8 cm, and the height is 6 cm, so we
can solve for the volume:
Volume = 12 * 8 * 6
Volume = 576 cm^3

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∫e^x dx = e^x + C
where C is the constant of integration
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