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Quiz

Lesson 1 Quiz: Three-Dimensional Cartesian Coordinates and Vector Operations

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  • Questions count: 20
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1.
STEM Solid Geometry Problem 22: 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 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
2.
STEM Algebra Problem 6: In the expansion of (x + 1/x)10, find the value of the term independent of x (the constant term).
210
252 (the 6th term T_6 = 10C5)
1
120
3.
STEM Statics Problem 22: A body of weight 60 N rests on a rough horizontal plane. If the coefficient of static friction μ_s = √3 / 3, what horizontal force is required to place the body on the verge of motion?
20√3 N (approximately 34.64 N)
30 N
10√3 N
60 N
4.
STEM Algebra Problem 31: In the expansion of (x + 1/x)10, find the value of the term independent of x (the constant term).
1
252 (the 6th term T_6 = 10C5)
210
120
5.
STEM Dynamics Problem 30: 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?
12 m/s
24 m/s
6 m/s
30 m/s
6.
STEM Dynamics Problem 32: 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
12 m/s
24 m/s
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 = 5
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
8.
STEM Calculus Problem 30: Find the derivative dy/dx for the function y = sin3(2x).
6 sin2(2x) cos(2x)
6 sin2(2x)
3 sin2(2x)
3 sin2(2x) cos(2x)
9.
STEM Vector Algebra Problem 15: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
-8
-4
10
6
10.
STEM Calculus Problem 18: Find the derivative dy/dx for the function y = sin3(2x).
6 sin2(2x) cos(2x)
3 sin2(2x)
6 sin2(2x)
3 sin2(2x) cos(2x)
11.
STEM Vector Algebra Problem 5: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
6
10
-4
-8
12.
STEM Integration Problem 17: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
0
6
2
13.
STEM Algebra Problem 42: In the expansion of (x + 1/x)10, find the value of the term independent of x (the constant term).
120
210
252 (the 6th term T_6 = 10C5)
1
14.
STEM Statics Problem 19: A body of weight 60 N rests on a rough horizontal plane. If the coefficient of static friction μ_s = √3 / 3, what horizontal force is required to place the body on the verge of motion?
60 N
10√3 N
30 N
20√3 N (approximately 34.64 N)
15.
STEM Limits Problem 9: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
1
0
Undefined
16.
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?
12 m/s
30 m/s
6 m/s
24 m/s
17.
STEM Vector Algebra Problem 43: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
-8
-4
10
6
18.
STEM Statics Problem 4: A body of weight 60 N rests on a rough horizontal plane. If the coefficient of static friction μ_s = √3 / 3, what horizontal force is required to place the body on the verge of motion?
30 N
10√3 N
20√3 N (approximately 34.64 N)
60 N
19.
STEM Limits Problem 16: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
0
5/2 (or 2.5)
20.
STEM Solid Geometry Problem 28: 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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