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Unit 3

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Unit 5

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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 Integration Problem 7: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
2
0
6
4
2.
STEM Integration Problem 28: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
6
0
2
3.
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
4.
If y = (2x + 1) * (3x - 4), then dy/dx evaluated at x = 1 equals:
1
-5
12
7
5.
If (x - 1, x + 2, 3x) form a geometric sequence, the positive value of x is:
6
3
4
2
6.
STEM Integration Problem 29: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
0
6
2
7.
STEM Integration Problem 35: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
2
6
0
8.
STEM Limits Problem 10: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
1
5/2 (or 2.5)
Undefined
9.
What is the rigorous mathematical principle for: Binomial Theorem for Positive Integer Exponent n?
The expansion has exactly n terms
The coefficients nCr always decrease monotonically from start to finish
The sum of coefficients in (a + b)n is equal to n2
The expansion of (a + b)n contains exactly (n + 1) terms, with general term T_(r+1) = nCr * an − r * br
10.
If a, b, c form a geometric sequence of positive real numbers, the geometric mean b equals:
b = (a + c) / 2
b = a2 + c2
b = + sqrt(a * c)
b = a * c
11.
STEM Limits Problem 41: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
Undefined
5/2 (or 2.5)
1
0
12.
STEM Vector Algebra Problem 9: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
10
-4
-8
6
13.
STEM Integration Problem 19: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
0
6
2
4
14.
STEM Limits Problem 8: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
Undefined
0
1
15.
STEM Integration Problem 43: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
2
4
0
6
16.
STEM Limits Problem 36: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
5/2 (or 2.5)
0
17.
STEM Solid Geometry Problem 38: 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
18.
STEM Limits Problem 23: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
0
Undefined
5/2 (or 2.5)
19.
STEM Integration Problem 16: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
6
2
0
20.
STEM Vector Algebra Problem 6: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
-8
10
6
-4
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