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Mathematics

Unit 1

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Unit 2

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Unit 3

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Unit 4

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Unit 5

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Unit 6

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Unit 7

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Quiz

Lesson 1 Quiz: Counting Principle, Permutations (nPr) and Combinations (nCr)

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  • Questions count: 20
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1.
STEM Solid Geometry Problem 9: 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
2.
STEM Integration Problem 12: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
0
6
4
2
3.
STEM Calculus Problem 5: Find the derivative dy/dx for the function y = sin3(2x).
6 sin2(2x)
3 sin2(2x) cos(2x)
6 sin2(2x) cos(2x)
3 sin2(2x)
4.
STEM Statics Problem 43: 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)
5.
STEM Limits Problem 44: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
Undefined
5/2 (or 2.5)
1
6.
STEM Integration Problem 10: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
0
6
4
2
7.
STEM Calculus Problem 29: Find the derivative dy/dx for the function y = sin3(2x).
3 sin2(2x)
3 sin2(2x) cos(2x)
6 sin2(2x) cos(2x)
6 sin2(2x)
8.
STEM Statics Problem 5: 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?
10√3 N
20√3 N (approximately 34.64 N)
60 N
30 N
9.
STEM Dynamics Problem 41: 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
10.
STEM Limits Problem 11: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
0
Undefined
5/2 (or 2.5)
11.
STEM Dynamics Problem 5: 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
12.
STEM Vector Algebra Problem 14: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
-8
10
-4
6
13.
STEM Limits Problem 37: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
Undefined
1
5/2 (or 2.5)
14.
STEM Statics Problem 35: 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
60 N
10√3 N
15.
STEM Calculus Problem 3: Find the derivative dy/dx for the function y = sin3(2x).
3 sin2(2x)
3 sin2(2x) cos(2x)
6 sin2(2x)
6 sin2(2x) cos(2x)
16.
STEM Integration Problem 3: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
6
2
0
17.
STEM Integration Problem 27: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
0
6
2
4
18.
STEM Limits Problem 10: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
1
0
Undefined
19.
STEM Limits Problem 13: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
0
Undefined
1
20.
If \(x = \sin t\) and \(y = \cos t\), then the second derivative \(\frac{d^2y}{dx^2}\) is equal to:
B) \(-sec^3 t\)
C) $-tan t$
D) \(csc^2 t\)
A) $-cos t$
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