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Quiz

Lesson 1 Quiz: Integration Techniques (Substitution and By Parts) and Definite Integrals

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  • Questions count: 20
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1.
STEM Solid Geometry Problem 31: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
x2 + y2 + z2 - 4x + 2y - 6z = 25
2.
STEM Dynamics Problem 18: A body of mass 5 kg moves in a straight line under a net force F = 30 N. Starting from rest, what is its velocity after 4 seconds?
24 m/s
12 m/s
30 m/s
6 m/s
3.
STEM Dynamics Problem 12: A body of mass 5 kg moves in a straight line under a net force F = 30 N. Starting from rest, what is its velocity after 4 seconds?
30 m/s
6 m/s
24 m/s
12 m/s
4.
STEM Calculus Problem 31: Find the derivative dy/dx for the function y = sin3(2x).
3 sin2(2x)
6 sin2(2x) cos(2x)
3 sin2(2x) cos(2x)
6 sin2(2x)
5.
The second derivative d2y/dx2 of the function y = x4 - 2 x3 + 5 is:
12 x2 - 6 x
12 x2 - 12 x
4 x3 - 6 x2
24 x - 12
6.
The slope of the tangent line to the curve y = x2 - 6 x + 5 at the point (4, -3) equals:
m = 2
m = 8
m = -3
m = -2
7.
STEM Solid Geometry Problem 6: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
8.
STEM Solid Geometry Problem 15: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
9.
STEM Solid Geometry Problem 34: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
10.
STEM Calculus Problem 30: Find the derivative dy/dx for the function y = sin3(2x).
3 sin2(2x)
6 sin2(2x)
3 sin2(2x) cos(2x)
6 sin2(2x) cos(2x)
11.
STEM Dynamics Problem 20: A body of mass 5 kg moves in a straight line under a net force F = 30 N. Starting from rest, what is its velocity after 4 seconds?
30 m/s
6 m/s
24 m/s
12 m/s
12.
STEM Calculus Problem 18: Find the derivative dy/dx for the function y = sin3(2x).
6 sin2(2x)
3 sin2(2x) cos(2x)
3 sin2(2x)
6 sin2(2x) cos(2x)
13.
STEM Dynamics Problem 2: A body of mass 5 kg moves in a straight line under a net force F = 30 N. Starting from rest, what is its velocity after 4 seconds?
24 m/s
6 m/s
30 m/s
12 m/s
14.
STEM Dynamics Problem 25: A body of mass 5 kg moves in a straight line under a net force F = 30 N. Starting from rest, what is its velocity after 4 seconds?
30 m/s
6 m/s
24 m/s
12 m/s
15.
STEM Dynamics Problem 13: A body of mass 5 kg moves in a straight line under a net force F = 30 N. Starting from rest, what is its velocity after 4 seconds?
24 m/s
12 m/s
30 m/s
6 m/s
16.
STEM Solid Geometry Problem 12: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
17.
STEM Solid Geometry Problem 14: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
x2 + y2 + z2 - 4x + 2y - 6z = 25
18.
STEM Calculus Problem 15: Find the derivative dy/dx for the function y = sin3(2x).
6 sin2(2x) cos(2x)
6 sin2(2x)
3 sin2(2x) cos(2x)
3 sin2(2x)
19.
STEM Solid Geometry Problem 42: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
20.
STEM Solid Geometry Problem 33: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
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