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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: Differentiation of Trigonometric, Exponential and Logarithmic Functions

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  • Questions count: 20
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1.
STEM Dynamics Problem 8: 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
30 m/s
6 m/s
12 m/s
2.
STEM Solid Geometry Problem 43: 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
3.
STEM Calculus Problem 17: Find the derivative dy/dx for the function y = sin3(2x).
6 sin2(2x)
3 sin2(2x)
6 sin2(2x) cos(2x)
3 sin2(2x) cos(2x)
4.
STEM Solid Geometry Problem 7: 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
5.
STEM Calculus Problem 44: 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)
6.
STEM Limits Problem 24: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
0
1
Undefined
7.
STEM Statics Problem 8: 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)
60 N
30 N
10√3 N
8.
STEM Limits Problem 41: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
1
5/2 (or 2.5)
Undefined
9.
STEM Algebra Problem 35: In the expansion of (x + 1/x)10, find the value of the term independent of x (the constant term).
252 (the 6th term T_6 = 10C5)
210
120
1
10.
STEM Statics Problem 10: 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)
11.
STEM Limits Problem 43: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
5/2 (or 2.5)
Undefined
0
12.
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
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
13.
STEM Vector Algebra Problem 11: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
-8
6
10
-4
14.
STEM Statics Problem 1: 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
20√3 N (approximately 34.64 N)
30 N
15.
STEM Limits Problem 14: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
Undefined
5/2 (or 2.5)
1
0
16.
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?
30 N
10√3 N
20√3 N (approximately 34.64 N)
60 N
17.
STEM Vector Algebra Problem 15: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
10
-4
6
-8
18.
STEM Calculus Problem 37: Find the derivative dy/dx for the function y = sin3(2x).
6 sin2(2x) cos(2x)
3 sin2(2x) cos(2x)
6 sin2(2x)
3 sin2(2x)
19.
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
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
20.
STEM Vector Algebra Problem 3: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
6
10
-4
-8
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