Curriculum
Login

Curriculum

Mathematics

Unit 1

0/12

Unit 2

0/14

Unit 3

0/13

Unit 4

0/8

Unit 5

0/12

Unit 6

0/8

Unit 7

0/10
Quiz

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

Submit quiz
Once you submit, you will no longer be able to change your answers. Are you sure you want to submit the quiz?
Cancel Submit
  • Questions count: 20
Start Quiz
1.
STEM Integration Problem 12: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
0
6
4
2
2.
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)
3.
STEM Limits Problem 44: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
Undefined
5/2 (or 2.5)
1
4.
STEM Integration Problem 10: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
0
6
4
2
5.
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)
6.
STEM Limits Problem 11: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
0
Undefined
5/2 (or 2.5)
7.
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
8.
STEM Limits Problem 37: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
Undefined
1
5/2 (or 2.5)
9.
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)
10.
STEM Integration Problem 3: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
6
2
0
11.
STEM Integration Problem 27: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
0
6
2
4
12.
STEM Limits Problem 10: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
1
0
Undefined
13.
STEM Limits Problem 13: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
0
Undefined
1
14.
STEM Vector Algebra Problem 2: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
-8
10
6
-4
15.
STEM Calculus Problem 41: 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)
16.
What is the rigorous mathematical principle for: Fundamental Theorem of Calculus and Definite Integrals?
Integration by parts states that ∫ u dv = u v + ∫ v du
The integral of 1/x is strictly x2 / 2
Definite integration always yields a family of functions with an arbitrary constant C
If f is continuous on [a, b] and F is an antiderivative of f, then ∫[a, b] f(x) dx = F(b) - F(a), representing net accumulated area under the curve
17.
STEM Vector Algebra Problem 34: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
-8
10
6
-4
18.
STEM Vector Algebra Problem 25: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
6
-4
10
-8
19.
STEM Algebra Problem 38: 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)
120
210
1
20.
STEM Calculus Problem 11: 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)
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
  • 11
  • 12
  • 13
  • 14
  • 15
  • 16
  • 17
  • 18
  • 19
  • 20